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.
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The authors would like to thank the editors and the referees whose comments and suggestions led to an improved article. The authors thank CAPES and CNPq of the Ministry for Science and Technology of Brazil, and FAPEMIG for a partial allowance to their researches.
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Santos, C.C., Loschi, R.H. Maximum likelihood estimation and parameter interpretation in elliptical mixed logistic regression. TEST 26, 209–230 (2017). https://doi.org/10.1007/s11749-016-0507-1
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DOI: https://doi.org/10.1007/s11749-016-0507-1