Research Article
A Robust Quantile Regression Model for Count Data: The Half Cauchy Transformation Approach
Issue:
Volume 13, Issue 2, April 2025
Pages:
27-33
Received:
27 March 2025
Accepted:
7 April 2025
Published:
29 April 2025
Abstract: This paper introduces an innovative approach to modelling count data through the introduction of a robust quantile regression model, the Half Cauchy Quantile Regression (HCQR). Count data is frequently challenged by outliers and skewed distributions. By integrating the heavy-tailed properties of the Half Cauchy distribution into the quantile regression framework, the HCQR model offers reliable estimates, particularly in the presence of extreme values. Quantile regression models, including HCQR, typically exhibit greater robustness to such extremes compared to traditional methods. The study highlights the limitations of traditional count regression models, such as the Negative Binomial Regression (NBR), particularly their performance inadequacies within the quantile regression framework. A comparative analysis using real-world crime data illustrates that the HCQR model substantially outperforms the NBR model. By integrating the half Cauchy distribution into the quantile regression framework, the HCQR model was formulated. In the Half Cauchy Quantile Regression Model, the Half Cauchy quantile function is used to transform the traditional quantile regression outputs, accommodating the characteristics of the Half Cauchy distribution. This superiority is demonstrated through improved metrics such as lower Standard Deviation, Skewness, Kurtosis, Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC), establishing HCQR's enhanced robustness and predictive accuracy.
Abstract: This paper introduces an innovative approach to modelling count data through the introduction of a robust quantile regression model, the Half Cauchy Quantile Regression (HCQR). Count data is frequently challenged by outliers and skewed distributions. By integrating the heavy-tailed properties of the Half Cauchy distribution into the quantile regres...
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Research Article
Analyzing Within-Group Changes in an Experiment: To Deal with Retest Effects, You Have to Go Latent But Not All Latents Are Equal
Issue:
Volume 13, Issue 2, April 2025
Pages:
34-44
Received:
27 February 2025
Accepted:
10 March 2025
Published:
14 May 2025
DOI:
10.11648/j.sjams.20251302.12
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Abstract: Analyzing within-group change in an experimental context, where the same group of people is measured before and after some event, can be fraught with statistical problems and issues with causal inference. Still, these designs are common from political science to developmental neuropsychology to economics. In cases with cognitive data, it has long been known that a second administration, with no treatment or an ineffective manipulation between testings, leads to increased scores at time 2 without an increase in the underlying latent ability. We investigate several analytic approaches involving both manifest and latent variable modeling to see which methods are able to accurately model manifest score changes with no latent change. Using data from 760 schoolchildren given an intelligence test twice, with no intervention between, we show using manifest test scores, either directly or through univariate latent change score analysis, falsely leads one to believe an underlying increase has occurred. Second-order latent change score models also show a spurious significant effect on the underlying latent ability. Longitudinal structural equation modeling with measurement invariance correctly shows no change at the latent level when measurement invariance is tested, imposed, and model fit tested. When analyzing within-group change in an experiment, analyses must occur at the latent level, measurement invariance tested, and change parameters explicitly tested. Otherwise, one may see change where none exists.
Abstract: Analyzing within-group change in an experimental context, where the same group of people is measured before and after some event, can be fraught with statistical problems and issues with causal inference. Still, these designs are common from political science to developmental neuropsychology to economics. In cases with cognitive data, it has long b...
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Maureen Tobe Nwakuya
