Journal Article

Outlier and Leverage Point Detection Procedures in Nonlinear Regression Models

Abstract

A major problem that statisticians have been confronted with, while dealing with regression analysis, is presence of outliers in data and a suitable method to detect it. Therefore, the detection of outliers and influential points is an important step of the regression analysis. Even though, some methods of detections have been provided in literature but to the best of our knowledge, the areas on nonlinear regression and detection comparison with respect to the strength and proportion of outliers have not been exploited. Therefore, in this study, the performance of methods of detecting outlier were compared at different proportion and strength of outliers, and sample sizes. Simulation study was conducted to investigate the performance of Dixon, Chi-square and Grub’s test in the detection of outliers at different proportion of outliers in first, second or both independent variables. Data were generated based on multiple nonlinear regression model with only two independent variables. Certain proportion (10%. 20, and 30%) of outliers were injected into first, second, and both independent variables at different sample sizes of 10, 30 and 100 to represent small, moderate and large sample sizes respectively. The normal distribution was assumed for the simulation while outliers were from uniform distribution. It was concluded that Deffits (DDi) has the highest probability to detect the actual number of the outliers injected over the sample size from the smallest to the highest followed by Cook’s Distance (CDi).

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