The Relationship Between the Standardized Root Mean Square Residual and Model Misspecification in Factor Analysis Models

We argue that the definition of close fitting models should embody the notion of substantially ignorable misspecifications (SIM). A SIM model is a misspecified model that might be selected, based on parsimony, over the true model should knowledge of the true model be available. Because in applications the true model (i.e., the data generating mechanism) is unknown, we investigate the relationship between the population standardized root mean square residual (SRMR) values and various model misspecifications in factor analysis models to better understand the magnitudes of the SRMR. Summary effect sizes of misfit such as the SRMR are necessarily insensitive to some non-ignorable localized misspecifications (i.e., the presence of a few large residual correlations in large models). Localized misspecifications may be identified by examining the largest standardized residual covariance. Based on the findings, our population reference values for close fit are based on a two-index strategy: (1) largest absolute value of standardized residual covariance <= 0.10, and (2) SRMR <= 0.05x the average R-2 of the manifest variables; for acceptable fit our values are 0.15 and 0.10x, respectively.