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 mod-
els, 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 per-
formed showing the utility of heavy-tailed mixed logistic model. Among the main
conclusions, we note that the misspecification of the random effect distribution influ-
ences the fixed effects interpretation and the quantification of the among clusters
heterogeneity.

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• Maximum likelihood estimation and parameter interpretation in elliptical mixed logistic regression