A mixed Bell regression model for overdispersed medical count data

Naiara C.A. dos Santos, Jorge L. Bazán and Artur J. Lemonte

Journal of Applied Statistics, 2026, vol. 53, issue 5, 855-873

Abstract: In this article, we consider the discrete Bell distribution to introduce a new mixed-effects regression model that may be an interesting alternative to traditional mixed-effects models for count response variables. The new regression model can be applied in several areas including health data. We consider the frequentist and Bayesian approaches to perform inferences in this class of mixed regression models. We provide Monte Carlo simulation experiments to verify the performance of these approaches in estimating the mixed Bell regression model parameters. The simulation results are quite promising and indicate that these approaches are effective in doing that. We also consider model comparison criteria based on the frequentist and Bayesian approaches and simulations are considered to verify the performance of these criteria. Two empirical applications to real data of the proposed mixed-effects model are provided, and comparisons with the Poisson mixed-effects model, as well as the Poisson inverse Gaussian mixed-effects model, are made. The real data applications confirm that the proposed mixed-effects Bell regression model can be an interesting alternative in the modeling of count response variables.

Date: 2026
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DOI: 10.1080/02664763.2025.2538084

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