Marginalized random-effects models for clustered binomial data through innovative link functions

Abstract

Random-effects models are frequently used to analyze clustered binomial data. The direct computation of the marginal mean response, when integrated over the distribution of random effects, is challenging due to taking nonclosed-form expressions of the marginal link function. This paper extends the marginalized modeling methodology using innovative link functions, where the marginal mean response is modeled in terms of covariates and random effects. To derive the explicit closed-form representation of both marginal and conditional means, the regression structure is designed through an original strategy to introduce particular random-effects distributions. It will consequently allow for a reasonable interpretation of covariate effects. A Bayesian approach is employed to make the statistical inference by implementing the Markov chain Monte Carlo scheme. We conducted simulation studies to show the usefulness of our methodology. Two real-life data sets, taken from the teratology and respiratory studies, have been analyzed for illustration. The findings confirm that our new modeling methodology offers convenient settings for analyzing binomial responses in practice. © 2021, Springer-Verlag GmbH Germany, part of Springer Nature.