Detection of Outliers in Circular Regression Model Via DFBETAcIS Statistic

Abstract

The outlier issues in circular regression models have recently received much attention. The presence of outliers may cause the sign and magnitude of regression coefficients to vary, resulting in inaccurate model development and incorrect prediction. Many methods for detecting outliers in a circular regression model have been proposed in previous studies such as COVRATIO, D, M, A, and Chord statistics, but it is suspected that they are not very successful in the presence of multiple outliers in a data set since the masking and swamping is not considered in their studies. This study aimed to develop an outlier detection procedure using DFBETAc statistic for circular cases, where this new statistic will investigate and identify multiple outliers in the Jammalamadaka and Sarma circular regression model (JSCRM) by considering masking and swamping effect. Monte Carlo simulations are used to determine the corresponding cut-off point and the power of performance is investigated. The performance of the proposed statistic is evaluated by the proportion of detected outliers and the rate of masking and swamping. The simulation procedure is applied at 10% and 20% contamination levels for varying sample sizes. The results show that the proposed DFBETAcIS statistic for JSCRM successfully detect the outliers. For illustration purposes, this process is applied to wind direction data.