We study the properties of a three-step approach to estimating the parameters of a latent structure model for categorical data and propose a simple correction for a common source of bias. Such models have a measurement part (essentially the latent class model) and a structural (causal) part (essentially a system of logit equations). In the three-step approach, a stand-alone measurement model is first defined and its parameters are estimated. Individual predicted scores on the latent variables are then computed from the parameter estimates of the measurement model and the individual observed scoring patterns on the indicators. Finally, these predicted scores are used in the causal part and treated as observed variables. We show that such a naive use of predicted latent scores cannot be recommended since it leads to a systematic underestimation of the strength of the association among the variables in the structural part of the models. However, a simple correction procedure can eliminate this systematic bias. This approach is illustrated on simulated and real data. A method that uses multiple imputation to account for the fact that the predicted latent variables are random variables can produce standard errors for the parameters in the structural part of the model.

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Our results indicate that the multiple PS method is a feasible method to adjust for observed pretreatment differences in nonrandomized studies where the number of pretreatment differences is large and multiple treatments are compared.

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A basic assumption of latent structure models is that of local independence: given the score on the latent variable, the scores on the manifest variables are independent of each other. This basic assumption is violated when test-retest effects, response consistency effects, correlated response errors, and so forth are present. However, it is possible to reformulate the latent class model in such a way that these direct relations between the indicators (manifest variables) can be accounted for. The reformulation proposed here, takes place within the framework of log-linear modeling.