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A Note on Applying the BCH Method Under Linear Equality and Inequality Constraints

Author

Listed:
  • L. Boeschoten

    (Tilburg University
    Statistics Netherlands)

  • M. A. Croon

    (Tilburg University)

  • D. L. Oberski

    (Utrecht University)

Abstract

Researchers often wish to relate estimated scores on latent variables to exogenous covariates not previously used in analyses. The BCH method corrects for asymptotic bias in estimates due to these scores’ uncertainty and has been shown to be relatively robust. When applying the BCH approach however, two problems arise. First, negative cell proportions can be obtained. Second, the approach cannot deal with situations where marginals need to be fixed to specific values, such as edit restrictions. The BCH approach can handle these problems when placed in a framework of quadratic loss functions and linear equality and inequality constraints. This research note gives the explicit form for equality constraints and demonstrates how solutions for inequality constraints may be obtained using numerical methods.

Suggested Citation

  • L. Boeschoten & M. A. Croon & D. L. Oberski, 2019. "A Note on Applying the BCH Method Under Linear Equality and Inequality Constraints," Journal of Classification, Springer;The Classification Society, vol. 36(3), pages 566-575, October.
    • Handle: RePEc:spr:jclass:v:36:y:2019:i:3:d:10.1007_s00357-018-9298-2
    DOI: 10.1007/s00357-018-9298-2
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    References listed on IDEAS

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    1. Vermunt, Jeroen K., 2010. "Latent Class Modeling with Covariates: Two Improved Three-Step Approaches," Political Analysis, Cambridge University Press, vol. 18(4), pages 450-469.
    2. Bolck, Annabel & Croon, Marcel & Hagenaars, Jacques, 2004. "Estimating Latent Structure Models with Categorical Variables: One-Step Versus Three-Step Estimators," Political Analysis, Cambridge University Press, vol. 12(1), pages 3-27, January.
    3. 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.
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