Access Type

Open Access Dissertation

Date of Award

January 2019

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Education Evaluation and Research

First Advisor

Shlomo S. Sawilowsky

Abstract

Researchers in social and behavioral sciences usually interested in study the relationship between a response variable Y_i and one or more independent predictors〖 X〗_i either for the purpose of explanation or prediction. Ordinary Least Square Regression is a parametric approach used to study this kind of relationship. One of the disadvantages of Ordinary Least Square is it does not fit well in the presence of outliers in the response variable Y_i or both in the response variable Y_i and the predictor variable〖 X〗_i, also if the data were sampled from a non-normal distribution. Quantile Regression, Theil-Sen regression, and the modified Theil-Sen Siegel regression are non-parametric approaches that can also be used to study the relationship and are more robust methods to outliers and non-normality of the distribution.

Several comparisons are made between Ordinary Least Square Regression, Quantile Regression, Theil Sen Regression, and Theil Sen Siegel Regression, but no direct comparison is yet made between Quantile Regression, Theil Sen Regression and Theil Sen Siegel Regression in the presence of outliers. In order to investigate this claim, Monte Carlo simulation study were employed and observations were generated from three theoretical and eight Micceri family distributions. Similarly, observations for the Monte Carlo simulations will be randomly generated with different sample sizes in the presence of 10% and 20%, 30% and 50% outliers. A comparison based on Mean Bias, Median Bias, Standard Deviation (S.D), Standard Errors (S.E), Root Mean Square Error (RMSE), Relative Root Mean Square Error (RRMSE), Median Absolute Error (MEDAE), and Relative Median Absolute Error (RMEDAE) of the four regression procedures are used to evaluate the model fitting.

The results of the study showed, under the normality assumption with no outliers Ordinary Least Square Regression should be the most suitable regression procedure followed by Quantile Regression, Theil Sen Regression, and Theil Sen Siegel Regression. When there are outliers in both X and Y direction Theil Sen Siegel Regression should be the most suitable followed by Quantile Regression and Theil Sen Regression. Under the non-normality assumption Quantile Regression, Theil Sen Regression and Theil Sen Siegel Regression have more or less same performance. For, Micceri family distribution overall Theil Sen Siegel Regression might be a suitable regression procedure.

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