Estimating Binomial Denominators

Abstract

Count data from registers are likely to exhibit underreporting and thus it is of high relevance to obtain an estimate of the true number of cases. One approach is to model counts as binomial variables with both parameters unknown. Estimation of the binomial denominator n is known to be problematic even in the simple random sample case, if Їy/s2 is small. Several methods of stabilization, including a beta-binomial model, have been proposed to circumvent this. We suggest to use a regression model for n in the binomial and the beta-binomial case, and to estimate the parameters by maximum likelihood. Applying the proposed models to real data from the Austrian crime register we obtain estimates of the unknown total number of crimes, the so-called dark figure. The results of a simulation study show the good performance of the method.