In statistics, confirmatory factor analysis (CFA) is a special form of factor analysis. It is used to assess the number of factors and the loadings of variables. In contrast to exploratory factor analysis, where all loadings are free to vary, CFA allows for the explicit constraint of certain loadings to be zero. CFA has built upon and replaced older methods of analyzing construct vailidity such as the MTMM Matrix as described in Campbell & Fiske (1959).
A typical example of a CFA on a 50 item personality test that claimed to be measuring the Big_Five_personality_traits, might assess the fit of the proposed model. A model could be developed that assumed structure, where each item loads on only one factor. The correlations between latent factors could be free to vary or they could be constrained to be zero. Model fit measures could then be obtained to assess how well the proposed model captured the covariance between all the items on the test. If the fit is poor, it may be due to some items measuring multiple factors. It might also be that some items within a factor are more related to each other than others.
Structural Equation Modeling software is typically used for performing the analysis. CFA is also frequently used as a first step to assess the proposed measurement model in a Structural Equation Model. Many of the rules of interpretation regarding assessment of model fit and model modification in Structural Equation Modeling apply equally to CFA. CFA is distinguished from Structural Equation Modeling by the fact that in CFA, there are no directed arrows between latent factors.