This repository contains an Online Supplement and R scripts and files for the paper "Understanding Ability and Reliability Differences Measured with Count Items: The Distributional Regression Test Model and the Count Latent Regression Model" published in Multivariate Behavioral Research: Beisemann, M., Forthmann, B., & Doebler, P. (2024). Understanding Ability and Reliability Differences Measured with Count Items: The Distributional Regression Test Model and the Count Latent Regression Model. Multivariate Behavioral Research, (Advance online publication), 1-21. https://doi.org/10.1080/00273171.2023.2288577 The paper introduces two new explanatory IRT models for count data; one that includes item covariates (Distributional Regression Test Model) and one that included person covariates (Count Latent Regression Model). The models are extensions of the Two-Parameter Conway-Maxwell-Poisson Model, a two-parameter count IRT model which allows for modeling over- as well as underdispersion in conditional item responses.