Ordinal regression models for zero-inflated and/or over-dispersed count data

Denis Valle,Kok Ben Toh,Qing Zhao,Gabriel Zorello Laporta

doi:10.1038/s41598-019-39377-x

Abstract

Count data commonly arise in natural sciences but adequately modeling these data is challenging due to zero-inflation and over-dispersion. While multiple parametric modeling approaches have been proposed, unfortunately there is no consensus regarding how to choose the best model. In this article, we propose a ordinal regression model (MN) as a default model for count data given that this model is shown to fit well data that arise from several types of discrete distributions. We extend this model to allow for automatic model selection (MN-MS) and show that the MN-MS model generates superior inference when compared to using the full model or more traditional model selection approaches. The MN-MS model is used to determine how human biting rate of mosquitoes, known to be able to transmit malaria, are influenced by environmental factors in the Peruvian Amazon. The MN-MS model had one of the best fit and out-of-sample predictive skill amongst all models. While A. darlingi is strongly associated with highly anthropized landscapes, all the other mosquito species had higher mean biting rates in landscapes with a lower fraction of exposed soil and urban area, revealing a striking shift in species composition. We believe that the MN and MN-MS models are valuable additions to the modelling toolkit employed by environmental modelers and quantitative ecologists.

Highlights

Count data are ubiquitous in natural sciences[1,2,3,4,5,6,7,8] and other fields[9,10,11,12,13]
In our second set of simulations, we aim to examine if the multinomial model with model selection (MN-MS model) can adequately identify the few important www.nature.com/scientificreports
We have proposed a new statistical model that relies on a multinomial distribution to fit data from a wide range of different discrete distributions and automatically perform model selection

Summary

Introduction

Count data are ubiquitous in natural sciences[1,2,3,4,5,6,7,8] and other fields[9,10,11,12,13]. We propose a Bayesian ordinal regression model that can flexibly fit count data that arise from various distributions, regardless of zero-inflation and/or over-dispersion, circumventing the need to choose the most appropriate distribution. We extend this model to allow for model selection and parameter estimation within a single coherent modeling framework, enabling researchers to more fully explore the information from covariates (e.g., by accounting for non-linear relationships). We end this article with a discussion on important topics for future research

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