A comparison between robust and quantile regression model use the medical data - Faqe, Mohammad M.; Mohammad, Soran H. (Sulaimani Journal for Humanities, 2021)
Regression analysis is a statistical method for estimating the relationships between a response variable and one or more explanatory variables. The classical method, Ordinary Least Squares (OLS), is used to estimate the linear regression parameters when assumptions are available. When some of these assumptions are not available, the estimates and results may be inaccurate. Particularly, when the data contain outliers, outliers violate the assumption of normal distribution of residuals in the least squares regression. Consequently, the robust and quantile regression model can be used as alternative method for Ordinary Least Squares which have been developed to estimate the parameters when the data have outliers. In this study, the robust M-estimator regression method, the weighting function (M-Huber and M-Bisquare) and three quartile ( ) were used in the quantile regression model. The sampling of this study was taken from Royal Hospital (Infertility Center) in Sulaymaniyah Governorate, which consists of (230) women suffering from infertility, and a set of variables were taken as follows: The first group represents (6) explanatory variables which are {Age, and Hormone Thyroid Stimulation (TSH), Luteinizing Hormone (LH), Follicle Stimulating Hormone (FSH), Prolactin (PL), and Progesterone (P4) }. While the second group represents the response variable, which is number of eggs (oocyte). The robust regression model and quantile regression model were used as a suitable statistical method for the study sample. By analyzing the study data, it was found that the quantile regression model with quartile (τ = 0.50) is the best fit model for the data compared to the robust regression (M-Estimator) and the weighting function (M- Bisquare and M-Huber) depending on the value of the criteria{average absolute error (MAE), the symmetric mean absolute error of percentage (SMAPE), and also relative absolute error (RAE) which was less than the value of the criteria (M-Estimator) in the robust regression model.
Keywords: Outliers; Robust; Quantile; Weighting function; Infertility