A comparison of robust and least squares regression models using actual and simulated dat

The purpose of this study was to compare several robust regression techniques to ordinary least squares (OLS) regression when analyzing bivariate and multivariate data. The bivariate analysis compared of the performance of alternative robust procedures in regard to the detection of outliers versus the standard OLS regression techniques. The bivariate analysis demonstrated the weaknesses of OLS regression and the standard OLS outlier diagnostic techniques when multiple outliers are present. In addition, this research assessed the empirical performance of alpha and power under three non-normal probability density functions using a Monte Carlo simulation.;The first analysis focused on several bivariate data sets. Each data set was plotted and each of the regression models used to analyze the data. The usual results (e.g., R$sp2$, regression coefficients, standard errors, and regression diagnostics) were examined to give a visual as well as empirical analysis of the models' performance in the presence of multiple outliers.;The second component of this study entailed a Monte Carlo simulation of five robust regression models and OLS regression under four probability density functions. The variables included in the study were placed in one 2$sp1$3$sp2$ and two 3$sp2$ factorial design repeated over four probability density functions, resulting in a total of 90 experimental runs of the Monte Carlo simulation. Random samples were generated and then transformed to fit desired distributional moment characteristics. The incremental null hypothesis was used as the basis to calculate empirical alpha and power values calculated.;The analysis demonstrated the inadequacies of the standard OLS based outlier detection methods and explained how regression analysis could be improved if a robust regression method is used in parallel with OLS regression. The multivariate analysis demonstrated the robustness of the OLS regression model to three nonnormal populations. It further demonstrated a moderate inflation of alpha for the M-class of robust regression model and a lack of power stability with the rank transform regression method.;Based on the results of this study, recommendations were made for using robust regression methods and suggestions for future research offered.