Modified Skew Discrete Laplace Regression Models for Integer-Valued Data With Applications to Paired Samples

Modeling events associated with discrete-valued observations arises in several practical situations. Until now, research on statistical methods for discrete data has primarily focused on modeling count data. Nevertheless, discrete observations that may assume any value in the set of integers $Z=\{\text{…},-2,-1,0,1,2,\text{…}\}$ are also found in various contexts. This paper introduces a general parametric modeling framework for the analysis of integer-valued data, with applications to paired discrete observations. The proposed model is based on the modified skew discrete Laplace distribution. Our approach enables a straightforward interpretation of regression coefficients in terms of mean and dispersion, while properly accounting for the discrete nature of the data. We adopt a frequentist approach to perform inference and define diagnostic tools to assess goodness-of-fit. Additionally, we conduct several simulation studies to examine the asymptotic properties of the estimators and test statistics, as well as the distribution of the residuals. We illustrate the usefulness of the proposed model with two real datasets: one from an experimental study conducted in a French penitentiary, and another involving diagnostic imaging to assess kidney function through dynamic and static scintigraphy. Estimation and inference procedures for the new regression model are implemented in the R package sdlrm.