Testing structural equation models: the impact of error variances in the data generating process

Abstract

Yet another paper on fit measures? To our knowledge, very few papers discuss how fit measures are affected by error variance in the Data Generating Process (DGP). The present paper deals with this. Based upon an extensive simulation study, this paper shows that the effects of increased error variance differ significantly for various fit measures. In addition to error variance the effects depend on sample size and severity of misspecification. The findings confirm the general notion that good fit as measured by the chi-square, RMSEA and GFI etc. does not necessarily mean that the model is correctly specified and reliable. One finding is that the chi square test may give support to misspecified models in situations with a high level of error variance in the DGP, for small sample sizes. Another finding is that the chi-square test looses power also for large sample sizes when the model is negligible misspecified. Other results include incremental fit indices as NFI and RFI which prove to be more informative indicators under these circumstances. At the end of the paper we formulate some guidelines for use of different fit measures.