Decomposing model fit: measurement vs. theory in organizational research using latent variables

Goodness-of-fit indices have an important role in structural equation model evaluation. However, some studies (e.g., McDonald & Ho, 2002; Mulaik et al., 1989) have raised concerns that overall fit values primarily reflect the fit of the measurement model, and this allows significant misspecification among the latent variables to be masked. Using an approach analogous to Anderson and Gerbing's (1988) 2-step approach that isolates the measurement component of a composite model, we present the rationale and evidence for the root mean square error of approximation of the path component (RMSEA-P), a relatively new fit index that isolates the path component. We reviewed 5 of the top organizational behavior/human resources journals from 2001 to 2008 and identified 43 studies using structural equation modeling in which the overall composite model could be decomposed into its measurement and path components. The RMSEA-P for these studies generally showed unfavorable results, with many values failing to meet commonly accepted standards. Incorporating the RMSEA-P and its confidence interval into James, Mulaik, and Brett's (1982) framework for model testing, we provide evidence that many of the conclusions based upon the goodness of fit of the overall model may be inaccurate. We conclude with recommendations for how researchers can focus more attention on path models and latent variable relations and improve their model evaluation process.