Developments of Efficient Trigonometric Quantile Regression Models for Bounded Response Data

Abstract

The choice of an appropriate regression model for econometric modeling minimizes information loss and also leads to sound inferences. In this study, we develop four quantile regression models based on trigonometric extensions of the unit generalized half-normal distributions for the modeling of a bounded response variable defined on the unit interval. The desirable shapes of these distributions, such as left-skewed, right-skewed, reversed-J, approximately symmetric, and bathtub shapes, make them competitive models for bounded responses with such traits. The maximum likelihood method is used to estimate the parameters of the regression models, and Monte Carlo simulation results confirm the efficiency of the method. We demonstrate the utility of our models by investigating the relationship between OECD countries’ educational attainment levels, labor market insecurity, and homicide rates. The diagnostics reveal that all our models provide a good fit to the data because the residuals are well behaved. A comparative analysis of the trigonometric quantile regression models with the unit generalized half-normal quantile regression model shows that the trigonometric models are the best. However, the sine unit generalized half-normal (SUGHN) quantile regression model is the best overall. It is observed that labor market insecurity and the homicide rate have significant negative effects on the educational attainment values of the OECD countries.

Keywords

• unit distributions
• quantile regression models
• trigonometric models
• generalized half-normal
• residual analysis