Robust Regression Postestimation

[Stije Leopold]

Dear Statalisters,

I am hoping to use msregress to analyse fixed effects panel data models using Stata 14.1
(-findit- mmregress) (Reference: Verardi, Vincenzo, and Christophe Croux. 2009. Robust regression in Stata. Stata Journal 9, no. 3: 439-453.)

My question:

1) Are there any postestimation commands available to help perform variable selection in the presence of outliers using the robust regression msregress?

2) Would there be a recommended method to compare robust regression models? Is a robust version of the Akaike Information Criterion (AIC) an option in Stata? (Reference: https://feb.kuleuven.be/public/ndbaf...mClaeskens.pdf)

Thanking you in advance!

Ps. Alternative methods including rreg appear less favourable, as stated previously: http://www.stata.com/statalist/archi.../msg00416.html

[Joao Santos Silva]

Dear Stije,

As far as I know, you cannot really do fixed effects with "robust" regression, but I'll be happy to be corrected. Also, comparing different flavors of "robust" regression with goodness-of-fit criteria does not make much sense; you have to choose between the different methods based on their properties.

All the best,

Joao

[Stije Leopold]

Dear João,

Thank you very much for your reply, I am surely not an expert on this and would be happy to receive any advice. To clarify my question:

In the original article of Verardi and Croux, 2009 there is stated:

"We […] briefly describe the Stata command implemented (msregress) to compute it in practice. Note that this estimator can be particularly helpful in the fixed effects panel data models, as suggested by Bramati and Croux (2007)"

Here they reference: [Bramati, M. C. and C. Croux. 2007. Robust Estimators for the Fixed Effects Panel Data Model. Econometrics Journal 10(3): 521-540]
link: https://lirias.kuleuven.be/bitstream...1707/1/bramati

This led me to think there are as a matter of fact robust regression techniques useful for fixed effects panel data.

This led me to wonder which post-estimation/goodness of fit measures could be used for variable selection comparing robust regression models (equivalent to using likelihood ratio test or AIC to compare OLS regression models)?

Thank you!

Stije

[Joao Santos Silva]

Dear Stije,

First of all, I have to say that my views on this literature may be an outlier and therefore you may want to ignore them to have a "robust" view of the literature .

Anyway, the problem I have with these estimators is that it is not at all clear what they estimate. That is, they are estimators, but of what? Under certain conditions, "robust" estimators will be consistent for the conditional mean but these conditions are often violated in practice and therefore the estimators are not as robust as their name suggests.

Alternatively we can move our attention form the mean, which is not a "robust" measure of location, to the mode or to quantiles such as the median. However, in this case we cannot easily eliminate the fixed effects and we have an incidental parameters problem.

That is why I say that doing FE with robust methods is challenging, at least if we want to understand what we estimate.

All the best,

Joao

[Sanaullah Farooq]

I have conducted MM robust regression using mmregress command. However I need to do further analysis on its residuals. I cannot extract residuals of this regression from predict command ot by going in the menu and clicking on postestimation. Anybody please share the procedure/command for extracting the residuals and estimated line?

[Steve Samuels]

Sanulah: This is the second time that you have opened a quite old thread in order to ask only a tangentially related question Please start a new topic, as Carlo asked the first time.

[Joao Santos Silva]

Dear All,

I recently saw this thread again and, for the record, I would like to add something to my comment in #4. it is now possible to estimate quantile regression (which are robust measures of location) with fixed effects. If you are interested in doing this, please check the command xtqreg; make sure you read the help file and the references therein.

Best wishes,

Joao