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Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution

Author

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  • Jay Verkuilen

    (City University of New York)

  • Michael Smithson

    (The Australian National University)

Abstract

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite poorly modeled by the normal distribution. The authors extend the beta-distributed generalized linear model (GLM) proposed in Smithson and Verkuilen (2006) to discrete and continuous mixtures of beta distributions, which enables modeling dependent data structures commonly found in real settings. The authors discuss estimation using both deterministic marginal maximum likelihood and stochastic Markov chain Monte Carlo (MCMC) methods. The results are illustrated using three data sets from cognitive psychology experiments.

Suggested Citation

  • Jay Verkuilen & Michael Smithson, 2012. "Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution," Journal of Educational and Behavioral Statistics, , vol. 37(1), pages 82-113, February.
    • Handle: RePEc:sae:jedbes:v:37:y:2012:i:1:p:82-113
    DOI: 10.3102/1076998610396895
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    Cited by:

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    2. Wagner Hugo Bonat & Paulo Justiniano Ribeiro & Walmes Marques Zeviani, 2015. "Likelihood analysis for a class of beta mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 252-266, February.
    3. Hu, Hao & Yao, Weixin & Wu, Yichao, 2017. "The robust EM-type algorithms for log-concave mixtures of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 14-26.
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    5. Phillip Li, 2018. "Efficient MCMC estimation of inflated beta regression models," Computational Statistics, Springer, vol. 33(1), pages 127-158, March.

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