A New Incremental Fit Index for General Structural Equation Models

TLDR

Assessing overall model fit is crucial in general structural equation models, where Bentler and Bonett's (1980) normed index is widely used. The article proposes a new incremental fit measure that adjusts the normed index for sample size and degrees of freedom, explains its relation to other fit indices, and demonstrates its properties with an empirical example and Monte Carlo simulation. The authors derive this measure by modifying the normed index, compare it to other indices, and validate it through simulation and an empirical example. Simulations show the new measure’s mean remains near one across sample sizes and its standard deviation is lower than other indices, while empirical data confirm its stability across samples, indicating it is a useful complement to existing fit measures.

Abstract

Assessing overall model fit is an important problem in general structural equation models. One of the most widely used fit measures is Bentler and Bonett's (1980) normed index. This article has three purposes: (1) to propose a new incremental fit measure that provides an adjustment to the normed index for sample size and degrees of freedom, (2) to explain the relation between this new fit measure and the other ones, and (3) to illustrate its properties with an empirical example and a Monte Carlo simulation. The simulation suggests that the mean of the sampling distribution of the new fit measure stays at about one for different sample sizes whereas that for the normed fit index increases with N. In addition, the standard deviation of the new measure is relatively low compared to some other measures (e.g., Tucker and Lewis's (1973) and Bentler and Bonett's (1980) nonnormed index). The empirical example suggests that the new fit measure is relatively stable for the same model in different samples. In sum, it appears that the new incremental measure is a useful complement to the existing fit measures.