Random effects compound Poisson model to represent data with extra zeros

TL;DR

This paper introduces a novel compound Poisson random effects model for zero-inflated data, providing a scale-coherent alternative to mixture models, with applications demonstrated on marine macroinvertebrate datasets.

Contribution

It proposes a new hierarchical model for zero-inflated data based on compound Poisson processes, with inference via an EM algorithm incorporating importance sampling.

Findings

Model effectively captures zero-inflation in ecological data

EM algorithm performs well for parameter estimation

Parameter values influence confidence region coverage

Abstract

This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and predict species counts (discrete data) or abundance distributions (continuous data). Standard methods for modeling such data include mixture and two-part conditional models. Conversely to these methods, the stochastic models proposed here behave coherently with regards to a change of scale, since they mimic the harvesting of a marked Poisson process in the modeling steps. Random effects are used to account for inhomogeneity. In this paper, model design and inference both rely on conditional thinking to understand the links between various layers of quantities : parameters, latent variables including random effects and zero-inflated observations. The potential of these parsimonious hierarchical models for zero-inflated data is exemplified using two marine macroinvertebrate abundance datasets from a large scale scientific bottom-trawl survey. The EM algorithm with a Monte Carlo step based on importance sampling is checked for this model structure on a simulated dataset : it proves to work well for parameter estimation but parameter values matter when re-assessing the actual coverage level of the confidence regions far from the asymptotic conditions.