Should We Use F -Tests for Model Fit Instead of Chi-Square in Overidentified Structural Equation Models?

Abstract

Debate continues about whether the likelihood ratio test (T _ML) or goodness-of-fit indices are most appropriate for assessing data-model fit in structural equation models. Though potential advantages and disadvantages of these methods with large samples are often discussed, shortcomings concomitant with smaller samples are not. This article aims to (a) highlight the broader small sample issues with both approaches to data-model fit assessment, (b) note that what constitutes a small sample is common in empirical studies (approximately 20% to 50% in review studies, depending on the definition of “small”), and (c) more widely introduce F-tests as a desirable alternative than the traditional T _ML tests, small-sample corrections, or goodness-of-fit indices with smaller samples. Both goodness-of-fit indices and comparing T _ML to a chi-square distribution at smaller samples leads to overrejection of well-fitting models. Simulations and example analyses show that F-tests yield more desirable statistical properties—with or without normality—than standard approaches like chi-square tests or goodness-of-fit indices with smaller samples, roughly defined as N < 200 or N: df < 3.