On specifying the null model for incremental fit indices in structural equation modeling.

TLDR

Incremental fit indices compare a substantive model to a null model, yet the standard null model often yields improper comparisons because it unconstrains variance (and mean) of each manifest variable. The authors aim to explain how to formulate an acceptable, modified null model, predict changes in fit index values, provide illustrative examples, and discuss implications for theory and practice. They develop a modified null model, predict its effect on incremental fit indices, illustrate the changes with examples, and analyze the implications for structural equation modeling. When the standard null model is improper, software‑reported incremental fit indices have no interpretation and should be disregarded.

Abstract

In structural equation modeling, incremental fit indices are based on the comparison of the fit of a substantive model to that of a null model. The standard null model yields unconstrained estimates of the variance (and mean, if included) of each manifest variable. For many models, however, the standard null model is an improper comparison model. In these cases, incremental fit index values reported automatically by structural modeling software have no interpretation and should be disregarded. The authors explain how to formulate an acceptable, modified null model, predict changes in fit index values accompanying its use, provide examples illustrating effects on fit index values when using such a model, and discuss implications for theory and practice of structural equation modeling.