Processing k-Inflated Poisson-Binomial Distributed Longitudinal Data in Consumer Behavior

The first step in process mining of a business is to collect data on the process that is being analyzed. Sometimes the response variable in a longitudinal study of customers is a count variable. It may seem that the effect of some covariates related to the consumer can be modeled on the desired success probability via a binomial regression. However, the count variable may have inflation at the value k, and may also arise as the sum of consecutive Bernoulli variables with different success probabilities. In this paper, we will account for these features using a longitudinal (mixed effects) k-inflated Poisson-Binomial model. We demonstrate the utility of the introduced model by fitting it to a simulated data set related to the customers of a supermarket.