Modeling Response Bias in Count: A Structural Approach With an Application to the National Crime Victimization Survey Data

This article considers modeling response bias when the response is a count. The authors adopt a “structural approach” by using a generalized negative binomial mixture of Poisson distribution to model misreported counts, assuming that the distribution of the true response follows a negative binomial distribution. The model may be interpreted as a “stopped-sum” model. A simulated maximum likelihood estimator is proposed, and its finite sample performance is investigated through Monte Carlo simulations. The approach is then applied to analyzing school victimization data drawn from the National Crime Victimization Survey, which allows the authors to identify the individual- and school-related characteristics that could contribute to school crime victimization and to the possible biases on the reported number of repeat victimizations. The authors find that for the reported number of thefts, about 12 percent of respondents overreport the numbers, most of whom actually have not had any item stolen at school.