The Impact of Partial Factorial Invariance on Cross-Group Comparisons

This study explored the impact of partial factorial invariance on cross-group comparisons of latent variables, including latent means, latent variances, structural relations (or correlations) with other constructs, and regression coefficients as predicting external variables. The results indicate that the estimates of factor mean differences are sensitive to violations of invariance on both factor loadings and intercepts. Noninvariant factor loadings were also found to influence the cross-group comparisons of factor variances and regression coefficients (slopes, in the raw metric) with external variables. However, cross-group comparisons of standardized slopes and interfactor correlations were not subject to noninvariance. Under conditions of partial invariance, we further compared the performance of four different model specification strategies. In general, fitting partially invariant models with all noninvariant parameters that were freely estimated yielded more accurate estimates of the parameters of interest. The implications of the major findings of this work, as well as recommendations and guidelines for future empirical researchers, are discussed below.