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Divisive Latent Class Modeling as a Density Estimation Method for Categorical Data

Author

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  • Daniël W. Palm

    (Cito)

  • L. Andries Ark

    (University of Amsterdam)

  • Jeroen K. Vermunt

    (Tilburg University)

Abstract

Traditionally latent class (LC) analysis is used by applied researchers as a tool for identifying substantively meaningful clusters. More recently, LC models have also been used as a density estimation tool for categorical variables. We introduce a divisive LC (DLC) model as a density estimation tool that may offer several advantages in comparison to a standard LC model. When using an LC model for density estimation, a considerable number of increasingly large LC models may have to be estimated before sufficient model-fit is achieved. A DLC model consists of a sequence of small LC models. Therefore, a DLC model can be estimated much faster and can easily utilize multiple processor cores, meaning that this model is more widely applicable and practical. In this study we describe the algorithm of fitting a DLC model, and discuss the various settings that indirectly influence the precision of a DLC model as a density estimation tool. These settings are illustrated using a synthetic data example, and the best performing algorithm is applied to a real-data example. The generated data example showed that, using specific decision rules, a DLC model is able to correctly model complex associations amongst categorical variables.

Suggested Citation

  • Daniël W. Palm & L. Andries Ark & Jeroen K. Vermunt, 2016. "Divisive Latent Class Modeling as a Density Estimation Method for Categorical Data," Journal of Classification, Springer;The Classification Society, vol. 33(1), pages 52-72, April.
    • Handle: RePEc:spr:jclass:v:33:y:2016:i:1:d:10.1007_s00357-016-9195-5
    DOI: 10.1007/s00357-016-9195-5
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    References listed on IDEAS

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    1. Linzer, Drew A., 2011. "Reliable Inference in Highly Stratified Contingency Tables: Using Latent Class Models as Density Estimators," Political Analysis, Cambridge University Press, vol. 19(2), pages 173-187, April.
    2. Herbert Hoijtink & Annelise Notenboom, 2004. "Model based clustering of large data sets: Tracing the development of spelling ability," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 481-498, September.
    3. Pascal Hattum & Herbert Hoijtink, 2009. "Market Segmentation Using Brand Strategy Research: Bayesian Inference with Respect to Mixtures of Log-Linear Models," Journal of Classification, Springer;The Classification Society, vol. 26(3), pages 297-328, December.
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    Cited by:

    1. Boeschoten Laura & Oberski Daniel & de Waal Ton, 2017. "Estimating Classification Errors Under Edit Restrictions in Composite Survey-Register Data Using Multiple Imputation Latent Class Modelling (MILC)," Journal of Official Statistics, Sciendo, vol. 33(4), pages 921-962, December.
    2. Douglas L. Steinley, 2018. "Editorial," Journal of Classification, Springer;The Classification Society, vol. 35(1), pages 1-4, April.

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