A Discrete-Continuous Modeling Framework for Long-Distance,

Leisure Travel Demand Analysis

by

Caleb Van Nostrand

A thesis submitted in partial fulfillment

of the requirements for the degree of
Master of Science in Civil Engineering
Department of Civil and Environmental Engineering
College of Engineering
University of South Florida

Major Professor: Abdul Pinjari, Ph.D.

Yu Zhang, Ph.D.
Steven Polzin, Ph.D.
John Lu, Ph.D.

Date of Approval:
March 23, 2011

Keywords: Long Distance Travel, Vacation Travel Demand, National Travel Model,
Kuhn-Tucker Demand Model Systems, Destination Choice

Copyright © 2011, Caleb Van Nostrand

 UMI Number: 1490510

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 Dedication

This thesis is dedicated to my parents, Al and Jeannine, for their constant

support and encouragement in everything I do, and for always being there. It is from

them that I learned what hard work is, and I am grateful to attribute my success thus far

to them.

I would also like to dedicate this thesis to Danielle. She has continually supported

me with patience and understanding despite all the late work nights and busy weekends,

and I look forward to opportunities to return the favor in the future.

 Acknowledgements

I would first like to thank my advisor, Dr. Abdul Pinjari, for his guidance and

support in completing this thesis. He has consistently been available and supportive, and

has provided invaluable insight throughout the process. I would also like to thank Dr. Yu

Zhang, Dr. Steve Polzin, and Dr. John Lu for serving on my Master’s thesis committee.

They have all supported me in and out of classes during my tenure at USF. Thanks to

the NBRTI team at CUTR, especially my supervisor Brian Pessaro, for their help and

understanding during the thesis. Working at CUTR for the past few years has been

pleasure. Finally, thanks to Vijay Sivaraman for his assistance throughout the project.
 Table of Contents

List of Tables ................................................................................................................ iii

List of Figures ................................................................................................................ iv

Abstract……... ................................................................................................................. v

Chapter 1: Introduction .................................................................................................... 1

1.1 Background .................................................................................................... 1
1.2 Literature on long distance leisure destination choice analysis ....................... 3
1.3 Objectives of this thesis ................................................................................. 6
1.4 Organization of this thesis ............................................................................ 10

Chapter 2: 1995 American Travel Survey ...................................................................... 12

2.1 Survey description ....................................................................................... 12
2.2 Description of the household demographics file ........................................... 15
2.3 Description of the household trip file ............................................................ 21

Chapter 3: Model Structure………… ............................................................................. 26

3.1 The MDCEV model for vacation destination choice analysis ........................ 26
3.2 The MDCEV model with minimum required consumptions ........................... 30

Chapter 4: Data ............................................................................................................. 37

4.1 1995 American Travel Survey ...................................................................... 37
4.1.1 Data set preparation ......................................................................37
4.1.2 Leisure subset selection ................................................................39
4.1.3 Destination alternatives .................................................................41
4.2 Secondary data sources .............................................................................. 45
4.2.1 Level of service variables ..............................................................45
4.2.2 Destination attraction variables ...................................................... 49
4.3 1995 ATS leisure subset data description .................................................... 51
4.3.1 Household demographics .............................................................. 51
4.3.2 Household trips..............................................................................54

Chapter 5: Results and Discussion ................................................................................ 57

5.1 Auxiliary mode choice model specification ................................................... 57
5.2 Destination choice model specification ......................................................... 59
5.2.1 Baseline marginal utility specification............................................. 60
5.2.2 Satiation ( γ k ) function specification ............................................... 64
5.3 Destination choice model validation ............................................................. 69

i
Chapter 6: Conclusions and Future Research ............................................................... 74

References Cited ........................................................................................................... 78

ii
 List of Tables

Table 1: Description of variables found in the 1995 American Travel Survey ................. 15

Table 2: Household demographics of the 1995 American Travel Survey ....................... 19

Table 3: Household aggregate trip statistics .................................................................. 21

Table 4: Household trip statistics ................................................................................... 24

Table 5: Reclassification of modes from 1995 ATS........................................................ 38

Table 6: Recoding methodology for trip purpose and transportation .............................. 39

Table 7: Primary mode used for long distance leisure travel - 1995 ATS ....................... 41

Table 8: Destination alternatives.................................................................................... 42

Table 9: Non-MSA to non-MSA area proxies for select states ....................................... 46

Table 10: Origin-destination pair variables created from DB1B survey .......................... 48

Table 11: Household demographics and leisure travel characteristics in

1995 ATS ........................................................................................................ 52

Table 12: Leisure trip characteristics in 1995 ATS ......................................................... 55

Table 13: Auxiliary mode choice model specification ..................................................... 59

Table 14: Destination choice model specification .......................................................... 68

iii
 List of Figures

Figure 1: Modeling framework ......................................................................................... 9

Figure 2: Alternative modeling framework ........................................................................ 9

Figure 3: Description of additional stops ........................................................................ 13

Figure 4: Sub-utility curves with a combined linear and non-linear form......................... 32

Figure 5: Model validation results based on distances to chosen destinations ............... 71

Figure 6: Model validation results based on the number of destinations visited

in a year .......................................................................................................... 71

Figure 7: Model validation results based on the total distance to the chosen
destinations..................................................................................................... 72

iv
 ABSTRACT

This study contributes to the literature on national long-distance travel demand modeling

by providing an analysis of households’ annual destination choices and time allocation

patterns for long-distance leisure travel purposes. An annual vacation destination choice

and time allocation model is formulated to simultaneously predict the different

destinations that a household visits and the time it spends on each of these visited

destinations, in a year. The model takes the form of a Multiple Discrete-Continuous

Extreme Value (MDCEV) structure (Bhat, 2005; Bhat, 2008). The model assumes that

households allocate their annual vacation time to visit one or more destinations in a year

to maximize the utility derived from their choices. The model framework accommodates

variety-seeking in households’ vacation destination choices in that households can

potentially visit a variety of destinations rather than spending all of their annual vacation

time for visiting a single destination. At the same time, the model accommodates corner

solutions to recognize that households may not necessarily visit all available

destinations. An annual vacation time budget is also considered to recognize that

households may operate under time budget constraints. Further, the paper proposes a

variant of the MDCEV model that avoids the prediction of unrealistically small amounts

of time allocation to the chosen alternatives. To do so, the continuously non-linear utility

functional form in the MDCEV framework is replaced with a combination of a linear and

non-linear form.

v
 The empirical data for this analysis comes from the 1995 American Travel

Survey Data, with the U.S. divided into 210 alternative destinations. The empirical

analysis provides important insights into the determinants of households’ leisure

destination choice and time allocation patterns.

An appealing feature of the proposed model is its applicability in a national, long-

distance leisure travel demand model system. The annual destination choices and time

allocations predicted by this model can be used for subsequent analysis of the number

of trips made (in a year) to each destination and the travel choices for each trip. The

outputs from such a national travel modeling framework can be used to obtain national-

level Origin-Destination demand tables for long-distance leisure travel.

vi
 Chapter 1: Introduction

1.1 Background

In several countries, a significant portion of the travel comes from long distance travel,

especially for leisure purposes. For example, in the United States, in the year 1977,

Americans made approximately 521 million long distance person trips1, totaling

approximately 382 billion miles traveled (BTS, 1998). Within the next two decades, per

the data in year 1995, the long distance travel more than doubled to about 1 billion

person trips and 827 billion miles (BTS, 1998). While this increase may be attributed to

an increase in travel for all purposes (business, social, and leisure, etc.), leisure travel is

of particular importance due to several reasons. First, leisure travel constitutes a

significant share of long distance travel (27% of all long distance trips made by US

households in 1995 were for leisure; see BTS, 1997), as well as a significant share of

the increase in long-distance travel (long-distance travel for leisure increased by 122%

between 1997 and 1995; see BTS 1998, pp. 149). It also appears that the recent

economic slowdown did not have a substantial impact on the vacation travel intentions of

Americans. For instance, despite perceiving an increase in the vacation price, 84% of

the respondents to a poll conducted by Priceline.com indicated that they still planned to

travel (Hotel News Resource, 2007). Perhaps leisure travel is such an integral part of

Americans’ lifestyle (LaMondia and Bhat, 2008) that it is difficult to part with even in poor

economic climates. Second, as the demographic makeup of several countries changes

toward an increasingly ageing population, the amount of long-distance leisure travel is

1
A long-distance trip is defined as roundtrip travel of at least 100 miles from home (BTS, 1998).
1
likely to continue to increase. Traveling and “exploring the world” appears to be an

ambition that people pursue in their retirement years with substantial amounts of time

and wealth at their discretion (Focalyst, 2007). On the same lines, several studies report

that the baby boomers (those born between 1946 and 1964) allocate significant amounts

of time and money to vacation travel (Mallet and McGuckin, 2000; Davies 2005). As the

baby boomers have started to enter their late sixties, growth in vacation travel is likely to

accelerate over the next several years. Third, leisure travel has a significant impact on

the economy as it is highly consumption-oriented. For instance, a recent consumer

expenditure report estimates that in the year 2008, U.S. households spent, on average,

$1,415 per annum on activities such as dining, lodging, shopping, entertainment and

recreation while on vacation and pleasure trips (BLS, 2010). It is not surprising that the

economy of several destinations thrives on the tourism/leisure travel industry.

Due to the above-discussed and various other reasons, long-distance leisure

travel behavior is one of the most studied topics in the tourism literature and is steadily

gaining importance in the transportation literature. Several dimensions of leisure travel

behavior have been studied to date, including whether to travel or not (Morley, 1992;

Seddighi and Theocharous, 2002; Nicolau and Mas, 2005), travel purpose (LaMondia et

al., 2008), length of stay and time/money budget allocation (Morley, 1992; Thornton et

al., 1997; Money and Crotts, 2003; Nicolau and Mas, 2005), frequency of travel (Kubas

et al., 2005), destination of travel (Train, 1998; Phaneuf and Smith, 2005) and mode of

travel (LaMondia et al., 2009). Notable among these dimensions is the destination

choice. From a tourism standpoint, a better understanding of where people travel for

their vacation can aid in taking measures to enhance the attractiveness of the

destinations and increase the tourism demand and revenue. Further, understanding the

destination preferences of different types of travelers can help in devising targeted

2
promotional campaigns to specific traveler segments. From a transportation planning

perspective, understanding the vacation travel flow patterns helps in assessing national

and local infrastructure needs and implementing appropriate transportation control

policies.

This thesis contributes to the literature on long-distance leisure travel demand

analysis by an analysis of households’ long-distance, vacation travel destination choices

in a year. Specifically a multiple discrete-continuous extreme value (MDCEV) model is

used to analyze the different destinations that a household visits in a year and the time

allocated to each of the visited destinations. The remainder of this section reviews the

literature on long-distance leisure destination choice analysis and positions the current

work vis-à-vis existing literature.

1.2 Literature on long distance leisure destination choice analysis

Leisure destination choice has been extensively studied in the tourism/leisure travel

literature (Moutinho 1987; Eugenio-martin, 2003). A popular approach to analyze

destination choices is the discrete choice analysis method using multinomial logit or

nested logit models (Seddighi and Theocharous, 2002; Eymann and Ronning, 1997;

Hong et al., 2006; Simma et al., 2001; and LaMondia et al., 2009). A variety of other

methods have also been used to analyze various aspects related to destination choice.

Examples include: (a) descriptive statistics (Bansal and Eislet, 2004; Crompton, 1979;

Um et al., 1990) and regression analysis (Rugg, 1973; Molina and Esteban, 2006) , (b)

factor analysis, determinant analysis and cluster analysis of destination image formation

(Jiang et al., 2000; Castro et al., 2007), (c) structural equations modeling of beliefs,

attitudes, and norms and past behavior on the intent to choose a destination (Lam and

Hsu, 2006; Greenridge, 2001), (d) open ended surveys, cognitive mapping and

qualitative analysis of the processes leading to destination choices (Woodside and

3
MacDonald, 1994; Woodside and Lyonski, 1989). Some of these studies2 focus on

analyzing the outbound tourism demand from one origin (usually a country) to multiple

destinations, while others3 analyze the inbound tourism demand from multiple origins to

a single destination, such as a city or country. It appears that very few leisure studies

analyze destination choices between multiple origins and multiple destinations.

Specifically, LaMondia et al. (2009) analyzes vacation travel between several European

Union countries, while Simma et al. (2001) analyzes leisure travel between the

municipalities of Switzerland.

In the transportation planning/modeling literature, though several studies focus

on short-distance leisure travel behavior within metropolitan areas (Yamamoto and

Kitamura, 1999; Bhat and Gossen, 2004; Schlich et al., 2004; Lanzendorf, 2002), very

little exists explicitly on long-distance leisure travel. Although long-distance travel

analysis is a regular exercise in the form of statewide travel models4 in the U.S. and

intercity travel demand models5, leisure travel is dealt with in very limited ways. For

example, in statewide models, inter-state trips6 are categorized as external, through, or

visitor trips and the trip flows are estimated using aggregate, growth factor or gravity-

based methods. Several national-level travel demand models also exist, predominantly

2
Eymann and Ronning (1997), Gonzalez and Moral (1995), DeCrop and Snelders (2004), Lise and Tol
(2001), Haliciolgu (2008)
3
Greenridge (2001), Castro et al. (2005), Garin-Munoz, 2000; Chan et al. (2005)
4
Horowitz (2006), Horowitz (2008), Cambridge Systematics (2007), Outwater et al. (2010)
5
Thakuriah (2006), Koppelman and Sethi (2005), Bhat (1995), Baik et al. (2007), Yao and Morikawa
(2005)
6
A significant portion of long-distance leisure trips tend to be inter-state trips.

4
in the European context7 and some for the US (Moeckel and Donnelly, 2010) and other

nations. (see Zhang et al., 2010; Lundgvist and Mattsson, 2001 for extensive reviews).

However, most models use aggregate trip distribution methods (couched within the

traditional four-step modeling system) and/or do not pay explicit attention to vacation

travel. This is not to say that disaggregate methods are not used or vacation travel is not

paid any attention. Some statewide models in the U.S. (e.g., Outwater et al., 2010) and

several European national models (e.g., Hackney, 2004) use disaggregate discrete

choice MNL or nested logit models to analyze destination choices. A few studies analyze

the destination choices with an explicit focus on vacation trips (LaMondia et al., 2010,

Simma et al., 2002; Louviere and Timmermans, 1990). Furthermore, some models are

built based on more behaviorally oriented activity-based and tour-based approaches

(e.g., the Danish national model PETRA and the Dutch national model; Fosgerau, 2001)

and agent-based methods (Parker and Epstein, 2008).

Despite all the advances, a drawback of most previous studies in both the travel

demand literature and in the tourism literature is that their analysis is limited to smaller

time frames such as a day (e.g., Cambridge Systematics, 2007; the Danish national

model), a few weeks (e.g., the British national model) or months. Some studies (e.g., the

Swiss national model) use a single trip, typically the most recent trip, as the unit of

analysis, which restricts the ability to understand how the decisions pertaining to that trip

are related to other vacation trips over longer time frames. Most data collection efforts

also appear to collect travel information for smaller time frames other than a few

exceptions such as the 1995 US American Travel Survey (ATS) and the DATELINE

7
These include the national model systems for Denmark (PETRA, Fosgerau, 2001), Sweden (SAMPERS;
Beser and Algers, 2001), Holland (LMS, HCG 1990), Germany (VALIDATE; Vortsih and Wabmuth,
2007), UK, Switzerland
5
survey8 that collected respondent’s travel information for one year. However, as

indicated in Eugenio-martin’s (2003) theoretical framework for tourism demand analysis

and in Morley (1995), longer time frames such as a year may be more appropriate for

vacation travel analysis (also see Little, 1979).

Existing studies with longer time frames such as a year use one of the two

approaches: (1) Aggregate (e.g., gravity-based) methods for estimating annual vacation

travel flows, (2) Employ disaggregate methods, but first predict the frequency of vacation

trips for a given time frame and then perform a piecemeal analysis of the destination

choices (and other decisions) for each trip. Studies belonging to the second category

include van Middlekoop et al’s (2004) microsimulation system for annual leisure

activity/travel patterns and the long-distance holiday travel module in the recent version

of the TRANS-TOOLS model for travel demand prediction in and between the European

Union countries (see Rich et al., 2009). LaMondia et al.’s (2008) annual vacation time-

use model is the only exception found that attempts a comprehensive analysis of the

annual vacation time-use patterns by different vacation purposes. They do not, however,

delve into destination choices.

1.3 Objectives of this thesis

In this paper, we propose an annual vacation destination choice and time allocation

model to simultaneously analyze the different destinations that a household visits, and

the time it spends on each of these visited destinations, in a year. Specifically, the

recently emerging multiple discrete-continuous extreme value (MDCEV) model (Bhat,

2005; Bhat, 2008) is employed to analyze the factors influencing households’ annual

8
DATELINE Survey collects only holiday travel data for one year. This data is used estimate the travel
models in the second version of the TRANS-TOOLS model for travel demand prediction in and between
the European Union countries (see Rich et al., 2009). In this model, the total frequency of yearly long-
distance holiday trips is first generated. These trips are then distributed to different destinations using a
joint destination and mode choice model.
6
vacation destination choices and time allocation patterns. The model assumes that

households allocate the annual vacation time available at their disposal to one or more

destinations in a year in such a way as to maximize the utility derived from their choices.

As described in LaMondia et al. (2008), the utility maximization framework is consistent

with Iso-Ahola’s (1983) optimal arousal concept of vacation behavior that people “suffer

psychologically and physiologically from understimulating and overstimulating

environments” and seek an “optimally arousing experience.” The model framework

accommodates variety-seeking in households’ vacation choices in that households can

potentially visit a variety of destinations rather than spending all of their annual vacation

time for visiting a single destination. Households may seek variety in destination choices

due to several reasons. First, different members of a household may have different

preferences, leading to a variety in destinations choices. For example, children might

prefer to spend a week at the Disney land while elderly might prefer a calm and warm

winter resort. Second, households might visit multiple destinations due to satiation

effects of increasing time allocation to a destination (i.e., they experience boredom and

start seeking variety). Such satiation effects in vacation travel behavior have been noted

in previous studies both in the context of visiting multiple destinations within a single

vacation trip (Lue et al., 1993) as well as budgeting annual leisure time expenditures for

different purposes (LaMondia et al., 2008). Third, people might take vacations for

pursuing multiple types of activities (adventure, sightseeing, etc.) and/or during multiple

seasons of the year but no single destination may be ideal for all purposes and/or during

all time periods (hence a variety of destination choices over a year). The MDCEV model

incorporates variety in destination choices by employing a non-linear utility framework

that allows diminishing marginal utilities of increasing time allocation to a destination. At

the same time, the model recognizes that households may not necessarily visit all

7
available destinations, by incorporating corner solutions that allow zero time allocations

to certain destinations. An annual vacation time budget is also considered to recognize

that households may operate under time budget constraints.

The proposed model is couched within a larger vacation travel modeling

framework as depicted in Figure 1. First, households are assumed to allocate annual

time and money budgets for leisure travel. Next they are assumed to allocate the time

and money budgets to visit one or more destinations. Subsequently, for each destination

they choose to visit, they decide the number of trips to make to that destination, and

travel choices for each trip, including mode choice, time (i.e., season) of the year, and

length of stay. The analyst can apply this framework to all households in the nation and

obtain a national-level Origin-Destination demand table for vacation travel. Of course,

other decision elements, such as the travel party composition for each vacation trip,

could be included in the framework. Further, the framework could be refined to include

another step (between steps 1 and 2) where households allocate the annual vacation

time to different purposes (recreation, sightseeing, etc.) and then decide the destinations

to visit depending on the purposes they wish pursue. Alternatively, a slightly different

framework that assumes an alternative hierarchy of decisions could be used (as shown

in Figure 2). Specifically, in the second step the analyst can model the households’

allocation of annual vacation time/money budgets into different purposes and different

seasons (or times of the year). Subsequently, (s)he could model the destination choices

and other travel decisions (e.g., mode choice) for each purpose and time of the year.

8
 Figure 1: Modeling framework

Figure 2: Alternative modeling framework

9
 Notwithstanding which framework represents households’ annual vacation

decisions better (which is yet to be empirically tested), this thesis is focused on the

annual vacation destination choice and time allocation decisions. Further, the thesis

recognizes that mode choice decisions are generally closely tied to destination choices

(Hackney, 2004) and estimates an auxiliary mode choice model that feeds the level of

service characteristics into the destination choice model in the form of a log-sum

variable. The empirical data used in this study comes from the 1995 American Travel

Survey Data, with the U.S. divided into 210 destination choice alternatives. Thus, the

study provides an opportunity to estimate, apply, and assess the performance of the

MDCEV model for an empirical context with a large number of choice alternatives.

Finally, on the methodological front, we propose a variant of the MDCEV model

that allows for the possibility that once a good is chosen, at least a certain reasonable

amount of the good is consumed, as opposed to an unrealistically small amount of it.

This is because satiation effects may start kicking in only after a certain amount of the

good is consumed rather than right after the first infinitesimal consumption. In the

current, long-distance vacation context, it is reasonable to expect that households

allocate at least a certain minimum amount of time (say, at least half a day; as opposed

to a few minutes or hours) to long-distance destinations. To accommodate such

minimum required time allocation, the continuously non-linear utility functional form in

the MDCEV framework is replaced with a combination of a linear and non-linear form, as

described in Chapter 3.

1.4 Organization of this thesis

The remainder of this thesis is organized as follows. The next chapter will provide an

extensive overview of the 1995 American Travel Survey (ATS), including a description of

the household demographics and household trip file. Chapter 3 will provide a thorough

10
explanation of the multiple discrete-continuous extreme value (MDCEV) model structure

to be used for destination choice estimation in this thesis. Chapter 4 will provide a

detailed methodology for the preparation of the 1995 ATS data set, including the leisure

subset selection and selection of the 210 destination alternatives (4.1). The 1995 ATS

does not provide level of service variables or variables indicating the attractiveness of a

destination. The collection effort for these variables is also provided in Chapter 4 (4.2).

Lastly, a descriptive analysis of the 1995 ATS leisure subset is provided in Chapter 4.

Chapter 5 will provide the model estimation results and related discussion, followed by a

model validation exercise. Finally, Chapter 6 concludes the thesis and identifies

directions for possible future research.

11
 Chapter 2: 1995 American Travel Survey

2.1 Survey description

The 1995 American Travel Survey (ATS) is the primary source of data used in this

analysis. The 1995 ATS is an in-depth, long-distance nationwide travel survey of the

United States that collects information on households’ long-distance travel (i.e., trips of

at least 100 miles) for an entire year. Admittedly, the data is a bit old, but no other recent

dataset exists with information on one year worth of long-distance travel in the U.S. To

be sure, a similar long-distance survey, the 2001 National Household Travel Survey

(NHTS), was conducted recently to collect data on long-distance travel, although with a

limited collection time per household (1 month) it is somewhat limited in the number of

long-distance trips captured per household.

The ATS was conducted by the Bureau of Transportation Statistics between April

1995 and March 1996 and was designed to gather passenger flow data, as well as

demographic information and other related data such as travel distance, trip purpose,

mode used, length of the trip, and types of lodging used. The primary focus of the ATS is

to examine long-distance trips, defined as trips with a round trip distance of 100 miles or

more, excluding commuter trips (BTS, 1995). Similar data was previously collected in

1977 and so the 1995 ATS provided a much needed update.

Approximately 80,000 households taken from the 1980 Current Population

Survey sample were selected to be interviewed for the ATS. Each household was

interviewed three to four times, or every three months, over the course of the year to

attempt to capture all long-distance trips. Computer aided telephone interviews (CATI) or

computer aided personal interviews (CAPI) were utilized to attempt to limit respondent
12
and interviewer burden. The sample for this survey consists of civilian households, group

quarters (dormitories), religious group dwellings, and family-type housing on military

bases. Military barracks and institutional group dwellings such as nursing homes and

prisons are not included. The final number of responses is 62,609 households with

48,527 reporting at least one long-distance trip. A total of 337,520 household trips are

recorded by the 1995 ATS (BTS, 1995).

Since the focus of the ATS is to provide passenger flow data, a detailed trip

itinerary is included for each case. Additional details for each of the 12 potential side

stops within the overarching trip including four stops to the final destination, four stops

from the final destination, and four side trips originating at the final destination are

provided. These include the side stop location at the metropolitan statistical area or state

level, number of nights spent at the side stop, lodging accommodations utilized at the

side stop, reason for the side stop, and transportation used to arrive at the side stop.

This information is not provided in any later U.S. national travel survey and makes the

1995 ATS a valuable source of detailed information for long distance trip making. These

additional stops are illustrated in Figure 1.

Stops from
Side stops

Origin Destination

Stops to

Figure 3: Description of additional stops

The 1995 ATS data is comprised of four different data sets; household trips,

household demographics, person trips, and person demographics. For the purposes of
13
this thesis, only the household data files will be used. The household demographic data

set contains one record for each of the 62,609 households, of which 48,527 made at

least one long distance trip during the survey year. The household demographic data set

contains variables describing socio-economic characteristics (including race, education

level, age, and income) and geographic characteristics (including the origin state and

metropolitan statistical area). The household trip data set includes household

demographic characteristics (such as age, education level, race, and household size)

and trip characteristics (such as round trip distance, nights spent away, primary mode of

transportation, origin, destination, and similar details on any side stops). Further details

on the available variables contained within the 1995 ATS are provided in Table 1.

Additionally, weights are provided within the household trip file to expand the contained

trips to represent national totals. Unique household and trip identification variables are

present in each of the household demographics and household trip files to allow for

combining of files if necessary.

14
 Table 1: Description of variables found in the 1995 American Travel Survey
Variable Name Description of Variable
Race The race of the householder or person.
The age of the householder or person. This
Age
continuous variable was categorized.
Education Level The education level of the householder or person.

Household Income The combined annual income of the household.

Determines if household lives in a rented or owned
Tenure
property.
Structure Type The structure type of the household residence.

Household Size The number of persons residing in the household.

Indicates the presence of children in the household
Children in Household
by age.
The number of personal vehicles available at the
Number of Vehicles Available
start of this trip.
The census division in which the household is
Census Division Origin
located.
The census division of the primary destination of the
Census Division Destination
trip.
The number of route miles traveled within the United
U.S. Route Distance Traveled States for this trip. Route miles are not available
outside of the United States.
The composition of the travel party, i.e., the presence
Travel Party Type
of adults and/or children.
Travelers in Party The number of travelers in the party.
The originating day of the trip, either a weekday or
Trip Start Day
weekend.
The primary mode of transportation used for this trip.
Primary Mode of Transportation This variable was re-coded as noted in the previous
section.
The primary purpose for this trip. This variable was
Primary Purpose
re-coded as noted in the previous section.

2.2 Description of the household demographics file

An overview of the demographic characteristics for all households recorded in

the 1995 American Travel Survey is provided in Table 2. For comparison, the

demographic characteristics for all households that made at least one long distance trip

are provided. There are a total of 62,609 households recorded in the 1995 ATS, with

15
48,527 making at least one long distance trip. If applicable, the mean value of the

characteristic is provided in bolded text.

The majority of surveyed householders are white (86.8 percent), while black

travelers account for the second highest percentage at 8.1 percent. Approximately 70

percent of households surveyed are aged 25 to 64 with a mean age of 50.4 years. More

than 85 percent of householders have attained at least a high school diploma, while just

over one quarter have received a bachelor’s degree or better. Almost 50 percent of

those sampled for the survey make between $30,000 and $74,999 per year, falling into

the middle-income category. The 1995 ATS does not provide income as a continuous

variable and so a mean income is not provided. The majority of householders (58.3

percent) work full time. Retired householders make up the second largest portion of the

sample, accounting for 22.8 percent of households. The average number of private

vehicles available to a household is 1.89, with more than 85 percent of households

having access to at least one vehicle.

The majority of survey respondents indicated they own their home, accounting

for approximately three-quarters of the sample. Most (almost 80 percent) of households

in the sample live in a house, duplex, or modular home. Household size is not provided

as a continuous variable in the 1995 ATS, instead ending at 7 or more members of the

household. Therefore, average household size could not be provided. Almost one-

quarter (24.1 percent) of households consist of only one person, with two person

households accounting for another 34.5 percent. This corresponds with the large

proportion of households in the 1995 ATS with no children (there are no children, or no

children under the age of 18 in 68.9 percent of households). This may have some impact

on travel behaviors as effects of the presence of children can be very important as a

result of their different needs and the additional variety needed to satisfy all members of

16
the household. The census division variable indicates the region of the country in which

the household is based. The most represented census division is the South Atlantic

accounting for 16.7 percent of the households, while the Middle Atlantic accounts for 6.4

percent of the households. This appears to fairly represent the associated states, that is,

the proportions seem to match the relative size of the census division. The South

Atlantic division includes Delaware, Maryland, Washington, D.C., Virginia, North

Carolina, South Carolina, Georgia, and Florida while the Middle Atlantic division is

comprised of New York, New Jersey, and Pennsylvania.

The second column of Table 2 provides the household demographics for those

households that made at least one long distance trip during the surveyed year. When

comparing the entire sample of households, with sample of households that made at

least one long distance trip during the survey year, there are several differences. The

proportions of racial makeup between the two samples are very close to those seen in

the sample of households that made at least one long distance trip. Elderly households

(65 and older) tend not to make long distance trips, relative to middle aged households.

This can be seen in the decrease in the elderly proportion of the sample from 24.4

percent to 19.3 percent and the decrease in the average age from 50.4 to 48.4 when

comparing all households and trip making households. Households that reported at least

one long distance trip tend to be better educated, with the proportion of householders

with no high school diploma decreasing from 14.5 percent to 9.7 percent and the

proportion of householders with a bachelor’s degree or better increasing from 26.8

percent to 31.8 percent. Similarly, those households that made at least one long

distance trip tend to have a higher yearly income and are more likely to be employed full

time. The proportion of households that do not have a vehicle decreases in the sample

of households that made a long distance trip, relative to the entire sample.

17
 The housing characteristics (tenure and structure type) of the entire sample are

only slightly different from the sample of households that made at least one long

distance trip. In both cases, the majority of households owns their home and lives in a

standalone house. The characteristics of the household slightly changes between the

two samples. The typical household size is larger with an increase in 2 or more person

households from 75.9 percent of the entire sample to 80.2 percent of the sample of

households making long distance trips. Similarly, the proportion of households with no

kids is lower in the sample of households that made at least one long distance trip

decreasing from 68.9 percent to 65.9 percent. The shares of each census division do not

change much between the entire sample and the sample of household trips with at least

one long distance trip.

It is clear that the demographic characteristics of a household have some impact

on the likelihood of making a long distance trip. Income and the household type

(presence of kids and household size) are likely two of the major factors in the decision

to travel during the year.

18
 Table 2: Household demographics of the 1995 American Travel Survey
Households with at least
Characteristic All Households
one long distance trip
Sample Size 62,609 48,527
Race of Householder --- ---
White 86.8% 88.3%
Black 8.1% 6.5%
American Indian, Eskimo, Aleut 1.0% 1.0%
Asian or Pacific Islander 2.4% 2.5%
Other 1.7% 1.6%
Age of Householder 50.4 48.4
15 to 24 4.1% 4.5%
25 to 44 38.2% 41.1%
45 to 64 33.3% 35.1%
65 or older 24.4% 19.3%
Education of Householder --- ---
Less than high school 14.5% 9.7%
High school graduate 33.3% 31.2%
Some college, no degree 19.5% 20.9%
Associate’s degree 5.8% 6.4%
Bachelor’s degree 15.8% 18.4%
Some graduate or professional
1.8% 2.2%
school, no degree
Graduate or professional degree 9.2% 11.2%
Household Income --- ---
Under $30,000 41.4% 34.1%
$30,000 to $74,999 49.1% 54.3%
$75,000 or more 9.5% 11.6%
Activity of Householder --- ---
Working full-time 58.3% 64.0%
Working part-time 6.4% 6.5%
Looking for work 1.4% 1.2%
In armed forces 0.5% 0.6%
Homemaker 6.0% 4.8%
Going to school 2.1% 2.3%
Retired 22.8% 18.6%
Doing something else 2.6% 1.9%
Mean number of vehicles 1.89 2.05
0 13.4% 10.7%
1 28.3% 24.9%
2 34.4% 36.9%
3 14.2% 16.1%
4 or more 9.7% 11.4%

19
 Table 2: (continued)
Households with at least
Characteristic All Households
one long distance trip
Sample Size 62,609 48,527
Tenure --- ---
Owned or being bought 74.6% 76.5%
Rented for cash 23.5% 21.7%
No cash paid 1.9% 1.8%
Structure Type --- ---
House, townhouse, duplex,
79.2% 81.4%
modular home
Apartment 13.8% 12.2%
Mobile home 5.7% 5.1%
Other 1.2% 1.3%
Household Size --- ---
1 24.1% 19.8%
2 34.5% 34.9%
3 16.5% 17.7%
4 or more 24.9% 27.7%
Presence of Children in
--- ---
Household
Children under 6 6.5% 7.1%
Children 6-17 18.7% 20.7%
Children under 6 and
6.0% 6.4%
children 6-17
No Children 28.6% 24.7%
No children under 18 40.3% 41.2%
Census Division --- ---
New England 14.3% 13.8%
Middle Atlantic 6.4% 6.0%
East North Central 9.5% 9.3%
West North Central 12.5% 13.2%
South Atlantic 16.7% 16.1%
East South Central 9.5% 8.7%
West South Central 7.0% 6.9%
Mountain 15.2% 16.7%
Pacific 8.7% 9.4%

The aggregate household trip statistics are provided in Table 3. The mean

number of trips taken annually by each household is 5.40, with 22.5 percent not taking

any long-distance trips and 14.7 percent making more than 10 trips. The average

20
household makes 2.34 long-distance trips per year, with 64.2 percent making at least

one per year. The average total route distance traveled for long-distance trips within the

United States is 4,572.82 per household. This does not include any travel overseas, as

route distance traveled is not available outside of the United States.

Table 3: Household aggregate trip statistics

Households with at
Characteristic All Households least one long distance
trip
Sample Size 62,609 48,527
Number of trips taken 5.40 6.96
0 22.5% 0.0%
1 16.0% 20.7%
2 11.4% 14.7%
3 8.6% 11.1%
4 6.6% 8.5%
5 to 10 20.1% 26.0%
Greater than 10 14.7% 12.3%
Number of vacation trips taken 2.34 3.02
0 35.8% 17.1%
1 20.8% 26.8%
2 12.9% 16.7%
3 8.5% 11.0%
4 5.9% 7.7%
5 4.2% 5.4%
Greater than 5 11.9% 15.3%
Yearly long distance route miles
4,572.82 5,899.80
traveled within US
Under 100 miles or no trips made 23.0% 0.7%*
100-2,000 miles 26.7% 34.4%
2,001-4,000 miles 16.1% 20.8%
4,001-6,000 miles 10.2% 13.1%
6,001-8,000 miles 6.7% 8.7%
8,001-10,000 miles 4.5% 5.8%
Over 10.000 miles 12.8% 16.5%
* Route distances less than 100 miles are due to international travel

2.3 Description of the household trip file

An overview of the household trips recorded in the 1995 ATS is provided in Table

4. The first numeric column provides the un-weighted descriptions for each variable and

the second numeric column provides the weighted descriptions for each relevant
21
variable. When relevant, the mean value for each variable is provided in bold text. There

are 337,520 household trips provided in the 1995 ATS. When weights are applied, this

represents over 684 millions trips.

Most travelers selected personal owned vehicles as the primary mode of

transportation for their trip, accounting for 76.8 percent of all trips within the sample and

74.8 percent of all weighted trips. Air travel is the second most used mode of

transportation, accounting for 19.3 percent of all trips within the sample and 21.0 percent

of all weighted trips. The three most commonly provided reasons for taking a trip are

work/business, visiting friends and relatives, and leisure accounting for 28.0 percent,

27.5 percent, and 24.8 percent of all trips within the sample respectively. Similar

proportions are seen when weights are applied. The travel party composition, especially

the presence of children, can potentially have some impact on travel behavior and

influence the type of travel patterns used, due to additional variety seeking seen when

kids and additional people are introduced to the travel party. Most trips are made by

single adults with no children accounting for 58.8 percent of trips, while two adults with

no children make up another 22.4 percent of all trips. Children are present on 17.4

percent of all long-distance trips. Again, similar proportions are seen for the travel party

type when weights are applied. The mean number of travelers present per long-distance

trip is 2.83 within the sample and 2.77 when weights are applied.

Typically, long distance household trips begin on a weekday (61.3 percent in the

sample and 59.5 percent after applying weights) although when taking into account the

fact that weekends constitute only 2 of 7 days per week, there does seem to be a

tendency to start a trip on a weekend. The average number of nights spent away is 3.29

within the sample and 3.62 after weights are applied. In both the sample and weighted

cases, approximately one quarter of all trips are completed in one day and no nights are

22
spent away from home. The average length of all trips (excluding international travel, for

which no route distances are available) is 848.25 miles, with 57.2 percent of trips

ranging between 100 and 500 miles and another 18.8 percent of trips ranging between

500 and 1,000 miles. Only 3.5 percent of all recorded trips are to international

destinations. Similar proportions are observed when weights are applied.

The origins and destinations show the greatest amount of variability between the

un-weighted sample and the weighted total. When weights are not applied, the

proportion of trips departing from a census division ranges from a low of 7.1 percent for

West South Central (Oklahoma, Texas, Arkansas, and Louisiana) to 17.5 percent from

the Mountain division (Idaho, Nevada, Arizona, Utah, Wyoming, Montana, Colorado, and

New Mexico). The proportion of trips arriving at a census division ranges from a low of

7.3 percent to the East South Central division (Kentucky, Tennessee, Mississippi, and

Alabama), to 17.7 percent to the Mountain division. When weights are applied, the

proportion of trips departing from a census division ranges for a low of 4.8 percent from

New England (Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, and

Connecticut) to 17.5 percent for the South Atlantic (Delaware, Maryland, Washington,

D.C., Virginia, North Carolina, South Carolina, Georgia, and Florida). The proportion of

trips arriving at a census division ranges from a low of 4.5 percent to New England, to

18.8 percent to the South Atlantic.

23
 Table 4: Household trip statistics
Demographic Variable Un-Weighted Weighted
Sample Size/Population Size 337,520 684,661,562
Primary Mode of Transportation
POV 76.8% 74.8%
Airplane 19.3% 21.0%
Bus 0.3% 0.4%
Intercity Rail 0.6% 0.6%
School Bus 0.6% 0.4%
Other 2.5% 2.7%
Purpose
Work/Business 28.0% 27.0%
Combined Business and Pleasure 2.3% 2.2%
Shopping 2.4% 1.6%
School-related 3.1% 2.8%
Family/Personal Business 11.9% 11.0%
Visit friends or relatives 27.5% 29.4%
Leisure 24.8% 26.1%
Other 0.0% 0.0%
Travel Party Type --- ---
One adult, No children under 18 56.3% 58.8%
Two adults, No children under 18 24.6% 22.4%
Three or more adults, No children
1.4% 1.3%
under 18
One adult, Children under 18 4.8% 4.4%
Two adults, Children under 18 9.5% 9.2%
Three or more adults, Children under
0.8% 0.8%
18
No adults, One child under 18 2.3% 2.6%
No adults, Two or more children under
0.3% 0.4%
18
Travelers in Party 2.83 2.77
1 35.3% 36.9%
2 32.8% 31.3%
3 12.1% 11.7%
4 9.4% 9.4%
5 or more 10.5% 10.7%

24
 Table 4: (continued)
Demographic Variable Un-Weighted Weighted

Sample Size/Population Size 337,520 684,661,562

Trip Start Day
Weekend 38.7% 40.5%
Weekday 61.3% 59.5%
Nights away from home 3.29 3.62
0 27.6% 24.3%
1 to 3 46.9% 48.0%
4 to 6 14.3% 15.4%
7 to 9 5.4% 6.0%
10 or more 5.8% 6.3%
Route Distance Traveled 848.25 867.24
100 to 500 miles 57.2% 54.0%
501 to 1,000 miles 18.8% 20.3%
1,001 to 2,000 miles 10.6% 11.1%
2,001 to 4,500 miles 7.5% 8.0%
Over 4,500 miles 2.4% 2.4%
International Destination 3.5% 4.1%
Householder Census Division Origin
New England 12.8% 4.8%
Middle Atlantic 4.9% 11.3%
East North Central 8.8% 16.4%
West North Central 14.7% 8.9%
South Atlantic 15.0% 17.5%
East South Central 8.7% 6.4%
West South Central 7.1% 12.1%
Mountain 19.8% 7.7%
Pacific 8.1% 14.9%
Householder Census Division
Destination
New England 8.9% 4.5%
Middle Atlantic 7.7% 9.5%
East North Central 9.9% 14.2%
West North Central 13.7% 8.6%
South Atlantic 16.0% 18.8%
East South Central 7.3% 6.2%
West South Central 8.2% 11.4%
Mountain 17.7% 9.7%
Pacific 10.6% 12.9%
International 3.5% 4.1%

25
 Chapter 3: Model Structure

The long-distance vacation travel destination choice model presented in this thesis is

based on Bhat’s (2005 and 2008) MDCEV framework. Thus, chapter 3.1 draws from

Bhat (2008) to present the MDCEV framework for annual vacation destination choice

and time allocation analysis. Chapter 3.2 extends the MDCEV framework to

accommodate a given minimum amount of vacation time allocation to each of the

chosen destinations.

3.1 The MDCEV model for vacation destination choice analysis

Let the U.S. be divided into K number of destination choice alternatives that a

household considers for vacation travel. Let t be the vector of vacation time

investments ( t1 , t 2 ,…, t K ) by the household at each of the vacation destination

alternatives k (k = 1,2,…,K). The time investments tk can either be zero or some positive

value expressed in number of nights spent. At least one element of t should be positive.

Whether or not a specific tk value (k = 1,2, …, K) is zero constitutes the discrete choice

component, while the magnitude of each non-zero tk value constitutes the continuous

choice component.

Now, consider the following additive, non-linear, functional form9 to represent the

utility accrued by a household from its annual vacation destination choices (index for the

household is suppressed in the notation):

K K
t 
U (t ) = ∑ u (tk ) = ∑ γ kψ k ln  k + 1 (1)
k =1 k =1 γk 

9
Some other utility function forms (as discussed in Bhat, 2008) were also considered, but the one presented
here provided the best data fit. These alternative forms are not discussed here for conciseness.
26
In the above expression, the total utility U (t ) derived from the time allocation to the K

destination choice alternatives is the sum of the sub-utilities u(tk ) derived from the time

allocation to each of the destinations k. Within the sub-utility function for an alternative k,

ψ k represents the marginal utility of unit vacation time investment for a destination

alternative k at the point of zero time investment for the destination. ψ k , labeled the

baseline marginal utility parameter, controls the discrete choice decision of the

household for alternative k. Specifically, at the point of zero time allocation to all

destinations, the destination with the highest baseline marginal utility value is allocated

the first unit of vacation time available to the household. Subsequently, with increasing

time allocation to that destination, the marginal utility derived from spending time at that

destination decreases (this diminishing marginal utility effect is called satiation). At some

point, when the marginal utility for another destination becomes stronger, the next unit of

time is allocated to that destination. This process of marginal time allocation to the

destination with the highest marginal utility continues until the household runs out of its

vacation time budget. As a result, the household derives the optimal utility from the

destinations it visits and the time it allocates to each of the visited destinations. In

summary, the household utility maximization problem can be viewed as an incremental

time allocation process, with each additional unit of time allocated to the alternative with

the highest marginal utility at that point of time allocation.

The satiation effect described above is captured in the model via a non-linear

utility form with respect to the tk terms (as in Equation (1)). In this context, the γk (

γ k > 0, ∀k ) terms serve the role of satiation parameters by accommodating differential

satiation rates across different alternatives. Specifically, the higher the γ k value for an

alternative k, the slower the satiation effect; hence, the amount of time allocated to
27
alternative is larger (Bhat, 2008). Further, the γ k terms serve as translation parameters

that allow for the possibility that the household may not choose (or invest no time for)

certain destinations.

In the utility function (1), socio-demographic and destination-specific attributes

are introduced in the ψ k and γ k terms as: ψ k = exp(β ' zk + ε k ) and γ k = exp(θ ' wk ) . zk

is the vector of exogenous variables influencing the baseline marginal utility for

alternative k. zk includes destination specific variables (e.g., leisure/tourism industry

employment, temperature, and whether at the destination), transportation level of service

variables (e.g., distance, travel times, costs), and interactions of these variables with

household socio-demographic attributes. wk is also a similar vector of variables

influencing the satiation rate for alternative k. β and θ are parameter vectors

corresponding to the explanatory variables in zk and wk , respectively. Finally, ε k (k =

1,2,…,K) are the random error terms representing the unobserved factors influencing the

baseline preference for each of the destination alternatives k (k = 1,2,…,K).

From the analyst’s perspective, a household maximizes the overall utility U (t )

subject to the vacation time budget constraint: ∑ k

tk = T , where T is the annual

vacation time (in number of days) available to that household.10 The optimal time

investments tk* (k = 1,2,...,K) can be determined by forming the Lagrangian function

corresponding to the households’ utility maximization problem and applying the Kuhn-

Tucker (KT) conditions, as below:

10
The reader will note here that we assume the total annual household vacation time, T, to be known a
priori and focus only on households who undertake some amount of vacation travel each year. As indicated
in Section 1.3, the total annual vacation time T could be modeled in a separate (prior) step, where the 365
days in a year would be split into non-leisure time, non-vacation leisure time (i.e., leisure time spent within
the neighborhood/urban area of residence), and vacation leisure time.
28
  tk  K 
Lagrangian, L = ∑ γ k [exp( β ′zk + ε k )] ln  + 1 − λ ∑ t k − T  , (2)
k γk   k =1 

where λ is the Lagrangian multiplier associated with the time constraint. The Kuhn-

Tucker (KT) first-order conditions for the optimal vacation time allocations (the t k* values)

are given by:

−1

[exp(β ′zk + ε k )]  tk + 1 − λ = 0 , if tk* > 0 , k = 1, 2,…, K

*
(3)
γk 
−1

[exp(β ′zk + ε k )]  tk + 1 − λ < 0 , if tk* = 0 , k = 1, 2,…, K

*

γk 

The optimal vacation destination choices and time allocations satisfy the above KT

conditions and the vacation time budget constraint ∑ *

t = T . The budget constraint
k k

implies that only K-1 of the t k* values need to be estimated, since the vacation time

invested for any one destination is automatically determined from the time invested for

all the other destinations. To accommodate this constraint, designate destination 1 as a

vacation destination to which the household allocates some non-zero amount of time.

The KT condition for this destination may then be written as:

−1
 t1* 
λ = [ exp(β z1 + ε1 )]  + 1
′ (4)
 γ1 

Substituting for λ from above into Equation (3) for the other destinations (k = 2, 3,…,K),

and taking logarithms, the K-T conditions can be rewritten as:

Vk + ε k = V1 + ε1 if tk* > 0 (k = 2, 3, …, K)

Vk + ε k < V1 + ε1 if tk* = 0 (k = 2, 3, …, K), where (5)

29
  t* 
Vk = β ' z k − ln k + 1 (k = 1, 2, …, K)
γk 

Assuming that the error terms ε k (k = 1, 2, …, K) are independent and identically

distributed across alternatives with a type 1 extreme value distribution, the probability

that the household allocates vacation time to the first M of the K destinations (for

* * * th
duration t1 in the first alternative, t2 in the second, … tM in the M alternative) is (see

Bhat, 2008):

 M 
 ∏ eVi 
 M
  M
1 
P(t1* , t 2* , t 3* ,...t M* ,0,0,0..0) = ∏ ci   ∑   i =1 M  ( M − 1)!, (6)
 i =1   i =1 ci    K Vk  
 ∑e  
  k =1  

 1 
where ci =  *  for i = 1, 2, …, M.
 ti + γ i 

3.2 The MDCEV model with minimum required consumptions

In the above discourse, the vacation time tk (k = 1,2,…,K) is treated as a continuous

variable. Thus it can potentially take a very small value (e.g., a few minutes or a few

hours) that may not necessarily be realistic in a long-distance vacation travel context. As

indicated earlier, it is reasonable to expect that households allocate at least a minimum

amount of time (say, half a day) as opposed to a few minutes or hours for visiting long-

distance destinations. However, the MDCEV model, in its original formulation, does not

accommodate this and can potentially result in unrealistically small amounts of time

spent for certain destinations. To address these issues, the continuously non-linear utility

function of the MDCEV model (as in Equation (1)) is replaced with a combination of a

linear and non-linear utility form, as below:

30
 K
U ( t ) = ∑ u (t k )
k =1

where u (tk ) = ψ k tk if tk ≤ t0 , (7)

t −t 
= ψ k t0 + γ kψ k ln  k 0 + 1  if tk ≥ t0 .
 γk 

In the above equation, t0 is the minimum amount of time allocated to the

destinations that the household chooses to visit. Thus, the utility derived from the time

allocation to a destination alternative k (if that destination is chosen) increases in a linear

fashion until the minimum required amount of time is allocated to that destination, after

which the functional form takes a non-linear shape. This is depicted in Figure 4, with the

linear and non-linear parts of the sub-utility functional form. The figure depicts the sub-

utility profiles for ψ k = 5 and different values of γ k . As can be seen from the figure, The

functional form of the sub-utility profiles is such that the marginal utility (i.e., the slope)

takes a constant value of ψ k until the consumption reaches t0 = 0.5, and then starts

decreasing to capture the diminishing marginal returns11. For any chosen destination,

households are assumed to experience satiation only after spending t0 amount of time,

as opposed to immediate satiation after the first unit consumption. This assumption

ensures that at least t0 amount of time is spent at any chosen destination, and helps

avoid destination choices with unrealistically small amounts of time allocation.

11
Note: marginal utility at tk = t0 is equal to ψ k for both the linear and non-linear parts of the sub-utility
curve.
31
 ψk = 5
t0 = 0.5

Figure 4: Sub-utility curves with a combined linear and non-linear form

To understand this, recall the incremental time allocation process discussed in

Chapter 3.1. At the point of zero time allocation to all destinations, the first unit of time is

allocated to the destination with the highest marginal utility (ψ k ) value. Subsequently,

unlike in the case of the MDCEV model, the marginal utility of time allocation to this

destination does not diminish until the time allocation reaches t0 . Given that the

marginal utility of this destination remains the same (and so remains greater than the

baseline marginal utility of other goods) until t0 , additional units of time are allocated to

this same destination until the cumulative time allocation for this destination reaches t0 .

It is only after a cumulative time allocation of t0 that the other destinations start

competing for the vacation time. As the marginal utility of time allocation for the first

chosen destination diminishes (after t0 amount of time is allocated to it), the destination

with the next higher baseline utility becomes stronger (in marginal utility) and gets its first

unit of time allocation. Again, until this next destination gets the minimum amount of time

32
( t0 ) allocated, no other destination competes for vacation time. This process continues

until the annual vacation time budget is exhausted. In summary, the sub-utility functional

form in Equation (7) with a linear form at the corner (until a minimum amount, t0 of time

allocation), followed by a non-linear form, relaxes the assumption of immediate satiation

effects at the corner (i.e., after first unit consumption). This helps ensure a minimum

amount ( t0 ) of time allocation for each chosen destination and thus, reduce the

possibility of unrealistically short vacation durations.12

As in chapter 3.1, the analyst can parameterize ψ k as ψ k = exp(β ' zk + ε k ) and

γ k as γ k = exp(θ ' wk ) , form a Lagrangian for the household’s constrained utility

maximization problem, and arrive at the KT conditions that form the basis for deriving the

vacation destination choice and time allocation probability expressions. The Lagrangian

is given by:

K 
L = ∑k k ∑
u (t ) − λ
k =1
tk − T  ,

(8)

where u(tk ) is as defined in Equation (7), and all other terms are as defined before. The

KT conditions for the optimal vacation time allocations are given by:

u′(tk* ) − λ = 0 , if tk* > 0 , k = 1, 2,…, K (9)

u′(tk* ) − λ < 0 , if tk* = 0 , k = 1, 2,…, K

∂
where, u′(tk* ) = (U (t ) ) = ψ k if tk* ≤ t0 ,
∂tk

12
The reader will note a subtlety here that not all chosen destinations may be allocated the required
minimum amount of time. Specifically, at the end of the incremental time allocation process, the last
chosen destination can potentially be allocated less than required minimum amount of time simply because
there is not enough time left. Thus, the model does not completely preclude destination choices with less
than required amounts of time allocated. However, it should help significantly reduce such unrealistic time
allocations.
33
 −1
 tk* − t0 
=ψ k  + 1 if tk* ≥ t0 .
 γk 

Next, without any loss of generality, designating alternative 1 as a vacation destination to

which the household allocates some non-zero amount of time and following the steps in

chapter 3.1, the above KT conditions can be rewritten as:

Vk + ε k = V1 + ε1 if tk* > 0 (k = 1, 2, …, K)

Vk + ε k < V1 + ε1 if tk* = 0 (k = 1, 2, …, K), (10)

where, Vk = β ' zk if tk* ≤ t0 ,

 t* − t 
= β ' zk − ln  k 0 + 1  if tk* ≥ t0 .
 γk 

Assuming that the error terms ε k (k = 1,2,…,K) are IID type 1 extreme value

distributed, the probability that the household allocates vacation time to the first M of the

* * * th
K destinations (for duration t1 in the first alternative, t2 in the second, … tM in the M

alternative) is:

 M 
 ∏ eVi 
 M
  M
1 
P(t1* , t 2* , t 3* ,...t M* ,0,0,0..0) = ∏ ci   ∑   i =1 M  ( M − 1)! (11)
 i =1   i =1 ci    K Vk  
∑e  
  k =1  

The Vk terms in the above equation take an expression β ' zk for all non-chosen

destinations (i.e., alternatives for which zero time is allocated), and the expression

34
  tk* − t0 
β ' zk − ln  + 1  for all chosen destinations. The ck terms for all k = 1,2,…,M take
 γk 

 1  13
an expression   .
 (ti − t0 ) + γ i 
*

The above probability expression can be used to form the likelihood and use the

familiar maximum likelihood estimation method to estimate the parameter vectors β and

θ . In this paper, the model estimation was performed using a maximum likelihood
estimation code written in the GAUSS mathematical system version 9.0 (Aptech

Systems, 2008).

A few notes before we move to the empirical analysis. First, we do not estimate

the minimum amount of vacation time t0 allocated to a chosen destination, but assume it

apriori as half a day. Limited experiments to estimate t0 with the current and other

cross-sectional datasets indicate that it is unnecessary to estimate t0 . One could simply

constrain t0 as the minimum time allocated to the chosen alternatives in the data.14

Second, the concept of minimum required consumption is not new to the consumer

demand analysis literature. For example, Pollak and Wales (1992, pp. 3) discus a linear

expenditure system (LES): U (Y ) = ∑ k

ak ln ( yk − bk ), in which the consumption

quantities yk must always be greater than a minimum amount bk . Note that their LES

utility function is not defined for consumption quantities below bk . The indifference

13
The reader will note the minor differences between the terms used in the above probability expression
(i.e., Vk and ck ) and the terms ( Vk and ck ) in the probability expression for the original MDCEV model in
Equation (6).
14
We assume half a day as the minimum required amount of time for any chosen vacation destination.
However, this is not to assert that no household ever allocates less than 0.5 days of time to visiting a long-
distance destination. By specifying a certain minimum required consumption, we are building a model
framework that can reduce the likelihood of unrealistically small consumptions (or time allocations).
35
curves implied by such an LES system are asymptotic to the consumption axes at bk ,

avoiding consumptions below bk (Pollak and Wales 1992, pp. 7). In this context, Deaton

and Muellbauer (1981, pp. 65) interpret bk as subsistence quantities or minimum

required quantities that are consumed first. It is important to note, however, that the

subsistence quantities discussed by them were in the context of only numeraire outside

goods that are always consumed. On the other hand, our discussion is for a general

case that includes inside goods that may not be consumed by some consumers (in fact,

our empirical context does not have an outside good). If a good is consumed, we are

able to accommodate a minimum required amount of its consumption. Besides, instead

of specifying undefined utility functions for consumptions below a subsistence amount,

we provide a basis for why a minimum amount is consumed by employing a combined

linear – non-linear utility functional form that avoids immediate satiation effects at the

corners. Third, although the proposed variant of the MDCEV model attempts to

accommodate a minimum required consumption of the chosen goods, the model does

not necessarily provide integer outputs for the consumptions. Vacation time is still

treated as a continuous entity. However, the concept we propose here can potentially be

extended to incorporate integer outputs from the utility maximization problem.

Specifically, instead of combining a linear utility piece at the corner with a subsequent

non-linear utility form, one can combine several linear utility pieces to form a piece-wise

linear, convex utility function that provides count data outcomes from the consumers’

utility maximization problem. This extension is beyond the scope of this thesis, but an

important topic for further exploration.

36
 Chapter 4: Data

4.1 1995 American Travel Survey

The 1995 American Travel Survey (ATS) is the primary source of data used in this

analysis. The 1995 ATS collected information from 62,609 American households on all

long-distance trips of 100 miles of more over the course of an entire year (BTS, 1995).

Admittedly, the data is a bit old. However, no other recent dataset exists with information

on one year worth of long-distance travel in the U.S. A similar long-distance survey was

conducted along with the 2001 National Household Travel Survey (NHTS). However, the

2001 NHTS elicits long-distance travel information over the period of only four weeks.

4.1.1 Data set preparation

The first step was to recode certain continuous variables into categorical variables

for ease of interpretation. The chosen categories are based on previous literature and

intuition. Income was re-coded into the same high (greater than $75,000), middle

($30,000 to $75,000), and low (less than $30,000) categories used by LaMondia and

Bhat (2008). Round trip distance traveled for each trip was also recoded into several

categories including: 100 to 500 miles, 501 to 1,000 miles, 1,001 to 2,000 miles, 2,001 to

4,500 miles, and greater than 4,500 miles. These categories were selected based on the

paper by LaMondia and Bhat (2008) which also utilized the 1995 ATS to study long

distance leisure travel. Age was divided into five groups; under 15, 15 to 24, 25 to 44, 45

to 64, and over 64. These age ranges were selected to match the U.S. 2000 Census.

Transportation mode and primary purpose for the trip have been re-coded into more

generalized, easier to interpret categories using similar methodology as that used by Hu

and Young (2001) although with some modification to the trip purpose. Tables 5 and 6
37
below indicates the methods used. By dividing these variables into more aggregated

groups, the values can provide greater meaning to the reader.

Table 5: Reclassification of modes from 1995 ATS

New Mode 1995 American Travel Survey Mode
Private ground Car, pickup truck, or van
Other truck
Rental car, truck, or van
Recreational vehicle or motor home
Motorcycle, moped, or motor bicycle
Commercial Air Commercial Airplane
Other City to City Bus
Charter bus or tour bus
School bus
Train
Taxi
Ship or boat
Cruise ship
Passenger line or ferry
Recreational boat, sailboat, pleasure boat,
or yacht
Bicycle
Other

38
 Table 6: Recoding methodology for trip purpose and transportation
Purpose Transportation
Business POV
Business Car, pickup truck, or van
Convention, seminar, or conference Other truck
Combined Business and Pleasure Rental car, truck, or van
Combined Business and Pleasure Recreational vehicle
Shopping Motorcycle
Shopping Airplane
School-related Commercial airplane
School-related Bus
Personal, family, or medical City to City bus
Personal, family, or medical Intercity Rail
Visit relatives or friends Intercity train
Visit relatives or friends School bus
Leisure School bus
Rest or relaxation Other
Sightseeing, or to visit a historic or scenic
Corporate/personal airplane
attraction
Outdoor recreation Charter bus or tour bus
Entertainment Ship or boat
Change trans/Spend Night/Passenger Cruise Ship
Spend the night Passenger line or ferry
Transfer from one airplane to another Recreational boat, sailboat, or yacht
Change to a different type of transportation Taxi
Drop off or pick up a passenger Bicycle
Other Other
Other

4.1.2 Leisure subset selection

Out of all the surveyed households in the 1995 ATS sample, 48,527 reported at least

one long-distance trip15. As such, a total of 337,520 trips were reported, along with the

information on the purpose, mode, and destination of travel and other travel attributes.

The scope of analysis of the current thesis consists of long distance

leisure/vacation travel within the United States. Therefore, only households that made at

least one long-distance trip for the purpose of relaxation, sightseeing, outdoor recreation,

or entertainment were considered. Trips for visiting friends and family were not

15
The reader will note here that in this survey a trip is defined as a travel out of home that eventually
returns home (which is usually called a tour in traditional metropolitan area travel modeling context).
39
considered in this study. This is because the factors that underlie the destination choice

decisions for this type of trips are quite different from the trips for other purposes.

Specifically, the primary determinants of a household’s destination choices for visiting

purpose may be the location of family and friends (i.e., social networks), rather than the

destination characteristics themselves. Unfortunately, the data does not contain any

social networks information.

Of the 337,520 trips reported in the 1995 ATS, 25% were for leisure purposes

(i.e., relaxation, sightseeing, outdoor recreation, or entertainment) made by 28,210

households. From these households, a small percentage of those who traveled to

destinations outside the United States were removed for the purpose of the current study

(3.5% of all leisure trips were made to international destinations).16 Next, only

households that used private ground (i.e., auto) and commercial air modes of travel were

considered (this was approximately 94% of the data as seen in Table 7). While it is

desirable to include these other households as well (especially those that use the inter-

city bus and rail modes and water modes), it was very difficult to gather the

transportation network and level of service characteristics for these modes for the year

1995. For this same reason, Hawaii was excluded as a destination (or origin). Thus, the

analysis is limited to the contiguous states of the U.S. After further processing to clean

households with missing information on important variables (income, travel information

for a big chunk of the year), the dataset was still sizeable with 22,215 households that

made 57,989 long-distance leisure trips. 6000 of these households were randomly

sampled to estimate the destination choice MDCEV model, while another 715 (again

randomly sampled) were kept for validation purposes.

16
Considering international destinations adds a layer of complexity to the model in terms of increasing the
number of alternative destinations in the choice set. Besides, the data does not contain information on
which country the trip was made to.
40
 Table 7: Primary mode used for long distance leisure travel - 1995 ATS
Frequency Percentage
Private ground 55,606 83.8%
Commercial air 6,704 10.1%
Other 4,014 6.1%
Total 66,324 100.0%

4.1.3 Destination alternatives

For the current analysis, the United States was divided into 210 alterative destinations.

Specifically, each of the Metropolitan Statistical Areas (MSAs) from each state was

counted as a destination alternative, resulting in 162 MSA destinations. Then, the

remaining non-MSA area in each state was counted as a single destination (one non-

MSA area for each state, with the exception of Rhode Island which was entirely included

in the Falls River-Warwick MSA). This resulted in 48 non-MSA destinations. All together,

the U.S. was divided into 210 destinations (162 MSAs plus 48 non-MSAs). While it is

desirable to divide the non-MSAs into smaller and more meaningful geographies, the

destinations reported in the data did not provide any further information other than MSAs

or non-MSAs. The labels of the destinations are provided in Table 8 below.

41
 Table 8: Destination alternatives
Origin Origin
Origin MSA Origin MSA
State State
AL Birmingham, AL MSA CT Connecticut - Not in MSA
AL Huntsville, AL MSA DE Wilmington, DE PMSA
AL Mobile, AL MSA DE Delaware - Not in MSA
AL Montgomery, AL MSA DC Washington, DC-MD-Va PMSA
AL Alabama - Not in MSA FL Daytona Beach, FL MSA
AK Anchorage, AK MSA FL Fort Lauderdale, FL PMSA
AK Alaska - Not in MSA FL Fort Myers-Cape Coral, FL MSA
AZ Phoenix-Mesa, AZ MSA FL Jacksonville, FL MSA
AZ Tucson, AZ MSA FL Lakeland-Winter Haven, FL MSA
Melbourne-Titusville-Palm Bay, FL
AZ Arizona - Not in MSA FL MSA
AR Little Rock-North Little Rock, AR MSA FL Miami, FL PMSA
AR Arkansas - Not in MSA FL Orlando, FL MSA
CA Bakersfield, CA MSA FL Pensacola, FL MSA
CA Fresno, CA MSA FL Sarasota-Bradenton, FL MSA
CA Los Angeles-Long Beach, CA PMSA FL Tallahassee, FL MSA
Tampa-St. Petersburg-Clearwater,
CA Modesto, CA MSA FL FL MSA
West Palm Beach-Boca Raton, FL
CA Oakland, CA PMSA FL MSA
CA Orange County, CA PMSA FL Florida - Not in MSA
CA Riverside-San Bernardino, CA PMSA GA Atlanta, GA MSA
CA Sacremento, CA PMSA GA Augusta, GA MSA
CA Salinas, CA MSA GA Macon, GA MSA
CA San Diego, CA MSA GA Georgia - Not in MSA
CA San Francisco, CA PMSA ID Boise City, ID MSA
CA San Jose, CA PMSA ID Idaho - Not in MSA
Santa Barbara-Santa Maria-Lompoc,
CA CA MSA
IL Chicago, IL PMSA

CA Santa Rosa, CA PMSA IL Peoria-Pekin, IL MSA

CA Stockton-Lodi, CA MSA IL Rockford, IL MSA
CA Vallejo-Fairfield-Napa, CA PMSA IL St. Louis, MO-IL MSA
CA Ventura, CA PMSA IL Illinois - Not in MSA
CA California - Not in MSA IN Fort Wayne, IN MSA
CO Boulder-Longmont, CO PMSA IN Gary, IN PMSA
CO Colorado, CO MSA IN Indianapolis, In MSA
CO Denver, CO PMSA IN South Bend, IN MSA
CO Colorado - Not in MSA IN Indiana - Not in MSA
CT Bridgeport, CT PMSA IA Des Moines, IA MSA
CT Hartford, CT MSA IA Iowa - Not in MSA
CT New Haven-Meriden, CT PMSA KS Wichita, KS MSA
CT New London-Norwich, CT MSA KS Kansas - Not in MSA
CT Stamford-Norwalk, CT PMSA KY Lexington, KY MSA

42
 Table 8: (continued)
Origin Origin
Origin MSA Origin MSA
State State
Middlesex-Somerset-Hunterdon, NJ
KY Louisville, KY MSA NJ PMSA
KY Kentucky - Not in MSA NJ Monmouth-Ocean, NJ PMSA
LA Baton Rouge, LA MSA NJ Newark, NJ PMSA
LA New Orleans, LA MSA NJ Trenton, NJ PMSA
LA Shreveport-Bossier City, LA MSA NJ New Jersey - Not in MSA
LA Louisiana - Not in MSA NM Albuquerque, NM MSA
ME Maine - Not in MSA NM New Mexico - Not in MSA
MD Baltimore, MD PMSA NY Albany-Schenectady-Troy, NY MSA
MD Maryland - Not in MSA NY Binghamton, NY MSA
MA Boston, MA PMSA NY Buffalo-Niagara Falls, NY MSA
MA Lowell, MA PMSA NY Dutchess County, NY PMSA
MA Springfield, MA MSA NY Nassau-Suffolk, NY PMSA
MA Worcester, MA PMSA NY New York, NY PMSA
MA Massachusetts - Not in MSA NY Newburgh, NY PMSA
MI Ann Arbor, MI PMSA NY Rochester, NY MSA
MI Detroit, MI PMSA NY Syracuse, NY MSA
MI Flint, MI PMSA NY Utica-Rome, NY MSA
Grand Rapids-Muskegon-Holland,
MI MI MSA
NY New York - Not in MSA

MI Kalamazoo-Battle Creek, MI MSA NC Charlotte-Gastonia, NC MSA

MI Lansing-East Lansing, MI MSA NC Fayetteville, NC MSA
Greenboro-Winston-Salem-High Point,
MI Saginaw-Midland, MI MSA NC NC MSA
MI Michigan - Not in MSA NC Hickory-Morganton, NC MSA
MN Minneapolis-St. Paul, MN MSA NC Raleigh-Durham-Chapel Hill, NC MSA
MN Minnesota - Not in MSA NC North Carolina - Not in MSA
MS Jackson, MS MSA ND North Dakota - Not in MSA
MS Mississippi - Not in MSA OH Akron, OH PMSA
MO Kansas City, MO-KS MSA OH Conton-Massillon, OH MSA
MO Springfield, MO MSA OH Cincinnati, OH-KY PMSA
MO Missouri - Not in MSA OH Cleveland-Lorain-Elyria, OH PMSA
MT Montana - Not in MSA OH Columbus, OH MSA
NE Omaha, NE MSA OH Dayton-Springfield, OH MSA
NE Nebraska - Not in MSA OH Hamilton-Middletown, OH PMSA
NV Las Vegas, NV MSA OH Toldeo, OH MSA
NV Reno, NV MSA OH Youngstown-Warren, OH MSA
NV Nevada - Not in MSA OH Ohio - Not in MSA
NH New Hampshire - Not in MSA OK Oklahoma City, OK MSA
NJ Atlantic-Cape May, NJ PMSA OK Tulsa, OK MSA
NJ Bergen-Passaic, NJ PMSA OK Oklahoma - Not in MSA
NJ Jersey City, NJ PMSA OR Eugene-Springfield, OR MSA

43
 Table 8: (continued)
Origin Origin
Origin MSA Origin MSA
State State
OR Portland-Vancouver, OR-WA PMSA TX Beaumont-Port Arthur, TX MSA
OR Salem, OR PMSA TX Corpus Christi, TX MSA
OR Oregon - Not in MSA TX Dallas, TX PMSA
Allentown-Bethlehem-Easton, PA
PA MSA
TX El Paso, TX MSA
PA Erie, PA MSA TX Fort Worth-Arlington, TX PMSA
PA Harrisburg-Carlisle, PA MSA TX Houston, TX PMSA
PA Lancaster, PA MSA TX Mcallen-Edinburg-Mission, TX MSA
PA Philadelphia, PA-NJ PMSA TX San Antonio, TX MSA
PA Pittsburgh, PA MSA TX Texas - Not in MSA
PA Reading, PA MSA UT Provo-Orem, UT MSA
Scranton-Wilkes Barre-Hazleton, PA
PA MSA
UT Salt Lake City-Ogden, UT MSA
PA York, PA MSA UT Utah - Not in MSA
PA Pennsylvania - Not in MSA VT Vermont - Not in MSA
Providence-Fall River-Warwick, RI Norfolk-Virginia Beach-Newport News,
RI MSA
VA VA MSA
RI Rhode Island - Not in MSA VA Richmond, VA MSA
Charleston-North Charleston, SC
SC MSA
VA Virginia - Not in MSA

SC Columbia, SC MSA WA Seattle-Bellevue-Everett, WA PMSA

SC Greenville-Spartanburg, SC MSA WA Spokane, WA MSA
SC South Carolina - Not in MSA WA Tacoma, WA PMSA
SD South Dakota - Not in MSA WA Washington - Not in MSA
TN Chattonooga, TN MSA WV Charleston, WV MSA
Johnson City-Kingsport-Bristol, TN
TN MSA
WV West Virginia - Not in MSA
TN Knoxville, TN MSA WI Appleton-Oshkosh-Neenah, WI MSA
TN Memphis, TN MSA WI Madison, WI MSA
TN Nashville, TN MSA WI Milwaukee-Waukesha, WI PMSA
TN Tennessee - Not in MSA WI Wisconsin - Not in MSA
TX Austin-San Marcos, TX MSA WY Wyoming - Not in MSA

44
4.2 Secondary data sources

4.2.1 Level of service variables

In addition to the data provided by the 1995 American Travel Survey (ATS), several

secondary data sources were utilized to compile other required information such as: (1)

the level of service variables, included as travel times and costs between each origin-

destination pair via air and auto modes, (2) destination size and attraction variables for

the year 1995, including land area, number of employees in different sectors (leisure

and/or hospitality, retail, etc.), total population, total gross domestic product, and gross

domestic product for amusement and recreation, and (3) destination climate variables

including mean monthly temperatures for different months in a year, miles of coastline at

the destination, and the annual number of freezing days experienced at the destination.

Gathering all this information required a significant amount of effort from multiple data

sources.

Ground travel times and costs were derived as a function of ground route

distances between each metropolitan statistical area (MSA) or non-MSA area. It is

assumed that route distances would not significantly change in the context of long-

distance travel between 1995 and 2010. Microsoft MapPoint 2010 software, in

conjunction with its Mile Charter add-on, was used to plot route distances between each

origin-destination pair (Microsoft, 2009; Winwaed Software Technology, 2009). The Mile

Charter add-on provides both the route distance, and travel times between all origins

and destinations in a simple matrix format. Some additional work was required to

aggregate origins and destinations from the city level, to the metropolitan statistical area

(MSA). When an MSA is made up of more than one city, the average distance between

each city to all possible destinations is taken. A similar methodology applies to a

destination MSA comprised of more than one city. For example, take MSA X as being

45
comprised of two cities, City 1 and City 2, while MSA Y is comprised of two cities, City 3

and City 4. The route distance between these cities is the average of the distance

between City1 and Cities 3 and 4 and City2 and Cities 3 and 4. It is not known from the

data which city within the MSA is the origin or destination so this provides the closest

proxy. When considering non-MSA areas, the level of service variables are more difficult

to derive. For MSA to non-MSA travel (or vice versa), the non-MSA area is taken as the

centroid of the state. The exception to this rule is the case where the origin and

destination are within the same state, in which case, the average travel distance

between the MSA area and the opposite borders of the state are used. When both the

origin and destination are non-MSA areas, the averages of all MSA to MSA routes within

that state are taken. This applies to both same state and different state combinations.

For some of these non-MSA to non-MSA cases, this is not possible as there is 1 or

fewer MSA areas within the state as defined by the 1995 ATS. In these cases, the route

distances and travel times are taken as those between a city near the border and a

centrally located city as shown in Table 9. While these distances, especially for non-

MSA areas, are not perfectly accurate, they do provide a reasonable assumption of

travel distance.

Table 9: Non-MSA to non-MSA area proxies for select states

State Origin city Destination city
Alaska Fairbanks Anchorage
Maine Dover-Foxcroft Portland
Montana Hobson Libby
New Hampshire Concord Gorham
North Dakota Underwood Marmarth
South Dakota Fort Pierre Sioux Falls
Vermont Morrisville Bennington
Wyoming Casper Jackson

Travel costs were derived as a function of travel distance, and average vehicle

miles per gallon. Lim (1997) found that private gasoline costs between origin and

46
destination are often used as a proxy for surface travel in tourism demand models. While

the cost of the vehicle, insurance, and maintenance are all a part of the trip, these costs

are paid separately from the cost of the trip and likely would not be considered. The

average vehicle fuel efficiency in 1996 was 19.7 miles per gallon (Grush, 1998).The cost

of gas is taken from the Energy Information Administration which provides gas prices for

1995 by region within the United States (Energy Information Administration, 1995). It is

assumed that while gas prices do vary by geographic area, they would not vary as much

within each region. To find the gas price paid by the traveler, an average gas price

between the origin region and the destination region was taken.

Air fare and air travel times were both taken from the Airline Origin and

Destination Survey (DB1B) provided through Transtats from the Research and

Innovation Technology Administration (RITA) at the USDOT (BTS, 1995). Due to smaller

sample sizes for lesser traveled routes the years 1994, 1995, and 1996 were used to

expand the sample size. The DB1B survey is comprised of three main data sources: the

market, itinerary, and coupon data sets. The two data sets used for this thesis are the

market and coupon surveys. The market survey provides market fare, market distance

traveled (actual distance traveled), nonstop miles (GCD distance traveled), and the

airport group (airport codes of all airports within the itinerary including origin and

destination).The coupon survey provided the fare class (coach, business, etc.) for each

ticket. To eliminate any fares that only cover tax, but not the base fare, all fares less than

fifty dollars were eliminated (National Transportation Library, 2010). Secondly, all first

class/business fares were eliminated. This was done to reduce the variance amongst

traveler costs and since the majority of travelers typically travel coach class it was

considered reasonable. The average cruising speed of a Boeing 757 (500 miles per

hour) was taken as the average air speed (Boeing, 2011).

47
 Four “ODPAIR” variables were created as a concatenation of the origin and

destination using SPSS within the DB1B survey. Table 10 provides the methodology

used to create each “ODPAIR” variable. These variables were created to mimic the

methodology used for finding ground distance for between destinations.

Table 10: Origin-destination pair variables created from DB1B survey

Variable O-D Pair Type Origin Destination
ODPAIR1 MSA to MSA airport code airport code
ODPAIR2 non-MSA to MSA state code airport code
ODPAIR3 MSA to non-MSA airport code state code
ODPAIR4 Non-MSA to non-MSA state code state code

In addition to the “ODPAIR” variables, a variable indicating the number of

layovers was created for each case. The airport group variable consists of each airport

code for the trip, including the origin and destination, each separated by a colon. Since

each airport code is three characters long, the number of characters in this variable is

directly related to the number of layovers. SPSS provides a function to compute the

length of a given variable and so a new variable called “layovers” was created based on

the character length of the airport group variable. For example, if the airport group

variable was seven, then there were no layovers. For every four characters beyond the

first seven there was one additional layover (airport code plus colon). The aggregate

function in SPSS using each of the “ODPAIR” variables as the break variable was used

to find the mean market fare, mean market distance, mean nonstop distance, and mean

layovers.

Each airport code is associated with one or more MSAs using the Places Rated

Almanac (Savageau and Loftus, 1997). Each state code is used as a proxy for the given

state as an origin or destination and accounts for all airports within the given state. The

only state with no airports identified in the DB1B for the 1994, 1995, and 1996 years was

Delaware. It was decided that Philadelphia International Airport (PHL) should be used as

48
this is the airport assigned to both Wilmington and Dover, the two MSA areas identified

in the Places Rated Almanac (Savageau and Loftus, 1997). Several MSAs are served by

multiple airports. This was dealt with in a similar manner to the ground distance and

travel times. The average of all possible connections was taken and used a proxy for the

given origin-destination pair.

The actual cost associated with commercial air travel is a function of both the

ticket prices, and the party size. Unlike the private car where the marginal cost of

another passenger can be considered negligible, the cost increases by the amount of an

individual’s airfare for each additional party member. In an exploratory analysis of the

1995 ATS, it was found that party size varies for only 10 percent of household trips to a

given destination. For these cases in which party size does vary, the variation is typically

quite low, with the difference typically being within one or two people. To avoid the issue

of determining the party size for all potential trips, the average party size was taken for

each household and used to compute air costs in the destination choice model.

4.2.2 Destination attraction variables

Data for several indices for the attractiveness of a destination were selected.

These include the number of leisure and/or hospitality employees, the number of retail

employees, the number of total non-farm employees, the total population, land area,

gross domestic product (including individual industries), miles of coastline, mean

monthly temperature, number of freezing days per annum.

State and local employment levels were taken from the Bureau of Labor

Statistics (BLS) (Bureau of Labor Statistics, 1995). The number of employees within

each industry in a given metropolitan statistical area (MSA) was taken as the sum of all

cities within the MSA. Statewide totals of employment, less the number of employees for

each MSA within the given state, were used for non-MSA areas. The statewide

49
employment data for Rhode Island is taken as zero since the Providence MSA covers

the entire state. In some cases, more than one value is given for a large MSA. In these

cases, the metropolitan division was used as it does not overlap with adjacent, but

separate, MSAs. Five MSAs cross state borders including Philadelphia, PA-NJ, Kansas

City, MO-KS, St. Louis MO-IL, Portland OR-WA, and Providence-Fall River-Warwick, RI-

MA. With the exception of Kansas City, the majority of the MSA falls within a single state

and so the MSA was assumed to fall completely within that state. The employment

values for Kansas City were provided separately for Kansas and Missouri. In a few rare

cases, the definition of an individual MSA was different from those defined in the 1995

ATS. Bridgeport, CT and Stamford-Norwalk, CT are considered as one MSA and so the

same employment totals were used for both. Cincinnati, OH and Hamilton-Middletown

are also considered as one MSA and so the same employment totals were used in this

case as well. In each of these cases, the employment totals were only subtracted from

the statewide totals once.

Population and land areas for each MSA and non-MSA area were taken from the

2000 Census (U.S. Census Bureau, 2000). In addition to employment within key leisure

related industries, the gross domestic product at the state level for all industries,

amusement and recreation services, and hotels and other services was taken from the

Bureau of Economic Analysis (Bureau of Economic Analysis, 1995) of the U.S.

Department of Commerce.

Miles of coastline and several climate variables were also included in the

destination attraction data set. The total miles of coastline, including the Great Lakes,

was taken from the National Oceanic and Atmospheric Administration’s Ocean and

Coastal Resource Management (NOAA, 2011). Information on the mean monthly

temperatures for both January and June and the total number of freezing days was

50
obtained from the Places Rated Almanac (Savageau and Loftus, 1997) for the year 1995

for all MSA areas. The same information for non-MSA areas was considered as the

average values of the MSA areas within the state (Savageau and Loftus, 1997).

4.3 1995 ATS leisure subset data description

4.3.1 Household demographics

Table 11 provides an overview of the socio-demographic makeup and the leisure travel

characteristics of all households surveyed within the 1995 ATS, the 1995 ATS leisure

subset (the subset of households who made at least one leisure trip, obtained after the

cleaning process explained in the “Primary Data Source” section), and a random sample

of 6,000 households from the leisure subset utilized for the destination choice model

estimation. There are a total of 62,609 households in the 1995 ATS, 22,215 households

within the leisure subset, and 6,000 households were sampled from the leisure subset

for the destination choice model estimation.

The average age of households in the 1995 ATS is 50, and drops to

approximately 46 in the leisure subset and the estimation sample. The elderly (65 or

older) are less represented in the leisure datasets; suggesting that the elderly are less

likely to take long-distance leisure trips. In terms of annual income, households who

made leisure trips appear to be slightly more affluent than the general ATS sample. This

makes intuitive sense as long-distance leisure travel can be considered as a luxury

which those with very low incomes are unlikely to be able to afford. Two person

households account for the highest proportion of household size in the data. Both the

leisure subset and the estimation sample tend to have somewhat larger households than

the overall 1995 ATS sample. There may be several reasons for this, including the

presence of children, for whom a household may tend to make leisure trips. The majority

of households within the leisure subset are married, accounting for nearly 70 percent of

51
the sample. Approximately half of these married couples have children, which likely has

some impact on the leisure travel pattern and destination choices.

Table 11: Household demographics and leisure travel characteristics in 1995 ATS
1995 Leisure Model estimation
Household Characteristics
ATS Subset* Sample
Sample size 62,609 22,215 6,000
Age of householder 50.4 46.4 46.7
15 to 24 4.1% 4.5% 3.9%
25 to 44 38.2% 45.4% 45.4%
45 to 64 33.3% 35.9% 36.0%
65 or older 24.4% 14.2% 14.7%
Household yearly income
Under $30,000 33.1% 27.1% 26.1%
$30,000 to $74,999 57.4% 60.2% 60.7%
$75,000 or more 9.5% 12.7% 13.2%
Household size
1 24.1% 15.5% 15.7%
2 34.5% 34.3% 34.7%
3 16.5% 18.8% 18.5%
4 or more 24.9% 31.4% 31.1%
Household type
Married couple family – with children under 18 25.3% 33.5% 32.9%
Married couple family – no children 33.7% 35.2% 35.4%
Other family – with children under 18 5.8% 5.4% 5.2%
Other family – no children 6.6% 5.2% 5.3%
Non family – not living alone 4.4% 5.2% 5.6%
Non family – living alone 24.2% 15.5% 15.8%
1995 Leisure Model estimation
Household Leisure Travel Characteristics
ATS Subset* Sample
Number of long distance leisure trips --- 2.61 2.64
1 --- 47.9% 46.9%
2 --- 21.3% 22.0%
3 --- 11.6% 11.7%
4 --- 6.5% 7.3%
5 or more --- 12.7% 12.1%
Number of destinations visited --- --- ---
1 --- 60.7% 60.1%
2 --- 24.3% 25.1%
3 --- 9.6% 9.3%
4 --- 3.3% 3.5%
5 or more --- 2.1% 2.0%
Number of trips made to a destination** --- --- ---
1 --- 78.3% 78.5%
2 --- 11.5% 10.9%
3 --- 4.2% 4.7%
4 --- 2.0% 1.9%
5 or more --- 4.0% 4.0%
*Leisure subset: Subset of households who made at least one leisure trip in the year.
**These proportions are of all destinations visited by each household.

52
 The next set of rows provides an overview of the leisure travel characteristics of

those households who made at least one leisure trip in the year. Several observations

can be made from the leisure subset column. First, on average, these households (who

made at least one leisure trip) made 2.61 leisure trips per year, with 52.1% making more

than one trip per year. Second, close to 40% of these households visited more than one

destination. Third, 78.3% of the households visit a destination (if they do so) only once.

That is, several households are likely to visit multiple destinations per year, but less

likely to re-visit a destination. This suggests multiple discreteness (choosing multiple

destinations) and variety-seeking behavior in households’ destination choices. As

discussed earlier, the multiple discreteness or variety in households’ leisure destination

choices comes from several reasons, including the satiation effects of increasing time

allocation to one destination, and the presence of different persons with a variety of

preferences in the household. Similar inferences can be made from the model estimation

households’ sample as well (the last column in the data).

Traditional discrete choice models assume that the destination choice

alternatives are perfect substitutes of each other. Thus, it is difficult to use the framework

for the current situation with multiple destination choices. This is not to say that one

cannot use discrete choice models for the current situation (e.g., a repeated discrete

choice framework can be used; see Herriges and Phaneuf, 2002). However, it is

cumbersome to do so. Further, such approaches are not based on a unifying utility

maximizing framework. The multiple discrete-continuous extreme value (MDCEV) model

(Bhat, 2005; Bhat, 2008) on the other hand, is based on a unifying utility maximizing

framework for modeling multiple discreteness. Given the total number of days per year a

household allocates to vacation, the analyst can use the MDCEV model to

simultaneously analyze all the destinations visited by the household in a year, and the

53
time allocations to each destination. In addition, the model accommodates satiation

effects (hence variety seeking) through a non-linear utility framework (Kim et al., 2002),

and recognizes that households operate under time budgets via a constrained utility

maximization framework.

4.3.2 Household trips

Table 12 provides an overview of the trip level characteristics of the 1995 ATS data for

the entire data, for the trips made by the leisure subset, and for the trips made by the

households n the estimation sample). The ATS contains records for 337,520 household

trips, of which 57,889 were leisure trips made by households in the leisure subset and

15,826 by the 6,000 household model estimation sample. The vast majority of all trips

made in the 1995 ATS utilize either private ground modes, or commercial air modes,

accounting for 96.1 percent of all trips. It is for this reason that the scope of this thesis is

confined to these two dominant modes of transportation. In both the leisure subset and

model estimation sample, approximately 90 percent of trips are made using private

ground modes and approximately 10 percent are made using commercial air modes of

transportation. In terms of trip distance, the majority of leisure trips are less than 500

miles, with the proportions of trips declining as distance increases. This makes intuitive

sense as longer distances typically equate to higher costs and travel times. The average

number of nights (away from home) spent on each vacation trip is 3.29 for the 1995

ATS, increasing slightly to 3.39 for leisure trips. Just under one-quarter of leisure trips

are day trips, which do not involve spending a night away from home. The highest

proportion of nights spent at the destination is two with a greater share of trips relative to

any other number of nights spent away. While additional nights spent at the destination

would increase the cost of the trip, travelers may also be less likely to spend too little

time at a destination due to the already expended time and cost involved with traveling.

54
For the current analysis and modeling purposes, the number of nights variable was

effectively considered as the number of days (away from home) spent on the trip. For all

day trips, it was considered that half a day was spent on the trip. For each household,

the sum of all the days spent across all the visited destinations was considered as the

annual household long-distance vacation time budget, T. This annual long-distance

vacation time budget varied from 0.5 (i.e., a single day trip) to as much as 352.50 days,

with an average value of 9.11 days in the leisure subset data (and similar values in the

model estimation data).

Table 12: Leisure trip characteristics in 1995 ATS

Model
Leisure
Characteristic 1995 ATS Estimation
Subset
Sample
Sample size 337,520 57,989 15,826
Primary mode of transportation --- --- ---
Private ground 76.8% 89.3% 89.5%
Commercial air 19.3% 10.7% 10.5%
Other 3.9% --- ---
Round trip U.S. route distance
848.25 780.13 770.86
(miles)
International Destination 3.5% --- ---
100 to 500 miles 57.2% 59.9% 61.1%
501 to 1,000 miles 18.8% 20.6% 19.9%
1,001 to 2,000 miles 10.6% 10.1% 9.6%
2,001 to 4,500 miles 7.5% 8.0% 7.9%
Over 4,500 miles 2.4% 1.5% 1.5%
No. of nights away from home on
3.29 3.39 3.39
trip*
0 (day trip) 27.6% 21.0% 21.3%
1 15.7% 14.8% 16.1%
2 20.2% 24.2% 23.2%
3 11.0% 12.6% 12.4%
4 7.7% 8.4% 8.0%
5 4.1% 4.1% 4.3%
6 2.5% 3.2% 3.2%
7 3.1% 4.4% 4.2%
8 1.3% 1.5% 1.6%
9 0.9% 1.2% 1.0%
10 or more 5.9% 4.6% 4.6%
* For current analysis, the number of nights variable was effectively considered as the number of days (away
from home) spent on the trip. For day trips, it was assumed that half a day (0.5 days) was spent on the trip.

55
 Finally, we conducted an exploratory analysis of the mode choices for long-

distance leisure trips in the data (not shown in the Tables). Specifically, we explored if

households changed their mode choices across the different destinations they visited, as

well as across the different trips they made to a single destination. The analysis

indicates, as expected, that households did change their mode choices across the

different destinations they visited. That is, a household’s mode choices may vary across

the different destinations they visit, depending on the transportation level of service

characteristics to the destinations by different modes (and household characteristics).

However, if households visited a destination more than once a year, a vast majority of

the times (99.5% of the times) the same mode was used to travel across all the different

trips made to that same destination. This suggests that long-distance leisure trip mode

choices depend primarily on the destination choices, and exhibit little variation (or

multiple-discreteness) across the different trips made to the same destination. Taking

advantage of this finding, we estimated a traditional discrete mode choice model with

data on all leisure destinations visited by the households (i.e., 36,263 destinations visited

by 22,215 households). This auxiliary mode choice model was used to construct the log-

sum variable to be fed into the destination choice MDCEV model as a composite

impedance measure that considers the travel times and costs by both air and auto

modes.

56
 Chapter 5: Results and Discussion

This section presents and discusses the model estimation results. First the auxiliary

mode choice model results are discussed (Section 5.1), and then the main destination

choice MDCEV model results are discussed (Section 5.2).

5.1 Auxiliary mode choice model specification

The results of the auxiliary mode choice estimation are provided in Table 13. The binary

choice (for choice between air and auto modes) includes an alternative specific constant,

household income categories, travel cost and travel time variables (between household

residential locations and their visited destinations) by alternative modes, and dummy

variables for origin or destination being an MSA. The first, income variable effects

indicate, as expected, that higher income households are more likely to travel via the air

mode while lower income households are least likely to do so. The next variable is the

travel cost variable, computed as the cost of travel for all persons in the travel party.

Several specifications were explored on the travel cost variable, including a simple linear

form, Box-Cox transformation (Mandel et al., 1997; Gaudry, 2002), logarithmic

transformation (Gunn, 2001), and a piece-wise linear specification (Pinjari and Bhat,

2006). The linear specification provided the worst model data fit, while all non-linear

specifications improved the model fit and suggested a dampening trend in the sensitivity

to costs (i.e., a decrease in the marginal disutility cost as costs increased). This trend is

widely noted in the long-distance travel literature (see, for example, Daly 2008). Box-Cox

transformation improved the model fit, but provided an unintuitive interpretation when

travel cost was interacted with household income category variables. Piece-wise linear

57
specification resulted in sudden discontinuities in the sensitivities from large values to

small values (see Daly, 2010 for warning on this same issue). The logarithmic

transformation on the cost variable provided the best model fit as well as an intuitive

interpretation, while not losing the generality when compared to the Box-Cox

transformation (the cost sensitivity vs. cost profiles of both log-cost and Box-Cox

transformations were very similar). To account for income-based heterogeneity in

households’ sensitivities to travel costs, the travel cost variable (in its logarithmic form)

was interacted with income category variables. The corresponding coefficients indicate,

as expected, that the low income households are most sensitive to travel costs, while

high income households are least sensitive. It was difficult to get such intuitive

interpretations from the Box-Cox specification.

The next, travel time variable was specified in the linear form because non-linear

specifications resulted in interpretation difficulties (e.g., Box-Cox resulted in an

unintuitive positive sign) as well as insignificant model improvements. Besides, several

long-distance mode choice studies in the past used a linear specification on travel time

(e.g., Gunn, 2001).

Dummy variables to indicate whether the origin and destinations are part of a

metropolitan statistical area (MSA) were introduced to the utility function for the air

mode. The positive coefficients on these variables indicate that the air more is more

attractive for those travelers who are departing from (i.e., reside in) an MSA or traveling

to destinations in an MSA, when compared to those who reside in or travel to a non-

MSA. This is a reasonable result as major airports (with good connectivity and cheaper

airfares) are generally closer to metropolitan statistical areas. Finally, the alternative

specific constant for the auto mode is positive, reflecting the higher auto mode share in

58
the sample. Overall the model results are reasonable and provide an understanding of

the factors influencing mode choice for long-distance leisure travel.

Table 13: Auxiliary mode choice model specification

Ground/Auto Air
Explanatory Variables
Parameter t-stat Parameter t-stat
Low income (< $30k/year) medium
-- -- -0.389 -2.81
income is base
High income (>$75k per year) medium
-- -- 0.581 8.99
income is base
LogCost = Log(Travel Cost in 100s of
-2.020 -55.50 -2.020 -55.50
Dollars)
Low income <$30k per year) dummy*
-0.166 -1.98 -0.166 -1.98
LogCost
Very high income (>$100k per year) *
0.180 4.36 0.180 4.36
LogCost
Travel Time in hours -0.028 -14.53 -0.028 -14.53
Dummy if origin is an MSA -- -- 0.606 14.400
Dummy if destination is an MSA -- -- 1.400 31.320
Alternative Specific Constant 0.764 8.19 0.000 fixed
Number of Cases 36263
Log Likelihood at Convergence -8024.04
Log Likelihood - Constants Only -14583.22
Adjusted Rho Square 0.449

5.2 Destination choice model specification

The empirical specification of the vacation destination choice and time allocation model

is provided in Table 14 for both the basic MDCEV model (as in section 2.1) as well as

the MDCEV model that incorporates minimum required time allocations (as in section

2.2). The table is divided into three main parts including the baseline marginal utility

function specification, satiation function specification, and model goodness of fit

measures, as discussed next.

59
5.2.1 Baseline marginal utility specification

As discussed earlier, the baseline marginal utility function governs the discrete choices,

since it represents the marginal utility derived at zero time investment before any

satiation effects begin to occur. A destination alternative with a higher baseline marginal

utility is more likely to be visited than that with a lower baseline marginal utility.

Between the two models (i.e., the MDCEV and the MDCEV with minimum

required time allocations), there are no significant differences in the baseline marginal

utility parameter estimates as well as the corresponding interpretations of the variable

effects. Thus, we discuss the variable effects for only one model without any

comparisons to the other model.

The first set of variables in the baseline marginal utility specification corresponds

to the transportation level of service characteristics. The first, log-sum variable, provides

a measure of composite impedance for the modes in the mode choice model. The

smaller the log-sum value is (i.e., the higher negative value it takes), greater is the

impedance between the origin (household’s residential location) and the alternative

destination. Thus, a positive and statistically significant coefficient of the log-sum

variable, as expected, indicates a lower attractiveness of destinations with higher

impedance to travel. The next variable is the highway travel distance between household

residential MSA/non-MSA and the destination MSA/non-MSA. As expected, farther away

destinations are less likely to be visited. At the same time, as shown by the demographic

interactions with the distance variable, demographic heterogeneity exists in households’

sensitivity to travel distance. Households with children are more sensitive to distance

(i.e., less likely to visit farther away destinations) than households without children,

perhaps due to the difficulty of traveling farther distances with children. The distance

variable was interacted with the annual income of the household. The hypothesis was

60
that higher income travelers would not be as sensitive (as lower income households

would be) to additional travel distances, as they can better afford the additional costs

associated with farther travel distances. The positive parameter associated with this

interaction variable confirmed the hypothesis. Lastly, householder age group dummy

variables were interacted with the distance variable, with the middle age group (25-64

years) as the base category. These householder age-group variables represent the life

cycle stage of the household. The corresponding coefficients indicate that both younger

(<25 years) and older (>64 years) age groups are likely to travel farther distances than

the middle age group households. These results make intuitive sense as both the

younger and older age groups may have lower time constraints and hence can

potentially visit farther away vacation destinations. The younger age group typically

comprises students and young adults with fewer time demands associated with a family

and career, while the older age group is typically in retirement and less likely to have the

time constraints associated with a full time career. For the middle age group, on the

other hand, career and familial responsibilities may impose time constraints that make

them less likely to travel farther away for vacation purposes. The next two variables in

the level of service characteristics correspond to indicators for the destination to be in

the same state (as the household is), and the adjacent state. The coefficients of these

variables are positive and significant, indicating a higher propensity of households to visit

familiar (and perhaps close by) locations within their state and adjacent states.

The first of the destination characteristics is a size measure (logarithm of the

area of the destination MSA or non-MSA) and used as a control to account for the

differences in the areas across the destinations. The coefficient of the size variable is

positive and smaller than one. This can be explained based on the spatial aggregation of

several elemental destination alternatives in the model. For example, several MSAs

61
defined in the model may include multiple destination cities (e.g., the Tampa–St.

Petersburg–Clearwater MSA with three different cities) and most non-MSAs defined in

the model are an aggregation of different individual destinations. As explained in Daly

(1982), a smaller than one coefficient on the size variable indicates a significant

presence of unobserved attributes that vary across these elemental destination

alternatives (i.e., non-homogeneity across the elemental destination alternatives within a

destination).

The next variable, MSA dummy, controls for differences between MSA

destinations and non-MSA destinations. The coefficient suggests that MSA destinations

tend to be more attractive than non-MSA destinations for long-distance leisure travel

purposes, perhaps due to the presence of more opportunities for recreation,

entertainment, and other leisure activities in MSAs.

The next variable “density of employment in the leisure and hospitality industry”

includes the employment levels in food services, arts, entertainment, recreation, and

accommodation sectors. As such, the variable is a surrogate measure for leisure activity

opportunities at the destination. A positive and statistically significant coefficient for this

variable indicates, as one would expect, that places that offer higher leisure activity

opportunities are more attractive as vacation destinations.17

The length of coastline was also included as a destination attractor. The

coefficient on this variable is positive and statistically significant, indicating, as expected

17
Other employment variables, including a total employment variable and a retail employment variable
were also explored in the model. A population density variable was explored too. Several of these variables
are highly correlated with leisure and hospitality employment and with each other. Thus, the variables were
introduced separately as well as together in different specifications. The signs on the coefficients of these
variables reversed and provided unintuitive results when introduced together rather than separately. Such
explorations were performed for each combination of variables and by using alternative functional forms
such as natural log of the employment variables as well as per area density of employment. After extensive
exploration, it was decided that using only the leisure/hospitality employment density variable (with no
other employment or populations variables) provided most intuitive interpretation for long distance leisure
travel without any substantial impact on the model fit to the data.
62
that destinations with longer coastlines are more attractive. This is because destinations

with longer coastlines offer a variety of leisure activity opportunities such as swimming,

fishing, boating, or sightseeing.

The next set of variables in the baseline utility function is associated with the

climate at the destination. First of these is the difference in the number of freezing days

per year between the destination and the origin. A freezing day is defined as a day in

which the temperature drops below 32 degrees Fahrenheit. The negative coefficient on

this variable suggests that households are less likely to visit destinations with more

freezing days per year than what they experience at their residential end. Colder

destinations are less attractive for vacations because freezing temperatures limit many

of the activities for which a household may want to travel. Besides, a greater number of

freezing days per year result in fewer available days for most vacation activities. In

addition to the annual freezing days variable, the mean temperatures for the destination

during the months of January and June were included in the model as a way to

understand the influence of winter and summer temperatures. Several specifications

were explored before arriving at the final specification that provided the best data fit and

offered an intuitive explanation.18 The January temperatures ranged from a maximum of

75 to a minimum of below freezing temperatures. The corresponding variables and

coefficients indicate that households prefer to visit destinations that offered the warmest

winter temperatures. As the winter temperatures drop below the 65-75 range, the

attractiveness of the destinations decreases. Specifically, ceteris paribus, destinations

with temperatures near or below freezing point are likely to be the least preferred. For

18
Note here that the temperatures used in the data are daily maximum temperatures averaged over a month.
Daily minimum and average temperatures values were also explored in the model, but the maximum daily
temperatures data provided a better model fit (albeit slightly better). Other explorations included,
specifying an annual average temperature variable (as opposed to separate, winter and summer
temperatures), which yielded a poor model fit and coefficients that were difficult to interpret.
63
summer temperatures, the results indicate that the utility of a destination does not vary

monotonously with temperature. Rather, a moderate temperature range might exist that

is comfortable for most people (Savageau and Loftus, 1997), and an increase or

decrease of temperatures beyond the moderate ranges may reduce the attractiveness of

destinations. We explored different temperature ranges and the best fitting model

suggested 65-75 degrees Fahrenheit as a comfortable temperature range.

Temperatures above or below this range were included as dummy variables of 5 degree

increments. Comparing coefficients of the 60-64 degree dummy variable with those of

the other variables suggests that destinations with temperatures below the comfort

range (65-75) in June have a higher disutility than those destinations with temperatures

above the comfort range. Comparison of the coefficients across January and June

temperature variables also suggests that the disutility associated with colder (than

moderate) climates is higher in magnitude than that of hotter (than moderate) climates.

5.2.2 Satiation ( γ k ) function specification

The satiation function coefficients in Table 4 refer to the elements of the θ vector, where

the satiation parameter γ k for vacation type k is written as exp(θ ' wk ) . A higher value of

the γ k parameter implies lower satiation for the destination alternative k (hence, larger

amount of time allocated for that destination). Thus, a positive θ coefficient on a positive

valued variable increases the satiation parameter, implying a slower rate of satiation (or

higher time allocation).

While there are perceivable differences between the satiation parameter

estimates of the two models (i.e., the MDCEV and the MDCEV with minimum required

time allocations), there are no significant differences in the interpretations of the variable

effects. Thus, we discuss the variable effects for only the latter model.

64
 The coefficient for travel distance has a positive sign and is significant. This

suggests that as the distance to a traveled destination increases, and thus the travel

time and costs associated with reaching the destination increase, travelers will be more

likely to allocate more time to that destination. That is, travelers will likely not make a

very long (and costly) trip for a very short stay. Perhaps they take advantage of the time

and money spent for the transport to farther away (and more exotic) destinations by

staying longer at those destinations. Another possibility is that farther away destinations

simply require longer travel times (hence longer time allocated). Travel distance was

also interacted with different levels of annual income of the household. The

corresponding coefficients indicate that high income households spend smaller portions

of time, where as low income households spend larger portions of annual vacation time

for farther away destinations. These income differences may be due to the differences in

the travel mode choices between different income groups. High income households may

travel by air which helps reduce their overall time spent on the vacation trip. Low income

households, on the other hand, may travel by slower modes and hence need more time

for their vacation trips. Besides, low income households might want to take advantage of

the money spent on longer trips by staying longer, while high income households might

not feel the same need to stay longer at a destination.

The next set of variables corresponds to household demographics – age of

householder and household size. Householder age was introduced in the form of

categorical variables with the 25-45 age range as the base category. The coefficients on

these age category variables suggest that older (age 46 and above) age groups are

likely to allocate relatively more time to a vacation destination than other age groups.

The relative magnitude of the coefficients indicate that households belonging to the

oldest age group (65 and above) tend to allocate the largest proportion of their time to a

65
destination followed by the older middle age (46-64), the youngest (15-24) age groups,

and finally the younger middle age group (25-45). This order makes intuitive sense as it

is reflective of the different levels of time constraints faced by households in different life

cycle stages (represented by the householder age groups). The oldest (65 and above)

householders include those in their retirement years with the least familial and career

oriented time constraints and a higher amount of time (and perhaps money) at their

disposal. Hence this age group is likely to spend longer vacation times at the

destinations they visit. The youngest (15-24) age group is also likely to have lesser time

constraints (hence spend more vacation time). The younger middle age (25-45) group

householders, on the other hand, are typically at an early state in their professional

career and with family related time constraints. Older middle age (46-64) group

householders are likely to be well established in their careers and not likely to have

young children. So their time constraints may not be as tight as those earlier in their

careers and at an early stage of their family life cycle.

The last variable in the satiation function is household size, which is a surrogate

measure for the number of travelers (i.e., the travel party size) on vacation trips. The

positive coefficient on this variable suggests that a larger household is likely to spend a

larger amount of time for a destination than a smaller household. A plausible reason for

this result is that larger households (hence larger travel party sizes) tend to travel by

slower ground modes than by expensive air modes, hence take longer time for visiting a

destination. Another reason is that larger households, typically with children, might prefer

to take more time at a destination for a relaxing vacation than making a quick and tiring

trip.

In summary, the MDCEV model estimates are reasonable and provide important

insights into the impact of the travel level of service attributes, destination

66
characteristics, and household socio-demographic characteristics on households’ annual

vacation destination choices. These results demonstrate the usefulness of the MDCEV

model framework for modeling annual vacation destination choices and time allocation

patterns.19 The model fit measures are reported in the last set of rows. The log-likelihood

values of both the models show significant improvement over a naïve model with no

explanatory variables. The Rho-squared value for the model is 0.260, an acceptable

value for an ambitious model framework that attempts to model all the annual destination

choices and the time allocations of households with a large choice set of 210

alternatives. Further, while the proposed variant of the MDCEV model does not offer

significantly different interpretations compared to the original MDCEV model, it provides

a better fit to the data.

19
It took about 90 minutes to estimate the parameters of the final model specification presented here (on a
2.6 GHz, 3.25 GB RAM, dual core processor desktop machine, with default starting values for the
parameters). The MDCEV model estimation code available at Bhat’s website was used as a starting point
for this study. His code was modified so that the model estimation input data could be stacked into as many
rows as the number of households times the number of destination choice alternatives, as opposed to the
usual way of stacking model estimation data into as many rows as the number of households (with one row
containing information on all the 210 destination choice alternatives for a household).
67
 Table 14: Destination choice model specification
MDCEV w/
minimum
MDCEV
required
consumption

Baseline Utility Function (Ψ) Specification Coeff t-stat Coeff t-stat

Distance and level of service characteristics
Log-sum variable from the mode choice model 0.3043 29.12 0.3034 29.03
Highway distance to Destination (100's of miles) -0.0578 -33.13 -0.0576 -33.10
Highway distance* Presence of Children (0-17) -0.0196 -10.25 -0.0203 -10.61
Highway distance*High income (> $75k) dummy 0.0186 8.75 0.0185 8.73
Highway distance* Householder age 15 to 24 (25-64 as base) 0.0109 2.63 0.0105 2.56
Highway distance* Householder age 65 or older (25-64 as base) 0.0129 5.35 0.0126 5.24
Dummy if destination in same state as household residence 1.5444 37.09 1.5426 37.02
Dummy if destination in adjacent state to household residence 0.8914 29.52 0.8900 29.46
Destination Characteristics
Log(Land area of the destination in sq. miles) 0.5453 35.91 0.5415 35.63
Destination is an MSA (Dummy variable) 1.3098 14.85 1.2848 14.55
Leisure Employment Density in 100's of employees/sq. mile 0.0953 45.09 0.0949 44.88
Length of coastline in 1000's of miles 0.0731 10.50 0.0733 10.54
Difference in number of freezing days (destination minus origin) -0.0092 -20.77 -0.0092 -20.76
Winter (January) temperatures (monthly avg of max daily values)
55 to 65 degrees Fahrenheit (65-75 degrees as base) -0.8337 -16.93 -0.8314 -16.88
45 to 55 degrees Fahrenheit (65-75 degrees as base) -1.5288 -26.71 -1.5349 -26.80
35 to 45 degrees Fahrenheit (65-75 degrees as base) -2.2623 -31.97 -2.2711 -32.06
Less than 35 degrees Fahrenheit (65-75 degrees as base) -2.3046 -27.68 -2.3182 -27.83
Summer (June) temperatures (monthly avg of max daily values)
60 to 65 degrees Fahrenheit (65-75 degrees as base) -3.4599 -12.89 -3.4246 -12.75
75 to 80 degrees Fahrenheit (65-75 degrees as base) -0.6770 -17.05 -0.6615 -16.66
80 to 85 degrees Fahrenheit (65-75 degrees as base) -0.4292 -9.74 -0.4254 -9.65
85 to 90 degrees Fahrenheit (65-75 degrees as base) -0.7987 -16.02 -0.8025 -16.10
More than 90 degrees Fahrenheit (65-75 degrees as base) -0.5090 -10.34 -0.5162 -10.49
Satiation Function (γ) Specification
Highway distance to Destination (100's miles) 0.0910 27.81 0.0991 31.31
Distance*Low income (under $30k) dummy ($30k-$75k is base) 0.0432 8.21 0.0361 7.00
Distance*High income (over $75k) dummy ($30k-$75k is base) -0.0392 -8.72 -0.0381 -8.66
Householder age 15 to 24 (25 to 45 is base) 0.5102 4.39 0.2555 2.32
Householder age 46 to 64 (25 to 45 is base) 0.4091 9.42 0.2830 7.07
Householder age 65 or older (25 to 45 is base) 0.9966 17.09 0.8883 16.11
Household size 0.2680 28.46 0.1850 20.83

68
 Table 14: (continued)
MDCEV w/ minimum
MDCEV required
consumption
Model Fit Measures
Log-likelihood at convergence: L (βˆ ,θˆ) -46891.91 -46027.30
Log-likelihood with no variables in the model: L(0) -63796.70 -62206.33
Rho-squared = 1- {L (βˆ ,θˆ) / L(0)} 0.265 0.260

5.3 Destination choice model validation

This section provides a validation analysis of the annual destination choice and time

allocation MDCEV models discussed earlier. The validation exercise was performed

using a sample of 715 households from the 1995 American Travel Survey that were not

a part of the 6000 household-sample used for model estimation.

Validation of an empirical MDCEV model requires the application of the MDCEV

modeling framework to simulate (or predict) households’ annual vacation destination

choices and time allocation patterns. In this study, we used a simple and computationally

very fast prediction algorithm that Pinjari and Bhat (2010) presented for using the

MDCEV model for prediction purposes. For each of the 715 households under

consideration, we used 50 sets of random draws from independent type-1 extreme value

distributions to simulate the unobserved heterogeneity (i.e., the ε k terms) in the model.20

For each household and each set of random draws, conditional upon the total annual

vacation time available to the household, the MDCEV model estimates were used to

predict the annual vacation destination choices and the time allocation to each predicted

destination. The prediction exercise was carried out for both the basic MDCEV model

and the proposed variant of the MDCEV model. Subsequently, histograms were plotted

20
Using the prediction procedure proposed in Pinjari and Bhat (2010), it took less than 1 minute to
complete the prediction simulation for all 715 households over all 50 sets of random draws. The Pinjari and
Bhat (2010) forecasting procedure was slightly modified to apply the proposed variant of the MDCEV
model that accommodates minimum required time allocations. Details are suppressed here to save space,
but available from the authors.
69
to obtain the distributions of the predicted choices over all 715 households and all 50

random draws for both the models. Such predicted distributions were compared to the

observed distributions over all the 715 households in the data. Figures 5, 6, and 7

provide both observed and predicted distributions (for both the models) and are

discussed next.

Figure 5 provides the distributions of the home-to-destination distances for the

destinations observed in the data as well as the destinations predicted by the models.

Both the models provide similar distributions that are reasonably consistent with the

observed distribution. However, the models seem to slightly under-predict destinations

within 1000 miles from the household locations, over-predict destinations in the 1000-

3500 mile range from the household locations, indicating a lower sensitivity of the model

to level of service variables. One way to improve these results is to jointly estimate the

destination choice and mode choice models. The travel time and travel cost sensitivities

embedded in the current destination choice MDCEV model (through the log-sum

variable) are based on households’ mode choice decisions. A joint model may help

incorporate the sensitivities (to the level of service variables) that are based on both

mode choices and destination choices and thereby improve the distance-based

validations.

Figure 6 provides the observed and predicted distributions of the total number of

destinations visited by households in the year. Note that the MDCEV framework does

not directly model the number of chosen destinations. Nonetheless, both the models

provide similar distributions that are consistent with the observed distribution. There are

minor differences in that the models slightly under-predict households that visited one

destination in a year, and slightly over-predict the households that visited more than 2

destinations. A few (although very small percentage) households were predicted to visit

70
as many as 16 destinations, where as the observed choices indicate a maximum of 7

destinations visited.

45.0
% of all visited (or predicted)

40.0
Observed (Mean = 1,093.69)
35.0
Predicted using the basic MDCEV model (Mean = 1,087.62)
30.0
destinations

Simulated using the proposed variant of MDCEV (Mean = 1,086.05)

25.0
20.0
15.0
10.0
5.0
.0

Distance in Miles
Figure 5: Model validation results based on distances to chosen destinations

70.0
Observed (Mean = 1.53)
60.0
Predicted using the basic MDCEV model (Mean = 1.68)
50.0
% of households

Simulated using the proposed variant of MDCEV (Mean = 1.70)

40.0

30.0

20.0

10.0

.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Number of destinations visited

Figure 6: Model validation results based on the number of destinations visited in a year

71
 30.0
Observed (Mean = 1,673.42)
25.0
% of all visited (or predicted) Predicted using the basic MDCEV model (Mean = 1,826.14)
20.0
Simulated using the proposed variant of MDCEV (Mean = 1,847.96)
destinations

15.0

10.0

5.0

.0

Annual Distance Traveled in Miles

Figure 7: Model validation results based on the total distance to the chosen destinations

Figure 7 provides the observed and predicted distributions of the total distance

from home location to all destinations visited in the year. Again, both the models provide

similar results, with under-predictions in the shorter distance ranges and over-prediction

in the longer distance ranges. This may be due to a combination of lower model

sensitivity to level of service variables (as discussed in the context of Figure 5) and the

over-prediction of the number of destinations visited (hence longer distances) for a small

percentage of households.

We also compared the observed and predicted distributions of the time (no. of

days) allocated to chosen destinations (figure not shown). By design, no household in

the data is observed to have spent less than 0.5 days for any chosen destination.

However, about 10% of the predicted destinations from the basic MDCEV model were

allocated less than half a day of time. The proposed variant of the MDCEV model

reduces such predictions with less than minimum amount of time allocation to only 2%,

although it doesn’t completely preclude very small time allocations.

72
 In summary, the validation results demonstrate the models’ ability to provide

reasonable predictions, at the least in the aggregate level.21 The results also provide

leads to improve the model specification. The basic MDCEV model and the proposed

variant of the MDCEV model provided similar validation results. However, the proposed

variant of MDCEV helped in reducing the percentage of choices with smaller than

minimum required amount of consumption. Thus, the proposed framework can

potentially be useful in situations where it is important to avoid predicting unrealistically

small amounts of consumption.

21
This is not to claim that reproducing aggregate observed distributions (even if in a validation sample) is a
sole yard stick for measuring model performance. It is important that the model demonstrate appropriate
sensitivity to changes in policy variables and the socio-demographic makeup.
73
 Chapter 6: Conclusions and Future Research

This thesis contributes to the literature on national travel demand modeling by providing

an analysis of households’ annual destination choices and time allocation patterns for

long-distance leisure travel purposes. More specifically, an annual vacation destination

choice and time allocation model is formulated to simultaneously predict the different

destinations that a household visits in a year, and the time it allocates to each of the

visited destinations. The model takes the form of a Multiple Discrete-Continuous

Extreme Value (MDCEV) structure. Given the total annual vacation time available for a

household, the model assumes that households allocate the annual vacation time to visit

one or more destinations in a year in such a way as to maximize the utility derived from

their choices. The model framework accommodates variety-seeking in households’

vacation destination choices in that households can potentially visit a variety of

destinations rather than spending all of their annual vacation time for visiting a single

destination. At the same time, the model accommodates corner solutions to recognize

that households may not necessarily visit all available destinations. An annual vacation

time budget is also considered to recognize that households operate under time budget

constraints.

The empirical data for this analysis comes from the 1995 American Travel

Survey (ATS) data, with the U.S. divided into 210 alternative destinations. Thus, the

study provides an opportunity to estimate, apply, and assess the performance of the

MDCEV model for an empirical context with a large number of choice alternatives. The

empirical analysis provides important insights into the determinants of long-distance

74
leisure destination choice and time allocation patterns. Select findings are summarized

here: (a) Destinations with larger impedance to travel are less attractive in general, but

especially so for households with children, low and medium income households, and

middle age group (25-64 years) householders. (b) Leisure and hospitality employment,

length of coastline, number of annual freezing days (relative to the origin), and winter

and summer temperatures are important determinants of travelers’ attractiveness to a

destination. Specifically, destinations that offer a greater number of leisure activity

opportunities, longer coastline, and moderate temperatures (65-75 degree Fahrenheit)

are more attractive than other destinations. (c) Low income households tend to spend a

longer time for vacations to farther destinations followed by medium income and high

income households, in that order. (d) Households with older (>64 years) householders

and those with larger number of individuals tend to spend longer time at a vacation

destination compared to other households.

On the methodological front, the paper proposes a variant of the MDCEV model

that helps reduce the prediction of unrealistically small amounts of time allocation to the

chosen alternatives. To do so, the continuously non-linear utility functional form in the

MDCEV framework is replaced with a combination of a linear and non-linear form. The

proposed variant of the MDCEV model provides a better model fit than the original

MDCEV model, and reduces the likelihood of destination choices with unrealistically

small amounts of time allocation.

The annual destination choice and time allocation models estimated in this study

were validated using a validation sample of 715 households. The validation results

demonstrated the models’ prediction ability in terms of producing reasonable aggregate-

level distributions of the predicted distances traveled and the number of destinations

visited in a year.

75
 An appealing feature of the proposed model is its applicability in a national, long-

distance leisure travel demand model system. While the proposed destination choice

model does not explicitly provide a nationwide origin-destination trip distribution table,

the knowledge of the annual destination choices and time allocations predicted by this

model can be used for subsequent analysis of the number of trips made (in a year) to

each destination and the travel choices for each trip, including mode choice, time (i.e.,

season) of the year, and length of stay. Thus, the models developed in this study can be

incorporated into a larger national travel modeling framework for predicting the national-

level, origin-destination flows for vacation travel. This larger national level travel

modeling framework would be of particular use to national and regional level tourism

boards and national level transportation agencies.

This study paves way to several avenues for further work. First, it will be useful to

implement a larger, national-level vacation travel demand system as described in

Figures 1 and 2. Additionally, an expanded modeling framework that includes additional

travel purposes, beyond leisure travel, can provide further improvements over traditional

modeling techniques. Many travelers will likely combine trips (e.g. travel for business,

but also incorporate some leisure activities) and so capturing the details of these trips,

and their impacts, will provide valuable insight to both transportation planners and

regional tourism agencies. Second, the current empirical study can be enhanced in

many ways, including: (a) a joint estimation of the mode choice and destination choice

models, (b) inclusion of inter-city bus and rail modes in the analysis, and (c) performing

policy simulations to assess model sensitivity to important policies. Third, the model

does not consider short-distance leisure travel (i.e., leisure travel within the residential

neighborhood such as going to a mall, a nearby beach etc.), because the 1995 ATS data

does not collect information on short-distance travel. It would be useful to understand the

76
potential substitution patterns between short-distance leisure travel and long-distance

leisure travel. Fourth, the current model considers time budget constraints and

allocation, but ignores money budgets both due to the unavailability of the data and the

lack of methods to do so. This is another important aspect for future research.

77
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