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Maximum likelihood estimation and parameter interpretation in elliptical mixed logistic regression

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  • Cristiano C. Santos

    (Universidade Federal de Minas Gerais)

  • Rosangela H. Loschi

    (Universidade Federal de Minas Gerais)

Abstract

We introduce the class of elliptical mixed logistic model with focus on the normal/independent subclass. Parameter interpretation in mixed logistic model is not straightforward since the odds ratio is random. For the proposed models, we obtain the odds ratio distribution and its summaries used to interpret the fixed effects and to measure the heterogeneity among the clusters thus extending previous results. Fisher information is also obtained. A Monte Carlo expectation-maximization algorithm is considered to obtain the maximum likelihood estimates. A simulation study is performed comparing normal and heavy-tailed models. It also address the effect of the misspecification of the random effect distribution and other model aspects in the parameter interpretation. A data analysis is performed showing the utility of heavy-tailed mixed logistic model. Among the main conclusions, we note that the misspecification of the random effect distribution influences the fixed effects interpretation and the quantification of the among clusters heterogeneity.

Suggested Citation

  • Cristiano C. Santos & Rosangela H. Loschi, 2017. "Maximum likelihood estimation and parameter interpretation in elliptical mixed logistic regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 209-230, March.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:1:d:10.1007_s11749-016-0507-1
    DOI: 10.1007/s11749-016-0507-1
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    References listed on IDEAS

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    1. Bates, Douglas & Mächler, Martin & Bolker, Ben & Walker, Steve, 2015. "Fitting Linear Mixed-Effects Models Using lme4," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 67(i01).
    2. Klaus Larsen & Jørgen Holm Petersen & Esben Budtz-Jørgensen & Lars Endahl, 2000. "Interpreting Parameters in the Logistic Regression Model with Random Effects," Biometrics, The International Biometric Society, vol. 56(3), pages 909-914, September.
    3. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    4. Thomas R. Ten Have & A. Russell Localio, 1999. "Empirical Bayes Estimation of Random Effects Parameters in Mixed Effects Logistic Regression Models," Biometrics, The International Biometric Society, vol. 55(4), pages 1022-1029, December.
    5. Aparecida Souza & Helio Migon, 2010. "Bayesian outlier analysis in binary regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(8), pages 1355-1368.
    6. Amy E. Wagler, 2014. "Confidence Intervals for Assessing Heterogeneity in Generalized Linear Mixed Models," Journal of Educational and Behavioral Statistics, , vol. 39(3), pages 167-179, June.
    7. Thaís C. O. Fonseca & Marco A. R. Ferreira & Helio S. Migon, 2008. "Objective Bayesian analysis for the Student-t regression model," Biometrika, Biometrika Trust, vol. 95(2), pages 325-333.
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