Adjusting For Mis-Reporting In Count Data

Any counting system is prone to recording errors including underreporting and overreporting. Ignoring the misreporting pattern in count data can give rise to bias in the estimation of model parameters. Accordingly, Poisson, negative binomial and generalized Poisson regression have been expanded in some instances to capture reporting biases. However, to our knowledge, no program has been developed to allow users to apply all of these models when needed. In the first part of the dissertation, we review the available models for underreported counts and develop a Stata command to estimate Poisson, negative binomial and generalized Poisson regression models for underreported data. Although considerable research has been devoted to underreporting models, less attention has been given to inflated counts. Based on the structural model proposed by Li et al. (2003), we will develop two models applicable to potentially misreported data. The first model covers situations where both the reported counts and the true counts follow a Poisson distribution. The second model would be relevant to cases where the actual observed counts are assumed to be from a generalized Poisson distribution and the reported counts are from a Poisson distribution. The proposed models adjust for both overreporting and underreporting. Our approach allows users to specify the individual’s characteristics that contribute to misreporting. With only observed counts at hand, our proposed models estimate the proportions of under/overreporting conditionally