Goodness-of-fit indexes in confirmatory factor analysis: The effect of sample size.

Abstract

In confirmatory factor analysis, hypothesized models reflect approximations to reality so that any model can be rejected if the sample size is large enough. The appropriate question is whether the fit is adequate to support the model, and a large number of fit indexes have been proposed for this purpose. In the present article, we examine the influence of sample size on different fit indexes for both real and simulated data. Contrary to claims by Bentler and Bonett (1980), their incremental fit index was substantially affected by sample size. Contrary to claims by Joreskog and Sorbom (1981), their goodness-of-ftt indexes provided by LISREL were substantially affected by sample size. Contrary to claims by Bollen (1986), his new incremental fit index was substantially affected by sample size. Hoelter's (1983) critical N index was also substantially affected by sample size. Of the more than 30 indexes considered, the Tucker-Lewis (1973) index was the only widely used index that was relatively independent of sample size. However, four new indexes based on the same form as the Tucker-Lewis index were also relatively independent of sample size. The purpose of the present investigation was to examine the influence of sample size on goodness-of-f it indicators used in confirmatory factor analysis (CFA). Although the present inves- tigation was limited to CFA, the problems, issues, and most of the results generalize to the analysis of covariance structures. The advantages of CFA are well-known, and numerous intro- ductions to the LISREL approach used in the present investiga- tion are available elsewhere (e.g., Bagozzi, 1980; Joreskog &