Construction Principles for Latent Trait Models

Abstract

Linear models in social science, psychlology, economics, and epidemiology are often formullated in latent continuous variables, which can be measured only with error or through two or more observed indicators. Henice, the latent variables are connected with the observed variables by a measurement model. If the observed indicators are metric, the covariance matrix of the observed variables is analyzed by using covariance structure models. Covariance structure models have been extended by MuthMn (1984) to deal with indicators that are metric and ordered categorical rather than metric alone. By abandoning the analysis of covariance structures and returning to some of the original ideas of latent structure analysis, we can extend the class of variables that may serve as indicators for latent variables utsed in a simultaneous equation system to include variables on any level of measurement. This class comprises observed variables that may be metric, censored metric, counts, ordered, or unordered categorical. A limited marginal maximum likelihood approach is used to estimate the model. Numerical procedures necessary to implement such an estimation are discussed.