In rdmatheus/sdlrm: Modified Skew Discrete Laplace Regression for Integer-Valued and Paired Discrete Data

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sdlrm: Modified SDL Regression for Integer-Valued and Paired Count Data

Rodrigo M. R. de Medeiros
Universidade Federal do Rio Grande do Norte, UFRN [e-mail]

Implementation of the modified SDL regression model proposed by Medeiros and Bourguignon (2025). The sdlrm package provide a set of functions for a complete analysis of integer-valued data, in which it is assumed that the dependent variable follows a modified skew discrete Laplace (SDL) distribution. This regression model is useful for the analysis of integer-valued data and experimental studies in which paired discrete observations are collected.

Installation

You can install the current development version of sdlrm from GitHub with:

devtools::install_github("rdmatheus/sdlrm")

To run the above command, it is necessary that the devtools package is previously installed on R. If not, install it using the following command:

install.packages("devtools")

After installing the devtools package, if you are using Windows, install the most current RTools program. Finally, run the command devtools::install_github("rdmatheus/sdlrm"), and then the package will be installed on your computer.

Example

This package provide complete estimation and inference for the parameters as well as normal probability plots of residuals with a simulated envelope, useful for assessing the goodness-of-fit of the model. The implementation is straightforward and similar to other popular packages, like betareg and glm, where the main function is sdlrm(). Below is an example of some functions usage and available methods.

# Loading the sdlrm package
library(sdlrm)

# Data visualization (Description: ?pss)

# Fit a double model (mean and dispersion)
fit0 <- sdlrm(difference ~ group | group, data = pss)

# Print
fit0

# Summary
summary(fit0)

By default, the mode ($\xi$) of the modified SDL distribution is fixed at $\xi = 0$. It is possible to specify a non-zero mode (it must be an integer value) using the xi argument. Alternatively, this parameter can be estimated via profile likelihood using the choose_mode() function:

## Mode estimation via profile likelihood
mode_estimation <- choose_mode(fit0)

The mode_estimation object, of class “choose_mode”, consists of a list whose elements represent a modified SDL regression fit for each value specified for the mode (by default, the sequence $-5, -4, \ldots, 4, 5$). We see that $\xi = 1$ generates the highest profiled likelihood.

## Double model with xi = 1
fit1 <- mode_estimation[[1]]

The constant dispersion test in the modified SDL regression can be performed with the disp_test() function:

## Test for constant dispersion
disp_test(fit1)

The tests do not reject the null hypothesis of constant dispersion. We can then specify an adjustment with regressors only on the mean:

## Fit with constant dispersion and mode = 1
fit <- sdlrm(difference ~ group, data = pss, xi = 1)

## Summary
summary(fit)

Currently, the methods implemented for "sdlrm" objects are

methods(class = "sdlrm")

The plot() method provides diagnostic plots of the residuals. By default, randomized quantile residuals are used:

par(mfrow = c(1, 2))
plot(fit, ask = FALSE)
par(mfrow = c(1, 1))

The envelope() function plots the normal probability of the residuals with a simulated envelope:

## Building the envelope plot
envel <- envelope(fit, plot = FALSE)

par(mfrow = c(1, 2))
# Plot for the randomized quantile residuals (default)
plot(envel)

# Plot for the Pearson residuals
plot(envel, type = "pearson")
par(mfrow = c(1, 1))

rdmatheus/sdlrm documentation built on June 15, 2025, 8:26 a.m.