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Inferential Tools for Assessing Dependence Across Response Categories in Multinomial Models with Discrete Random Effects

Author

Listed:
  • Chiara Masci

    (Politecnico di Milano)

  • Francesca Ieva

    (Politecnico di Milano
    Human Technopole)

  • Anna Maria Paganoni

    (Politecnico di Milano)

Abstract

We propose a discrete random effects multinomial regression model to deal with estimation and inference issues in the case of categorical and hierarchical data. Random effects are assumed to follow a discrete distribution with an a priori unknown number of support points. For a K-categories response, the modelling identifies a latent structure at the highest level of grouping, where groups are clustered into subpopulations. This model does not assume the independence across random effects relative to different response categories, and this provides an improvement from the multinomial semi-parametric multilevel model previously proposed in the literature. Since the category-specific random effects arise from the same subjects, the independence assumption is seldom verified in real data. To evaluate the improvements provided by the proposed model, we reproduce simulation and case studies of the literature, highlighting the strength of the method in properly modelling the real data structure and the advantages that taking into account the data dependence structure offers.

Suggested Citation

  • Chiara Masci & Francesca Ieva & Anna Maria Paganoni, 2024. "Inferential Tools for Assessing Dependence Across Response Categories in Multinomial Models with Discrete Random Effects," Journal of Classification, Springer;The Classification Society, vol. 41(3), pages 591-619, November.
    • Handle: RePEc:spr:jclass:v:41:y:2024:i:3:d:10.1007_s00357-024-09466-2
    DOI: 10.1007/s00357-024-09466-2
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    References listed on IDEAS

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    1. Harvey Goldstein & Jon Rasbash, 1996. "Improved Approximations for Multilevel Models with Binary Responses," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 159(3), pages 505-513, May.
    2. Hadfield, Jarrod D., 2010. "MCMC Methods for Multi-Response Generalized Linear Mixed Models: The MCMCglmm R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i02).
    3. Chiara Masci & Anna Maria Paganoni & Francesca Ieva, 2019. "Semiparametric mixed effects models for unsupervised classification of Italian schools," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1313-1342, October.
    4. Tutz, Gerhard & Hennevogl, Wolfgang, 1996. "Random effects in ordinal regression models," Computational Statistics & Data Analysis, Elsevier, vol. 22(5), pages 537-557, September.
    5. Germáan Rodríguez & Noreen Goldman, 1995. "An Assessment of Estimation Procedures for Multilevel Models with Binary Responses," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 158(1), pages 73-89, January.
    6. Chiara Masci & Francesca Ieva & Tommaso Agasisti & Anna Maria Paganoni, 2021. "Evaluating class and school effects on the joint student achievements in different subjects: a bivariate semiparametric model with random coefficients," Computational Statistics, Springer, vol. 36(4), pages 2337-2377, December.
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