Quantile Regression Analysis and Other Alternatives to Ordinary Least Squares Regression A Methodological Comparison on Corporal Punishment

Data analyses by classical ordinary least squares (OLS) regression techniques often employ unrealistic assumptions, fail to recognize the source and nature of heterogeneity, and are vulnerable to extreme observations. Therefore, this article compares robust and non-robust M-estimator regressions in a statistical demonstration study. Data from the Erlangen-Nuremberg Development and Prevention Project are used to model risk factors for physical punishment by fathers of 485 elementary school children. The Corporal Punishment Scale of the Alabama Parenting Questionnaire was the dependent variable. Fathers' aggressiveness, dysfunctional parent-child relations, various other parenting characteristics, and socio-demographic variables served as predictors. Robustness diagnostics suggested the use of trimming procedures and outlier diagnostics suggested the use of robust estimators as an alternative to OLS. However, a quantile regression analysis provided more detailed insights beyond the measures of central tendency and detected sources of considerable heterogeneity in the risk structure of father's corporal punishment. Advantages of this method are discussed with regard to methodological and content issues.