SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

Contributions: Abstract

Model selection in Structural Equation Models when the usual assumptions are violated

Ab Mooijaart
University of Leiden
The Netherlands

Model selection is one of the most important issues in Structural Equation Models (SEM). This selection is mostly based on goodness-of-fit measures. Computer packages like LISREL or EQS print out many such measures. A few of these measures do have a known statistical distribution when some statistical assumptions hold. The most common assumptions are that the variables are normally distributed and the sample size is large.

However, in most practical situations one or both assumptions do not hold. In this paper it will be shown that using some resampling technique, like a variant of the bootstrap, may lead to a procedure that would allow to decide whether a model holds or not. The basic feature of this procedure is that data are resampled under the condition that the model holds.

It will be shown by examples that for some well-known SEM models the procedure leads to a test with a proper type I error, under which conditions the test yields a good statistical power.