Mplus Users Guide v6.. - Muthén & Muthén

Examples: Confirmatory Factor Analysis AndStructural Equation ModelingCHAPTER 5EXAMPLES: CONFIRMATORYFACTOR ANALYSIS ANDSTRUCTURAL EQUATIONMODELINGConfirmatory factor analysis (CFA) is used to study the relationshipsbetween a set of observed variables and a set of continuous latentvariables. When the observed variables are categorical, CFA is alsoreferred to as item response theory (IRT) analysis (Baker & Kim, 2004;du Toit, 2003). CFA with covariates (MIMIC) includes models wherethe relationship between factors and a set of covariates are studied tounderstand measurement invariance and population heterogeneity.These models can include direct effects, that is, the regression of a factorindicator on a covariate in order to study measurement non-invariance.Structural equation modeling (SEM) includes models in whichregressions among the continuous latent variables are estimated (Bollen,1989; Browne & Arminger, 1995; Joreskog & Sorbom, 1979). In all ofthese models, the latent variables are continuous. Observed dependentvariable variables can be continuous, censored, binary, orderedcategorical (ordinal), unordered categorical (nominal), counts, orcombinations of these variable types.CFA is a measurement model. SEM has two parts: a measurementmodel and a structural model. The measurement model for both CFAand SEM is a multivariate regression model that describes therelationships between a set of observed dependent variables and a set ofcontinuous latent variables. The observed dependent variables arereferred to as factor indicators and the continuous latent variables arereferred to as factors. The relationships are described by a set of linearregression equations for continuous factor indicators, a set of censorednormal or censored-inflated normal regression equations for censoredfactor indicators, a set of probit or logistic regression equations forbinary or ordered categorical factor indicators, a set of multinomiallogistic regression equations for unordered categorical factor indicators,51