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Keywords:

  • Generalized linear model;
  • Maximum likelihood;
  • Negative binomial;
  • Overdispersion;
  • Poisson;
  • Two-part model

Abstract

On occasion, generalized linear models for counts based on Poisson or overdispersed count distributions may encounter lack of fit due to disproportionately large frequencies of zeros. Three alternative types of regression models that utilize all the information and explicitly account for excess zeros are examined and given general formulations. A simple mechanism for added zeros is assumed that directly motivates one type of model, here called the added-zero type, particular forms of which have been proposed independently by D. LAMBERT (1992) and in unpublished work by the author. An original regression formulation (the zero-altered model) is presented as a reduced form of the two-part model for count data, which is also discussed. It is suggested that two-part models be used to aid in development of an added-zero model when the latter is thought to be appropriate.