Diagnosing overdispersion in longitudinal analyses with grouped nominal polytomous data

TL;DR

This paper introduces a diagnostic tool for detecting overdispersion in longitudinal nominal polytomous data, crucial for selecting appropriate models in agricultural sciences, validated through simulations and a case study on pig behavior.

Contribution

It proposes a longitudinal multinomial dispersion index for diagnosing overdispersion, enhancing model selection accuracy in grouped nominal data analysis.

Findings

The index approaches one with high overdispersion.

Values near zero indicate low overdispersion.

Simulation results support the index's effectiveness.

Abstract

Experiments in Agricultural Sciences often involve the analysis of longitudinal nominal polytomous variables, both in individual and grouped structures. Marginal and mixed-effects models are two common approaches. The distributional assumptions induce specific mean-variance relationships, however, in many instances, the observed variability is greater than assumed by the model. This characterizes overdispersion, whose identification is crucial for choosing an appropriate modeling framework to make inferences reliable. We propose an initial exploration of constructing a longitudinal multinomial dispersion index as a descriptive and diagnostic tool. This index is calculated as the ratio between the observed and assumed variances. The performance of this index was evaluated through a simulation study, employing statistical techniques to assess its initial performance in different scenarios. We identified that as the index approaches one, it is more likely that this corresponds to a high degree of overdispersion. Conversely, values closer to zero indicate a low degree of overdispersion. As a case study, we present an application in animal science, in which the behaviour of pigs (grouped in stalls) is evaluated, considering three response categories.