Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

On a Skew t–discrete Gamma Alternative to the Normal-Poisson Model for Clustered Count Outcomes

Version 1 : Received: 24 August 2021 / Approved: 25 August 2021 / Online: 25 August 2021 (11:49:27 CEST)

How to cite: Tovissodé, C.F.; Glèlè Kakaï, R.L. On a Skew t–discrete Gamma Alternative to the Normal-Poisson Model for Clustered Count Outcomes. Preprints 2021, 2021080490 (doi: 10.20944/preprints202108.0490.v1). Tovissodé, C.F.; Glèlè Kakaï, R.L. On a Skew t–discrete Gamma Alternative to the Normal-Poisson Model for Clustered Count Outcomes. Preprints 2021, 2021080490 (doi: 10.20944/preprints202108.0490.v1).

Abstract

The normal and Poisson distribution assumptions in the normal-Poisson mixed effects regression model are often too restrictive for many real count data. Several works have independently relaxed the Poisson conditional distribution assumption for counts or the normal distribution assumption for random effects. This work couples some recent advances in these two regards to develop a skew t–discrete gamma regression model in which the count outcomes have full dispersion flexibility and random effets can be skewed and heavy tailed. Inference in the model is achieved by maximum likelihood using pseudo-adaptive Gaussian quadature. The use of the proposal is demonstrated on a popular owl sibling negotiation data. It appears that, for this example, the proposed approach outperforms models based on normal random effects and the Poisson or negative binomial count distribution.

Keywords

Discrete gamma distribution; correlated counts; sparse-grid quadrature; empirical Bayes estimators

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