# Marketing Chapter 5

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Examples: Confirmatory Factor Analysis And Structural Equation Modeling

CHAPTER 5

EXAMPLES: CONFIRMATORY FACTOR ANALYSIS AND STRUCTURAL EQUATION MODELING
Confirmatory factor analysis (CFA) is used to study the relationships between a set of observed variables and a set of continuous latent variables. When the observed variables are categorical, CFA is also referred to as item response theory (IRT) analysis (Baker & Kim, 2004; du Toit, 2003). CFA with covariates (MIMIC) includes models where the relationship between factors and a set of covariates are studied to understand measurement invariance and population heterogeneity. These models can include direct effects, that is, the regression of a factor indicator on a covariate in order to study measurement non-invariance. Structural equation modeling (SEM) includes models in which regressions among the continuous latent variables are estimated (Bollen, 1989; Browne & Arminger, 1995; Joreskog & Sorbom, 1979). In all of these models, the latent variables are continuous. Observed dependent variable variables can be continuous, censored, binary, ordered categorical (ordinal), unordered categorical (nominal), counts, or combinations of these variable types. CFA is a measurement model. SEM has two parts: a measurement model and a structural model. The measurement model for both CFA and SEM is a multivariate regression model that describes the relationships between a set of observed dependent variables and a set of continuous latent variables. The observed dependent variables are referred to as factor indicators and the continuous latent variables are referred to as factors. The relationships are described by a set of linear regression equations for continuous factor indicators, a set of censored normal or censored-inflated normal regression equations for censored factor indicators, a set of probit or logistic

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