A metric measure for direct comparison of competing models in covariance structure analysis

Comparing the fit of alternative models has become a standard procedure for analyzing covariance structure analysis. Comparison of alternative models is typically accomplished by examining the fit of each model to sample data. It is argued that rather than using this indirect approach, one should do direct comparisons of the similarities and differences among competing models. It is shown that among the existing goodness-of-fit indexes, the root mean square residual (RMSR) is the only one that can be used for this purpose. However, the RMSR fails to satisfy some important statistical desiderata. Rao's Distance (RD), an alternate measure, is shown to overcome this limitation of RMSR. The preference for RD over RMSR for model comparisons is illustrated through a detailed analysis of a particular sample of multitrait-multimethod data. A simulation study conducted to empirically investigate the sampling behavior of RD reveals that the true orderings of intermodel proximities are recovered (on average) with a fair degree of accuracy.