To Be Invariant or to Be Time-Varying: The Issue of Including Event-Related Covariates in the Zero-Truncated Poisson Regression Model

Abstract

The zero-truncated Poisson regression model is used to estimate the total size of populations that cannot be counted directly. In this model, covariates are used to account for variation within the population and produce an accurate estimate of the total population size. This study investigates the inclusion of event-related covariates in the model. These are covariates that represent a property of the capture itself that is only observed with the occurrence of a capture and whose value may vary over time. Consequently, multiple values may apply to one individual. However, since this information is mostly unobserved, including event-related covariates in the model is complicated. A simulation study is performed to investigate how event-related covariates should be included in the zero-truncated Poisson regression model. Three simulations are conducted in which an event-related covariate with two categories is respectively considered invariant and time-varying in the first two simulations, and a mixture of both in the third. Four methods are evaluated in the simulations: no covariate, one dummy, two dummies, and two count variables. This study shows that event-related covariates should not be included in the model when their value is assumed to be at least partially time-varying. Including event-related covariates regardless ensues misspecification of the model that results in biased estimates.