Model Fit

How well does a theoretical model fit a data set? For confirmatory factor analysis and structural equation modeling, this question is answered using fit indices, a process known as goodness-of-fit. The estimation of fit indices is based on testing the null hypothesis of Σ = Σ (θ). A test statistic allows the testing of the null hypothesis that the model specified by the researcher [Σ] leads to a reproduction of the population covariance matrix of the observed variables [Σ (θ)] and a comparison of the fit of other various models. To assess this goodness-of-fit, various fit indices—absolute and relative fit indices—have been developed (see Table 1).