SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

Contributions: Abstract

Testing differences between covariance structure models: power analysis and null hypotheses

Robert MacCallumLi Cai
University of North Carolina
Michael W. Browne
Ohio State University

In applications of structural equation modeling and related methods it is common for researchers to seek to evaluate competing alternative models and to identify which among two or more models is optimal in some sense. For comparing nested models, the standard procedure is to employ the likelihood ratio test of the difference in model fit, where the null hypothesis is that the two models fit equally well in the population.

A procedure for determining the statistical power of this test will be presented, and factors that affect statistical power will be delineated. In addition, a modification of the standard point null hypothesis of zero difference in fit will be proposed.

It can be argued that in practice this null hypothesis is virtually never true and is empirically uninteresting. A modified testing procedure will be presented that allows for an interval null hypothesis of a specified small difference in fit, versus an alternative hypothesis of a larger difference, along with corresponding power analysis procedures.