Analysis of rates in incomplete Poisson data

Abstract

subject to censoring processes which determine the incomplete classification that is reported in several practical situations. The paper describes a probabilistic model that can explain incomplete data referring to partitions of the original set of categories. We overcome the model's lack of identifiability by assuming a missingness at random censoring mechanism. On the basis of the subsequent statistical model the results required to fit further non-informative censoring models by maximum likelihood methodology are obtained. This preliminary analysis opens the way to the analysis of structural models for Poisson expected rates. The paper describes how to test the fit of structural models for the Poisson rates, whether taken individually or simultaneously with special censoring models. Then, the maximum likelihood methodology is specialized to the analysis of strictly linear and log-linear models in such a way that its computational implementation opens up for any count table. The methods developed throughout the work are illustrated with a breast cancer data set.