The Robustness of LISREL Estimates in Structural Equation Models with Categorical Variables

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Abstract
This study was an examination of the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical manifest variables. Two types of correlation matrices were analyzed: one containing Pearson product moment correlations and one containing tetrachoric, polyserial, and product moment correlations as appropriate. Using continuous variables generated according to the equations defining the population model, three cases were considered by dichotomizing some of the variables with varying degrees of skewness. When Pearson product moment correlations were used to estimate associations involving dichotomous variables, the structural parameter estimates were biased when skewness was present in the dichotomous variables. Moreover, the degree of bias was consistent for both the maximum likelihood and unweighted least squares estimates. The analysis of mixed matrices produced average estimates that more closely approximated the model parameters except in the case where the dichotomous variables were skewed in opposite directions.