Sensitivity analysis and calibration of population size estimates obtained with the zero-truncated Poisson regression model

Zero-truncated regression models for count data can be used to estimate the size of an elusive population. A frequently encountered problem is that the Poisson model underestimates the population size due to unobserved heterogeneity, while the negative binomial model is not identified. A sensitivity analysis using the negative binomial model with fixed dispersion parameter might provide inside in the robustness of the population size estimate against unobserved heterogeneity, but as yet there is no method to determine realistic values for the dispersion parameter. This article introduces an R-squared measure and the use of the Pearson dispersion statistic to alleviate this problem. As a spin-off, a method is proposed for calibration of population size estimates in monitoring studies where the number of covariates varies over the measurement occasions. The performance of these methods is evaluated in simulation studies, and is illustrated on a population of drunk drivers.