Which robust regression technique is appropriate under violated assumptions? A simulation study

Ordinary least squares (OLS) regression is widely employed for statistical prediction and theoretical explanation in psychology studies. However, OLS regression has a critical drawback: it becomes less accurate in the presence of outliers and non-random error distribution. Several robust regression methods have been proposed as alternatives. However, each robust regression has its own strengths and limitations. Consequently, researchers are often at a loss as to which robust regression method to use for their studies. This study uses a Monte Carlo experiment to compare different types of robust regression methods with OLS regression based on relative efficiency (RE), bias, root mean squared error (RMSE), Type 1 error, power, coverage probability of the 95% confidence intervals (CIs), and the width of the CIs. The results show that, with sufficient samples per predictor (n = 100), the robust regression methods are as efficient as OLS regression. When errors follow non-normal distributions, i.e., mixed-normal, symmetric and heavy-tailed (SH), asymmetric and relatively light-tailed (AL), asymmetric and heavy-tailed (AH), and heteroscedastic, the robust method (GM-estimation) seems to consistently outperform OLS regression.