SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

Contributions: Abstract

Categorical endogenous variables are common in social science research. These might be indicators of latent variables or single outcome variables. The dominant approach in structural equation models (SEMs) is to estimate the tetrachoric, polychoric, and polyserial correlations between the continuous latent indicators that underlie these categorical variables and any continuous observed variables. Then researchers use one of several iterative estimators that make use of the asymptotic covariance matrix of these correlations as a weight matrix in order to estimate the parameters in the SEM. This paper presents a Polychoric Two Stage Least Squares (P2SLS) estimator. It also derives the asymptotic properties of the estimator and illustrates it with an empirical example that compares this new estimator to other estimators for SEMs with categorical variables.