In this repository for the manuscript of the same title, you can find the R code and saved simulation results for the simulation study included in the manuscript. The R scripts contain all the information for how to use them at the top as a comment. The repository also contains a README which we advice to take a look at first to obtain more information about the contents of this repository. The manuscript for which this repository has been created proposes novel multidimensional item response models for count data. We focus on explanatory models, exploring both rotation and (lasso) penalization approaches for obtaining a simply structured discrimination matrix. We provide estimation algorithms for the models, assess them in a simulation study, and apply them to an empirical example for illustration. At this time, we blinded any further information from the repository, as the manuscript is currently under review. It will later be added to this repository together with a citation.