A Robustness Analysis of Logistic Quantile Regression Model with Contaminated Dataset (Published)
Traditional mean regression models may be inadequate when dealing with asymmetric response distributions. In such cases, quantile regression offers a more robust alternative, accommodating outliers and error distribution misspecification by characterizing the entire conditional distribution of the outcome variable. This paper proposes a robust logistic quantile regression model, which involves adding 0.5 and 0.05 differently to the numerator and denominator of the logit link model. The performance of these two models is evaluated and compared using goodness of fit, AIC, skewness, kurtosis, RMSE, and MSE. Results indicate that both models are robust, with the model adding 0.5 to both the numerator and denominator of the logit link function performing slightly better. This study underscores the importance of selecting an appropriate distribution in quantile regression analysis, particularly for modeling skewed and normal data.
Keywords: AIC, Logistic quantile regression, Pseudo R-square, RMSE