Estimating Latent Structure Models with Categorical Variables: One-Step Versus Three-Step Estimators

Political Analysis - Tập 12 Số 1 - Trang 3-27 - 2004
Annabel Bolck1, Marcel A. Croon2, Jacques A. Hagenaars2
1Netherlands Forensic Institute, 2288 GD Rijswijk, The Netherlands#N#
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2Department of Statistics and Methodology, Faculty of Social Sciences, Tilburg University, 5000 LE Tilburg, The Netherlands#N#
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Tóm tắt

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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Occasionally a third approach is proposed in which, first, an appropriate “stand-alone” measurement model is defined and its parameters are estimated. In the next step, the parameters of the causal model are estimated with the parameters of the measurement model fixed to their values obtained in the first step. This two-step approach will not be discussed further in this paper.

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Political Analysis

Tập 12 Số 1

3-27

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