A Fit Index to Assess Model Fit and Detect Omitted Terms in Nonlinear SEM

Abstract

A new descriptive fit measure, the Homoscedastic Fit Index (HFI), is proposed to detect omitted nonlinear terms (quadratic and interaction terms) in SEM by analyzing the dispersion of the residuals in the structural part of the model. The HFI is defined as a descriptive goodness-of-fit index for SEM. The Type I error rates of the HFI and the power to detect heteroscedasticity due to omitted nonlinear terms or nonnormally distributed variables are investigated in a Monte Carlo study. The results show that the new measure performs satisfactorily with regard to Type I error rates and power when sample size was sufficiently large. It is investigated under what conditions the Type I error rate was inflated. Nonnormally distributed error terms resulted in high power. Nonnormally distributed predictors had no influence on the Type I error rates.

Keywords:

• descriptive fit index
• homoscedasticity
• Monte Carlo study
• nonlinear SEM

FUNDING

This research was supported by Grant No. SCHE1412-1/1 from the German Research Foundation (DFG).

Notes

¹ Examples of measures based on model comparisons are the nonnormed fit index (NNFI/TLI, Bentler & Bonett, 1980; Tucker & Lewis, 1973), the normed fit index (NFI, Bentler & Bonett, 1980), the comparative fit index (CFI, Bentler, 1990), the goodness-of-fit index (GFI, Jöreskog & Sörbom, 1989; Tanaka & Huba, 1984), and the adjusted goodness-of-fit index (AGFI, Jöreskog & Sörbom, 1989).

Additional information

Funding

This research was supported by Grant No. SCHE1412-1/1 from the German Research Foundation (DFG).