Detection of outliers in multiple circular regression model

The multiple circular regression model (MCRM) describe the relationship between two or more circular variables. This model has many interesting properties and is sensitive enough to detect the occurrence of any outliers. However, no related studies have been found on outliers’ detection for more than one independent circular variable, which for MCRM. The aim here is to develop an outlier detection procedure in MCRM and how it unexplored problems related to this model. Firstly, is to examine the robustness of this model towards outliers. Secondly, five statistics of identifying outliers in the model are proposed, in which two of the proposals are from linear case to circular case i.e the DFBETAc statistic and the DFFITc statistic, and three of the proposals are extended from the single circular case to multiple circular cases i.e the COVRATIOc statistic, DMCEc and DMCEs statistics. A simulation study was done to identify the cut-off points through row deletion approach and the power performances of all five statistics were determined. Finally, all these proposed statistics were applied to the real data and the statistics were compared. Results of simulation studies shows that the proposed of five statistics perform well in detecting outliers in MCRM.