Modeling proportions and marginal counts simultaneously for clustered multinomial data with random cluster sizes

Abstract

Clustered multinomial data with random cluster sizes commonly appear in health, environmental and ecological studies. Traditional approaches for analyzing clustered multinomial data contemplate two assumptions. One of these assumptions is that cluster sizes are fixed, whereas the other demands cluster sizes to be positive. Randomness of the cluster sizes may be the determinant of the within-cluster correlation and between-cluster variation. We propose a baseline-category mixed model for clustered multinomial data with random cluster sizes based on Poisson mixed models. Our orthodox best linear unbiased predictor approach to this model depends only on the moment structure of unobserved distribution-free random effects. Our approach also consolidates the marginal and conditional modeling interpretations. Unlike the traditional methods, our approach can accommodate both random and zero cluster sizes. Two real-life multinomial data examples, crime data and food contamination data, are used to manifest our proposed methodology.

Keywords:

• best linear unbiased predictor
• clustered categorical data
• distribution-free random effects
• over-dispersion
• Poisson mixed models

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This research was partially supported by grants from the Natural Sciences and Engineering Research Council of Canada and Atlantic Association for Research in the Mathematical Sciences.