Confirmatory factor analysis (CFA) and exploratory factor analysis (EFA), as they are typically used, test different models of the relations among variables. CFA tests the latent variable model. A typical CFA is structured such that each hypothesized factor is represented by multiple, corresponding indicators. When there are multiple latent variables in a model (i.e., multiple factors), typical CFA models are testing the view that each factor's indicators are expressions of that factor and of no other factor; loadings from the latent variable to indicators of other variables are fixed to zero. Indicators of that factor are specified not to correlate with other factors, and the degree to which that specification accords with the data is evaluated with model fit indexes. Thus, the model to be tested specifies that each latent variable is homogeneous.
