Analyzing different causes of one–inflation in capture recapture models for criminal populations.

Our goal is the estimation of the size of various criminal populations on the basis of administrative data on criminal proceedings by exploiting capture– recapture models for repeated count data. The data at our disposal exhibit an abun- dance of units that are captured exactly once, which suggests the necessity of ex- plicitly modeling this deviation. We distinguish three possible causes for this phe- nomenon, namely, the erroneous inclusion of out–of–scope units, a particular be- havioural effect preventing subsequent captures after the first one, and missed links in a Record Linkage step. We then propose three families of “one–inflated” models to estimate the number of uncaptured units which we compare on datasets of Italian criminal proceedings.