Modelling truncated and clustered count data

Count response data often exhibit departures from the assumptions of standard Poisson generalized linear models. In particular, cluster level correlation of the data and truncation at zero are two common characteristics of such data. This paper describes a random components truncated Poisson model that can be applied to clustered and zero-truncated count data. Residual maximum likelihood method estimators for the parameters of this model are developed and their use is illustrated using a dataset of non-zero counts of sheets with edge-strain defects in iron sheets produced by the Mobarekeh Steel Complex, Iran. The paper also reports on a small-scale simulation study that supports the estimation procedure.