Technical notes: Robust regression for at least ordinal outcomes

Abstract

If the task is to conduct a regression analysis in order to examine the statistical associations between variables, many scientists think, of course, of OLS first. And it makes perfect sense: it’s probably the first regression technique you'll encounter - it's part of the basic repertoire of statistical analysis. Furthermore, OLS results are very informative. However, OLS needs a bunch of assumptions regarding the data at hand to be satisfied (Wooldridge 2010). If these assumptions are not met, results from OLS can be unstable, biased, or misleading. It is important to note that the assumptions of OLS are seldom fully met. Hence, to get stable results, we must apply robust regression techniques - that is, techniques which do not need some of the assumptions to be satisfied. I will discuss two scenarios where alternative regression techniques provide more robust results compared to OLS. Both are about handling certain characteristics of the dependent variable. First, we consider a scenario where the measurement level of the dependent variable is ordinal. In the second scenario, the outcome is metric, but its distribution is strongly skewed. Finally, it is outlined how robust inference statistics can be achieved for both scenarios. The techniques discussed are not only relevant but particularly so in the context of extended replications. Since replications aim to assess the stability of results, the application of alternative techniques aids in identifying methodological artifacts.