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.
Key words: EM algorithm, Importance Sampling, Compound Poisson Process,
Random Effect Model, zero-inflated Data
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