Grouped poisson regression models: theory and an application to public house visit frequency

In this paper we extend the Poisson regression model to deal with the situation in which the event count is observed le in “grouped” form, By this we mean that for some observations, all that is known about the count is that it falls within a certain range of integers, and the actual value is unknown, A typical likelihood contribution for this extended model is the sum of a set of consecutive Poisson probabilities, The log-likelihood function is derived for a general grouping rule, using a logarithmic link for the Poisson mean, This log-likelihood function is shown to be globally concave. The model is applied to grouped count data on the frequency of trips to pubs made over a one-week period by a sample of Norfolk young persons.