Abstract
In this chapter, we review the intimately related concepts of estimation and testing of structural equation models. We also make recommenda- tions about the usefulness of some of the alternatives that are available. Because the existing literature on these topics is not very thorough and is ambiguous in its results, we conducted our own study to provide a solid foundation for our recommendations. The structural equation model represents a series of hypotheses about how the variables in the analysis are generated and related. The parameters of the model are the regression coefficients and the vari- ances and covariances of independent variables, as will be seen below. These parameters are fundamental to interpreting the model, but they are not known and need to be estimated from the data. Thus estimation is a logical first step in the modeling process after model specification. The statistical test of the adequacy of a model, or the goodness-of-fit test statistic, is obtained simultaneously with the estimation. A goodness- of-fit test statistic indicates the similarity between the covariance ma- trix based on the estimated model, Σ(), and the population covariance matrix, Σ, from which a sample has been drawn.
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