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Confirmatory Factor Analysis
Confirmatory factor analysis (CFA) is a multivariate statistical procedure that is used to test how
well the measured variables represent the number of constructs. Confirmatory factor analysis
(CFA) and exploratory factor analysis (EFA) are similar techniques, but in exploratory factor
analysis (EFA), data is simply explored and provides information about the numbers of factors
required to represent the data. In exploratory factor analysis, all measured variables are related to
every latent variable. But in confirmatory factor analysis (CFA), researchers can specify the
number of factors required in the data and which measured variable is related to which latent
variable. Confirmatory factor analysis (CFA) is a tool that is used to confirm or reject the
measurement theory.
General Purpose - Procedure
1. Defining individual construct: First, we have to define the individual constructs. The first
step involves the procedure that defines constructs theoretically. This involves a pretest to
evaluate the construct items, and a confirmatory test of the measurement model that is
conducted using confirmatory factor analysis (CFA), etc.
2. Developing the overall measurement model theory: In confirmatory factor analysis
(CFA), we should consider the concept of unidimensionality between construct error
variance and within construct error variance. At least four constructs and three items per
constructs should be present in the research.
3. Designing a study to produce the empirical results: The measurement model must be
specified. Most commonly, the value of one loading estimate should be one per construct.
Two methods are available for identification; the first is rank condition, and the second is
order condition.
4. Assessing the measurement model validity: Assessing the measurement model validity
occurs when the theoretical measurement model is compared with the reality model to see
how well the data fits. To check the measurement model validity, the number of the
indicator helps us. For example, the factor loading latent variable should be greater than
0.7. Chi-square test and other goodness of fit statistics like RMR, GFI, NFI, RMSEA, SIC,
BIC, etc., are some key indicators that help in measuring the model validity.
Questions a CFA answers
From my 20 question instrument, are the five factors clearly identifiable constructs as measured by
the 4 questions that they are comprised of?
Do my four survey questions accurately measure one factor?
Assumptions
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The assumptions of a CFA include multivariate normality, a sufficient sample size (n >200), the
correct a priori model specification, and data must come from a random sample.
Key Terms:
Theory: A systematic set of causal relationships that provide the comprehensive
explanation of a phenomenon.
Model: A specified set of dependent relationships that can be used to test the theory.
Path analysis: Used to test structural equations.
Path diagram: Shows the graphical representation of cause and effect relationships of the
theory.
Endogenous variable: The resulting variables that are a causal relationship.
Exogenous variable: The predictor variables.
Confirmatory analysis: Used to test the pre-specified relationship.
Cronbach’s alpha: Used to measure the reliability of two or more construct indicators.
Identification: Used to test whether or not there are a sufficient number of equations to
solve the unknown coefficient. Identifications are of three types: (1) under-identified, (2)
exact identified, and (3) over-identified.
Goodness of fit: The degree to which the observed input matrix is predicted by the
estimated model.
Latent variables: Variables that are inferred, not directly observed, from other variables
that are observed.
Confirmatory factor analysis (CFA) and statistical software:
Usually, statistical software like AMOS, LISREL, EQS and SAS are used for confirmatory factor
analysis. In AMOS, visual paths are manually drawn on the graphic window and analysis is
performed. In LISREL, confirmatory factor analysis can be performed graphically as well as from
the menu. In SAS, confirmatory factor analysis can be performed by using the programming
languages.
Related Pages:
Exploratory Factor Analysis
Sample Size
SPSS Manual
To Reference This Page:
Statistics Solutions. (2013). Confirmatory Factor Analysis [WWW Document]. Retrieved from http://
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www.statisticssolutions.com/academic-solutions/resources/directory-of-statistical-
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