ABSTRACT
The Dutch government initiated a project to monitor the size of the illegal immigrant population in the Netherlands, which resulted in a series of publications with yearly estimates. The estimates are based on data extractions from police records involving illegal immigrants who had come into contact with the police. These police data consist of a single record for each police contact, and also include covariates such as age and gender. The basic zero-truncated Poisson regression model (ZTPR) assumes a closed population. This chapter presents the time-at-risk ZTPR and its results for the 2009 data. It reviews the existing theory on the ZTPR, and shows how the two-stage and time- at-risk ZTPR models account for violations of the closed population assumption. The chapter evaluates the performance of these models when the closed population assumption is violated. It compares the estimates of the models for the 2009 data and provides a discussion.
