Segmentation:Clustering

Krissie

2024-11-21

#----------------Segmentation---------------------#

##--------##Clustering##---------##

#1.Loading data
setwd("/Users/kitsanasudsaneh/Desktop/fall2024")
seg.raw <-read.csv("rintro-chapter5.csv")
str(seg.raw)

## ’data.frame’: 300 obs. of 7 variables:

## $ age : num 47.3 31.4 43.2 37.3 41 ...
## $ gender : chr "Male" "Male" "Male" "Female" ...
## $ income : num 49483 35546 44169 81042 79353 ...
## $ kids : int 2 1 0 1 3 4 3 0 1 0 ...
## $ ownHome : chr "ownNo" "ownYes" "ownYes" "ownNo" ...
## $ subscribe: chr "subNo" "subNo" "subNo" "subNo" ...
## $ Segment : chr "Suburb mix" "Suburb mix" "Suburb mix" "Suburb mix" ...

#2.Cleaning and Preparing the data: convert some variable to factor (chr > num)
seg.raw$gender <- factor(seg.raw$gender)
seg.raw$ownHome <- factor(seg.raw$ownHome)
seg.raw$subscribe <- factor(seg.raw$subscribe)
seg.raw$Segment <- factor(seg.raw$Segment)
str(seg.raw)

## ’data.frame’: 300 obs. of 7 variables:

## $ age : num 47.3 31.4 43.2 37.3 41 ...
## $ gender : Factor w/ 2 levels "Female","Male": 2 2 2 1 1 2 2 2 1 1 ...
## $ income : num 49483 35546 44169 81042 79353 ...
## $ kids : int 2 1 0 1 3 4 3 0 1 0 ...
## $ ownHome : Factor w/ 2 levels "ownNo","ownYes": 1 2 2 1 2 2 1 1 1 2 ...
## $ subscribe: Factor w/ 2 levels "subNo","subYes": 1 1 1 1 1 1 1 1 1 1 ...
## $ Segment : Factor w/ 4 levels "Moving up","Suburb mix",..: 2 2 2 2 2 2 2 2 2 2 ...

## group into 4 segments

#---Remove Segment column (column 7)

seg.df <- seg.raw[,-7]

#-------##Distance-based Methods##--------#

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library(cluster)
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#---Compute a Distance Matrix

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#---Perform Hierarchical Clustering
#ideal for exploring relationships.

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#---Cut the tree and Focus on a Branch

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plot(cut(as.dendrogram(seg.hc),h=0.5)$lower[[1]]) #cut 0.5

hclust (*, "complete")
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as.matrix(seg.dist)[1:4,1:4] #Distances of first 4 observations

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#3.Hierarchical Clustering Method:groups data based on a tree structure,

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seg.dist <- daisy(seg.df) #calculates distances for mixed data (numeric + categorical)

seg.hc <-hclust(seg.dist,method = "complete") #This method creates a tree structure (dendrogram)

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#---Comparing observations in branches
seg.df[c(128,137),] #similar

## age gender income kids ownHome subscribe

## 128 21.80737 Male 27807.24 2 ownNo subYes
## 137 24.88971 Male 23326.45 2 ownNo subYes

seg.df[c(141,89),] #less similar

## age gender income kids ownHome subscribe

## 141 25.17703 Female 20125.80 2 ownNo subYes
## 89 41.89570 Female 58871.48 3 ownNo subYes

#---Cophenetic Correlation Coefficient: how well the hierarchical clustering (dendrogram) represents
#the actual distances in the data (close to 1 > good)
cor(cophenetic(seg.hc),seg.dist)

## [1] 0.7682436

#---Getting K groups from the tree: Decide how many you decide how many groups (clusters) you want to ma
plot(seg.hc)
rect.hclust(seg.hc, k=4,border = "red")

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seg.dist
hclust (*, "complete")

seg.hc.segment <-cutree(seg.hc, k =4) #It assigns each data point to one of these 4 clusters.
table(seg.hc.segment) #counts how many observations fall into each cluster.

## seg.hc.segment
## 1 2 3 4
## 124 136 18 22

#4.Quick summary to inspect the variables in seg.df with reference to the 4 clusters.
seg.summ <- function(data, groups)
{
aggregate(data, list(groups), function(x) mean(as.numeric(x)))
}
seg.summ(seg.df,seg.hc.segment)

## Group.1 age gender income kids ownHome subscribe

## 1 1 40.78456 2.000000 49454.08 1.314516 1.467742 1
## 2 2 42.03492 1.000000 53759.62 1.235294 1.477941 1
## 3 3 44.31194 1.388889 52628.42 1.388889 2.000000 2
## 4 4 35.82935 1.545455 40456.14 1.136364 1.000000 2

#5.Relate to the clusters(seg.hc.segment),creates a scatterplot to visualize how two variables

#gender and subscribe
plot(jitter(as.numeric(seg.df$gender)) ~ jitter(as.numeric(seg.df$subscribe)),
col=seg.hc.segment, yaxt="n", xaxt="n", ylab="", xlab="")

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axis(1, at=c(1, 2), labels=c("Subscribe: No", "Subscribe: Yes"))
axis(2, at=c(1, 2), labels=levels(seg.df$gender))
Male
Female

Subscribe: No Subscribe: Yes

##the choice of variables (like gender and subscribe) depends on what we want to learn.
##For example:Are males more likely to subscribe?
#Do certain clusters have more females or males who subscribe?

##6.K-means clustering

#---Convert Factors to Numeric (K-means works only with numeric data)

seg.df.num <- seg.df
seg.df.num$gender <- ifelse(seg.df$gender == "Male",0,1)
seg.df.num$ownHome <- ifelse(seg.df$ownHome == "ownNo",0,1)
seg.df.num$subscribe <- ifelse(seg.df$subscribe == "subNo",0,1)
str(seg.df.num)

## ’data.frame’: 300 obs. of 6 variables:

## $ age : num 47.3 31.4 43.2 37.3 41 ...
## $ gender : num 0 0 0 1 1 0 0 0 1 1 ...
## $ income : num 49483 35546 44169 81042 79353 ...
## $ kids : int 2 1 0 1 3 4 3 0 1 0 ...
## $ ownHome : num 0 1 1 0 1 1 0 0 0 1 ...
## $ subscribe: num 0 0 0 0 0 0 0 0 0 0 ...

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#---Run K-means: minimizes the distance within clusters finding clusters by finding cluster centers
set.seed(96743) #Set seed for reproducibility
seg.k <- kmeans(seg.df.num, centers = 4)

#---Summarize Clusters
seg.summ <- function(data, groups)
{
aggregate(data, list(groups), mean)
}
seg.summ(seg.df,seg.k$cluster)

## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:

## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Group.1 age gender income kids ownHome subscribe

## 1 1 29.58704 NA 21631.79 1.063492 NA NA
## 2 2 55.40968 NA 89959.96 0.360000 NA NA
## 3 3 42.38909 NA 47799.84 1.434783 NA NA
## 4 4 43.66931 NA 63630.70 1.443299 NA NA

#---Visualize the Clusters: A plot show how well-separated the clusters are.

##--Boxplot: Use to compare group on 1 variable

boxplot(seg.df.num$income ~ seg.k$cluster,
xlab = "Segments", ylab = "Income", horizontal = TRUE,
main = "Boxplot of comparing income in each Segment")

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 Boxplot of comparing income in each Segment
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##--Clusplot: use to visualizing the overall clusters to see that they share similarities in the data va
library(cluster)
clusplot(seg.df, seg.k$cluster, color = TRUE, shade = TRUE, labels = 4,
lines = 0,main = "Clusplot of the overall segment")

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 Clusplot of the overall segment

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These two components explain 48.49 % of the point variability.
#--------Model-based Methods-------#

#1.poLCA(): use only categorical variables ; finds hidden groups (latent class) when they aren't directl

#---Convert Continuous Data to Catgories:numeric variables need to be grouped

seg.df.cut <-seg.df
seg.df.cut$age <- factor (ifelse(seg.df$age < median (seg.df$age),"LessAge","MoreAge"))
seg.df.cut$income <- factor(ifelse(seg.df$income < median(seg.df$income), "LessInc", "MoreInc"))
seg.df.cut$kids <- factor(ifelse(seg.df$kids < median(seg.df$kids),"Lesskids","Morekids"))
str(seg.df.cut)

## ’data.frame’: 300 obs. of 6 variables:

## $ age : Factor w/ 2 levels "LessAge","MoreAge": 2 1 2 1 2 2 1 1 2 1 ...
## $ gender : Factor w/ 2 levels "Female","Male": 2 2 2 1 1 2 2 2 1 1 ...
## $ income : Factor w/ 2 levels "LessInc","MoreInc": 1 1 1 2 2 2 1 1 1 2 ...
## $ kids : Factor w/ 2 levels "Lesskids","Morekids": 2 2 1 2 2 2 2 1 2 1 ...
## $ ownHome : Factor w/ 2 levels "ownNo","ownYes": 1 2 2 1 2 2 1 1 1 2 ...
## $ subscribe: Factor w/ 2 levels "subNo","subYes": 1 1 1 1 1 1 1 1 1 1 ...

#--- Create a formula: that combines multiple variable into one group.It prepares these variables to be
seg.f <- with(seg.df.cut,cbind(age, gender, income, kids, ownHome, subscribe)~1)

#2.Run model in different class (start with the smaller number) How well the data fits into n classes.
library(poLCA)

## Loading required package: scatterplot3d

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## Loading required package: MASS

set.seed(02807)
seg.LCA3 <- poLCA(seg.f, data = seg.df.cut,nclass = 3) # there are 3 latent (hidden) classes.

## Conditional item response (column) probabilities,

## by outcome variable, for each class (row)
##
## $age
## LessAge MoreAge
## class 1: 1.0000 0.0000
## class 2: 0.0000 1.0000
## class 3: 0.6555 0.3445
##
## $gender
## Female Male
## class 1: 0.4211 0.5789
## class 2: 0.4681 0.5319
## class 3: 0.6079 0.3921
##
## $income
## LessInc MoreInc
## class 1: 1.0000 0.0000
## class 2: 0.3803 0.6197
## class 3: 0.3746 0.6254
##
## $kids
## Lesskids Morekids
## class 1: 0.2818 0.7182
## class 2: 0.8065 0.1935
## class 3: 0.1575 0.8425
##
## $ownHome
## ownNo ownYes
## class 1: 0.7289 0.2711
## class 2: 0.2338 0.7662
## class 3: 0.6638 0.3362
##
## $subscribe
## subNo subYes
## class 1: 0.7496 0.2504
## class 2: 0.8948 0.1052
## class 3: 0.8960 0.1040
##
## Estimated class population shares
## 0.1974 0.341 0.4616
##
## Predicted class memberships (by modal posterior prob.)
## 0.2333 0.3467 0.42
##
## =========================================================
## Fit for 3 latent classes:
## =========================================================
## number of observations: 300

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## number of estimated parameters: 20
## residual degrees of freedom: 43
## maximum log-likelihood: -1092.345
##
## AIC(3): 2224.691
## BIC(3): 2298.767
## G^2(3): 42.77441 (Likelihood ratio/deviance statistic)
## X^2(3): 38.47647 (Chi-square goodness of fit)
##

seg.LCA4 <- poLCA(seg.f,data = seg.df.cut,nclass = 4) #there are 4 latent (hidden) classes.

## Conditional item response (column) probabilities,

## by outcome variable, for each class (row)
##
## $age
## LessAge MoreAge
## class 1: 0.6823 0.3177
## class 2: 0.0000 1.0000
## class 3: 1.0000 0.0000
## class 4: 1.0000 0.0000
##
## $gender
## Female Male
## class 1: 0.5853 0.4147
## class 2: 0.4810 0.5190
## class 3: 0.8466 0.1534
## class 4: 0.3277 0.6723
##
## $income
## LessInc MoreInc
## class 1: 0.4137 0.5863
## class 2: 0.3701 0.6299
## class 3: 0.5850 0.4150
## class 4: 1.0000 0.0000
##
## $kids
## Lesskids Morekids
## class 1: 0.0000 1.0000
## class 2: 0.8114 0.1886
## class 3: 1.0000 0.0000
## class 4: 0.2506 0.7494
##
## $ownHome
## ownNo ownYes
## class 1: 0.6540 0.3460
## class 2: 0.2688 0.7312
## class 3: 0.6537 0.3463
## class 4: 0.7721 0.2279
##
## $subscribe
## subNo subYes
## class 1: 0.8746 0.1254
## class 2: 0.8965 0.1035

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## class 3: 1.0000 0.0000
## class 4: 0.7203 0.2797
##
## Estimated class population shares
## 0.4101 0.3697 0.0643 0.1559
##
## Predicted class memberships (by modal posterior prob.)
## 0.41 0.3733 0.0667 0.15
##
## =========================================================
## Fit for 4 latent classes:
## =========================================================
## number of observations: 300
## number of estimated parameters: 27
## residual degrees of freedom: 36
## maximum log-likelihood: -1088.021
##
## AIC(4): 2230.041
## BIC(4): 2330.043
## G^2(4): 34.12473 (Likelihood ratio/deviance statistic)
## X^2(4): 31.50696 (Chi-square goodness of fit)
##

#---compare Model Fit using: BIC (A lower BIC value indicates a better fit)
seg.LCA3$bic

## [1] 2298.767

seg.LCA4$bic

## [1] 2330.043

#---Examine the 3-group model

seg.summ(seg.df, seg.LCA3$predclass) #function summarizes the dataset

## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:

## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Group.1 age gender income kids ownHome subscribe
## 1 1 28.22385 NA 30075.32 1.1285714 NA NA
## 2 2 54.44407 NA 60082.47 0.3846154 NA NA
## 3 3 37.47652 NA 54977.08 2.0793651 NA NA

table(seg.LCA3$predclass) #how many observations belong to each class

##
## 1 2 3
## 70 104 126

clusplot(seg.df, seg.LCA3$predclass, color = TRUE, shade = TRUE, lables = 4,

lines=0, main ="LCA plot (K=3)")

## Warning in plot.window(...): "lables" is not a graphical parameter

## Warning in plot.xy(xy, type, ...): "lables" is not a graphical parameter

## Warning in axis(side = side, at = at, labels = labels, ...): "lables" is not a

## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lables" is not a
## graphical parameter

## Warning in box(...): "lables" is not a graphical parameter

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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
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## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter

## Warning in polygon(z[[k]], density = if (shade) density[k] else 0, col =

13
## col.clus[jInd[i]], : "lables" is not a graphical parameter

## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical

## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter

14
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter

## Warning in polygon(z[[k]], density = if (shade) density[k] else 0, col =

## col.clus[jInd[i]], : "lables" is not a graphical parameter

## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical

## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter

15
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter

16
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter

## Warning in polygon(z[[k]], density = if (shade) density[k] else 0, col =

## col.clus[jInd[i]], : "lables" is not a graphical parameter

## Warning in plot.xy(xy.coords(x, y), type = type, ...): "lables" is not a

## graphical parameter
## Warning in plot.xy(xy.coords(x, y), type = type, ...): "lables" is not a
## graphical parameter
## Warning in plot.xy(xy.coords(x, y), type = type, ...): "lables" is not a
## graphical parameter

LCA plot (K=3)

3
2
Component 2

1
0
−1
−2
−3

−3 −2 −1 0 1 2 3 4

Component 1
These two components explain 48.49 % of the point variability.

#---Examine the 4-group model

seg.summ(seg.df, seg.LCA4$predclass) #function summarizes the dataset

## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:

## returning NA

## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:

## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:

17
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA

## Group.1 age gender income kids ownHome subscribe

## 1 1 36.62554 NA 52080.13 2.1951220 NA NA
## 2 2 53.64073 NA 60534.17 0.5178571 NA NA
## 3 3 30.22575 NA 41361.81 0.0000000 NA NA
## 4 4 27.61506 NA 28178.70 1.1777778 NA NA

table(seg.LCA4$predclass) #how many observations belong to each class

##
## 1 2 3 4
## 123 112 20 45

clusplot(seg.df, seg.LCA4$predclass, color = TRUE, shade = TRUE, lables = 4,

lines=0, main ="LCA plot (K=4)")

## Warning in plot.window(...): "lables" is not a graphical parameter

## Warning in plot.xy(xy, type, ...): "lables" is not a graphical parameter

## Warning in axis(side = side, at = at, labels = labels, ...): "lables" is not a

## graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lables" is not a
## graphical parameter

## Warning in box(...): "lables" is not a graphical parameter

## Warning in title(...): "lables" is not a graphical parameter

## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical

## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical

18
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter

## Warning in polygon(z[[k]], density = if (shade) density[k] else 0, col =

## col.clus[jInd[i]], : "lables" is not a graphical parameter

## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical

## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical

19
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter

## Warning in polygon(z[[k]], density = if (shade) density[k] else 0, col =

## col.clus[jInd[i]], : "lables" is not a graphical parameter

## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical

## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical

20
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter

## Warning in polygon(z[[k]], density = if (shade) density[k] else 0, col =

## col.clus[jInd[i]], : "lables" is not a graphical parameter

## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical

## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical

21
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical

22
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter
## Warning in segments(lx1, ly1, lx2, ly2, ...): "lables" is not a graphical
## parameter

## Warning in polygon(z[[k]], density = if (shade) density[k] else 0, col =

## col.clus[jInd[i]], : "lables" is not a graphical parameter

## Warning in plot.xy(xy.coords(x, y), type = type, ...): "lables" is not a

## graphical parameter
## Warning in plot.xy(xy.coords(x, y), type = type, ...): "lables" is not a
## graphical parameter
## Warning in plot.xy(xy.coords(x, y), type = type, ...): "lables" is not a
## graphical parameter
## Warning in plot.xy(xy.coords(x, y), type = type, ...): "lables" is not a
## graphical parameter

LCA plot (K=4)

3
2
Component 2

1
0
−1
−2

−2 0 2

Component 1
These two components explain 48.49 % of the point variability.

#2.Mclust:
#---Fit a Model-Based Clustering
library(mclust)

## Warning: package ’mclust’ was built under R version 4.3.2

## Package ’mclust’ version 6.1.1

## Type ’citation("mclust")’ for citing this R package in publications.

23
seg.mc <-Mclust(seg.df.num)
summary(seg.mc) #Fit a 3-Cluster Model

## ----------------------------------------------------
## Gaussian finite mixture model fitted by EM algorithm
## ----------------------------------------------------
##
## Mclust VEV (ellipsoidal, equal shape) model with 3 components:
##
## log-likelihood n df BIC ICL
## -5137.106 300 73 -10690.59 -10690.59
##
## Clustering table:
## 1 2 3
## 163 71 66

#---Fit a 4-Cluster Model

#The log-likelihood: how well the model fits the data: higher is better.
seg.mc4 <- Mclust(seg.df.num,G=4)
summary(seg.mc4)

## ----------------------------------------------------
## Gaussian finite mixture model fitted by EM algorithm
## ----------------------------------------------------
##
## Mclust VII (spherical, varying volume) model with 4 components:
##
## log-likelihood n df BIC ICL
## -16862.69 300 31 -33902.19 -33906.18
##
## Clustering table:
## 1 2 3 4
## 104 66 59 71

#---Compare Models Using BIC

BIC(seg.mc,seg.mc4) #Lower BIC is better

## df BIC
## seg.mc 73 10690.59
## seg.mc4 31 33902.19

#---Summarize Variables by Cluster

seg.summ(seg.df,seg.mc$class)

## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:

## returning NA

## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:

## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA

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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA

## Group.1 age gender income kids ownHome subscribe

## 1 1 44.68018 NA 52980.52 1.171779 NA NA
## 2 2 38.02229 NA 51550.98 1.422535 NA NA
## 3 3 36.02187 NA 45227.51 1.348485 NA NA

#---Visualize Clusters #if clusters overlap, it means some groups are less distinct.
library(cluster)
clusplot(seg.df, seg.mc$class, color= TRUE, shade = TRUE, labels = 4,
main = "Mcluster Plot")

Mcluster Plot

1
3
2

3
Component 2

2
1
0
−1
−2
−3

−3 −2 −1 0 1 2 3 4

Component 1
These two components explain 48.49 % of the point variability.

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Including Plots

You can also embed plots, for example:

800
600
pressure

400
200
0

0 50 100 150 200 250 300 350

temperature

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that
generated the plot.

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