  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.
