How and why is SEM used for confirmatory factor analysis, often as a preliminary step in SEM?
• When is a confirmatory factor analysis (CFA) model identified in SEM? CFA models in SEM have no causal paths (straight arrows in the diagram) connecting the latent variables. The latent variables may be allowed to correlate (oblique factors) or be constrained to 0 covariance (orthogonal factors). CFA analysis in SEM usually focuses on analysis of the error terms of the indicator variables (see previous question and answer). Like other models, CFA models in SEM must be identified for there to be a unique solution. In a standard CFA model each indicator is specified to load only on one factor, measurement error terms are specified to be uncorrelated with each other, and all factors are allowed to correlate with each other. One-factor standard models are identified if the factor has three or more indicators. Multi-factor standard models are identified if each factor has two or more indicators. Non-standard CFA models, where indicators load on multiple factors and/or measurement errors a
