Title: Item Characteristic Curve Poisson Counts Models Authors: Philipp Doebler, Anna Doebler, Heinz Holling Affiliation: WWU Münster Abstract: Many ability tests yield count data, e.g. the number of reading errors or the number of distinct ideas in tests of divergent thinking. Also a wide range of test formats present tasks under time constraints and the number of solved tasks - a count datum - is recorded. The traditional item response theory (IRT) model for such data is Rasch's Poisson counts model (RPCM). We present a new family of IRT models for count data that is also based on the Poisson distribution. Instead of the RPCM's log-linear approach, the expected score curve of an item is assumed to be proportional to a binary item characteristic curve. The one and two parameter logistic curve Poisson counts models (1PLPCM, 2PLPCM) are investigated in depth. We can show analytically, that the latter model is only weakly identified; this leads to the adoption of a conditional estimation approach for the 2PLPCM. The implementation of joint and marginal maximum likelihood estimation in R for this class of models is discussed.