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

Bolck, Annabel, Croon, Marcel, Hagenaars, Jacques·2004·Political Analysis

DOI 10.1093/pan/mph001

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Abstract

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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Authors: Bolck, A., Croon, M., & Hagenaars, J.
Affiliations: Netherlands Forensic Institute (NL)
Tilburg University (NL)
Venue: Political Analysis
Publisher: Cambridge University Press (CUP)
Published: 2004
Volume: 12
Issue: 1
Pages: 3-27
ISSN: 1047-1987 (ISSN-L)
1476-4989
DOI: 10.1093/pan/mph001
OpenAlex: W2061736358
Cited by: 1,406
References: 39
Citations by year: 2026: 284 · 2025: 186 · 2024: 148 · 2023: 140 · 2022: 131 · 2021: 130 · 2020: 95 · 2019: 74 · 2018: 62 · 2017: 43 · 2016: 38 · 2015: 24 · 2014: 14 · 2013: 14 · 2012: 4
FWCI: 3.15
Type: journal article
Language: en
Open access: closed
Licence: www.cambridge.org/core/terms (unspecified, 4752 d)
Locations: Political Analysis (publishedVersion)
Research portal (Tilburg University) (publishedVersion)
Data Archiving and Networked Services (DANS) (submittedVersion)
RePEc: Research Papers in Economics (submittedVersion)
Topics: Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Economic and Environmental Valuation
Keywords: latent structure models, categorical data, latent class models, one-step estimation, bias correction, measurement model, structural equation modeling, multiple imputation, standard errors, associative strength

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

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