Model Misspecification and Invariance Testing Using Confirmatory Factor Analytic Procedures

Reporting practices in 194 confirmatory factor analysis studies (1,409 factor models) published in American Psychological Association journals from 1998 to 2006 were reviewed and compared with established reporting guidelines. Three research questions were addressed: (a) how do actual reporting practices compare with published guidelines? (b) how do researchers report model fit in light of divergent perspectives on the use of ancillary fit indices (e.g., L.-T. Hu & P. M. Bentler, 1999; H. W. Marsh, K.-T., Hau, & Z. Wen, 2004)? and (c) are fit measures that support hypothesized models reported more often than fit measures that are less favorable? Results indicate some positive findings with respect to reporting practices including proposing multiple models a priori and near universal reporting of the chi-square significance test. However, many deficiencies were found such as lack of information regarding missing data and assessment of normality. Additionally, the authors found increases in reported values of some incremental fit statistics and no statistically significant evidence that researchers selectively report measures of fit that support their preferred model. Recommendations for reporting are summarized and a checklist is provided to help editors, reviewers, and authors improve reporting practices.

Confirmatory factor analytic tests of measurement invariance (MI) based on the chi-square statistic are known to be highly sensitive to sample size. For this reason, G. W. Cheung and R. B. Rensvold (2002) recommended using alternative fit indices (AFIs) in MI investigations. In this article, the authors investigated the performance of AFIs with simulated data known to not be invariant. The results indicate that AFIs are much less sensitive to sample size and are more sensitive to a lack of invariance than chi-square-based tests of MI. The authors suggest reporting differences in comparative fit index (CFI) and R. P. McDonald's (1989) noncentrality index (NCI) to evaluate whether MI exists. Although a general value of change in CFI (.002) seemed to perform well in the analyses, condition specific change in McDonald's NCI values exhibited better performance than a single change in McDonald's NCI value. Tables of these values are provided as are recommendations for best practices in MI testing. PsycINFO Database Record (c) 2008 APA, all rights reserved.