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Likelihood analysis for a class of beta mixed models

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  • Wagner Hugo Bonat
  • Paulo Justiniano Ribeiro
  • Walmes Marques Zeviani

Abstract

Beta regression is a suitable choice for modelling continuous response variables taking values on the unit interval. Data structures such as hierarchical, repeated measures and longitudinal typically induce extra variability and/or dependence and can be accounted for by the inclusion of random effects. In this sense, Statistical inference typically requires numerical methods, possibly combined with sampling algorithms. A class of Beta mixed models is adopted for the analysis of two real problems with grouped data structures. We focus on likelihood inference and describe the implemented algorithms. The first is a study on the life quality index of industry workers with data collected according to an hierarchical sampling scheme. The second is a study assessing the impact of hydroelectric power plants upon measures of water quality indexes up, downstream and at the reservoirs of the dammed rivers, with a nested and longitudinal data structure. Results from different algorithms are reported for comparison including from data-cloning, an alternative to numerical approximations which also allows assessing identifiability. Confidence intervals based on profiled likelihoods are compared with those obtained by asymptotic quadratic approximations, showing relevant differences for parameters related to the random effects. In both cases, the scientific hypothesis of interest was investigated by comparing alternative models, leading to relevant interpretations of the results within each context.

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  • 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.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:2:p:252-266
    DOI: 10.1080/02664763.2014.947248
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    References listed on IDEAS

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    2. Guillermo Ferreira & Jorge Figueroa-Zúñiga & Mário Castro, 2015. "Partially linear beta regression model with autoregressive errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 752-775, December.
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    5. Lucas Couri & Raydonal Ospina & Geiza da Silva & Víctor Leiva & Jorge Figueroa-Zúñiga, 2022. "A Study on Computational Algorithms in the Estimation of Parameters for a Class of Beta Regression Models," Mathematics, MDPI, vol. 10(3), pages 1-17, January.

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