Robust regression, bootstrapping and indirect effect


New Member
Hi there,

I am currently learning to do mediation analysis using bias-corrected accelerated bootstrap confidence intervals, similar to the procedure discussed by Hayes.

My question is: would it be statistically correct to use robust regressions (for outliers), rather than OLS regressions, to compute my indirect effect, and than bootstrapping it? Do I violate some assumptions by doing so? Does the indirect effect, and thus its confidence intervals, must be based on OLS regressions?

Thank you,

Are outliers so present in your data set that you need to abandon OLS? OLS has the benefits of being widely recognized/used and it's a real workhorse for analysis.

Are you wanting to take the absolute value of resides rather than squares or are you wanting to use a non-parametric or something exotic like a thiel-sen estimator?


New Member
It's really more a theoretical question that I had, not really related to a particular case that I have.

For robust regression, I was thinking about the rlm procedure from the MASS package.

Maybe my question would in fact require to have a specific case to be answered …


Theoretically there is nothing wrong. I can't think of one estimator that cannot be bootstrapped. It's one of the nice things about the central limit theorem.

I think the real issue is when it comes to not using OLS regression it's not whether you can do it technically but whether you should do it in the first place.

Let me give you a recent example. I was analyzing financial data from school districts in a state that stretched over the past 15 years. There were some troubling outliers within the data set. I am very conservative when it comes to outliers, though. Upon working with an expert in the field school finance I found out the reason that some of the districts were outliers will because large fluctuations in the prices of oil which led to extreme revenue increases for some school districts due to oil wells opening up. I was been able to model this effect.

My point is, sometimes outliers are not just noise. Sometimes they are very meaningful and contain important information in regards to the analysis. Sometimes you find out that the outliers really part of another population and should not be included in the analysis and other times you find out an important variable regarding that observation.