Joint regression modeling of location and scale parameters of the skew t distribution with application in soil chemistry data

• Published in: Journal of applied statistics Vol. 49; no. 1; pp. 195 - 213
• Main Authors: Prataviera, F., Batista, A. M., Libardi, P. L., Cordeiro, G. M., Ortega, E. M. M.
• Format: Journal Article
• Language: English
• Published: England Taylor & Francis 2022
• Subjects: Application Notes; Maximum likelihood; Other; quantile residuals; regression model; skew normal; skew t distribution; quantile residuals; regression model; Maximum likelihood; skew normal; skew t distribution
• ISSN: 0266-4763; 1360-0532
• DOI: 10.1080/02664763.2020.1801608

In regression model applications, the errors may frequently present a symmetric shape. In such cases, the normal and Student t distributions are commonly used. In this paper, we shall be concerned only to model heavy-tailed, skewed errors and absence of variance homogeneity with two regression structures based on the skew t distribution. We consider a classic analysis for the parameters of the proposed model. We perform a diagnostic analysis based on global influence and quantile residuals. For different parameter settings and sample sizes, various simulation results are obtained and compared to evaluate the performance of the skew t regression. Further, we illustrate the usefulness of the new regression by means of a real data set (amount of potassium in different soil areas) from a study carried out at the Department of Soil Science of the Luiz de Queiroz School of Agriculture, University of São Paulo.