For all models, a variety of global fit indices was used, including indices of absolute fit, indices of relative fit, and indices of fit with a penalty function for lack of parsimony. These include the traditional overall chi-square test of model fit (which should be statistically nonsignificant) and the following statistical criteria: the root mean square error of approximation (RMSEA, <0.08; McDonald & Ho, 2002; but see Hu & Bentler, 1998), the Test of Close Fit (p > .05), the comparative fit index (CFI > 0.95), and the standardized root mean square residual (S-RMR, <0.07). The stepwise testing of improvement of fit in the nested models was based on additional absolute model fit indices: the Akaike information criterion (AIC = −2 × model log-likelihood + 2 × number of model parameters), the Bayesian information criterion (BIC = −2 × model log-likelihood + log(n) × number of model parameters), and the sample-size adjusted BIC (i.e., the adjusted BIC). Low values for the AIC, BIC, and adjusted BIC indicate a good-fitting model (Muthén & Muthén, 2008). In addition to the global fit
