Studentized Residuals after Robust Regression

[Trevor Andrew]

I am estimating a regression with clustered standard errors and would like to obtain studentized residuals, but I am getting an error that it is not possible. Why is it not possible to obtain studentized residuals after robust regression? What is a work around?

[Nick Cox]

Are you alluding to rreg? My guess is that it is too far from the usual regression framework for the definition of Studentized residuals to make sense. If you have algebra to the contrary, I'd write to StataCorp.

rreg implements a particular hybrid flavour of robust regression that made some sense when it was proposed in 1985. Since then, robust regression seems to have moved in various different ways. None of the texts I've glanced at recently seem to mention it at all. Mind you, I don't think there is much agreement in robust regression circles on anything much except that robust regression is needed and best done in the authors' way.

[Trevor Andrew]

No I am using the regular regress command:

reg y x, cluster(cluster_var)

I am not sure I can follow you, what do you mean it is too far from the usual regression framework for the definition of Studentized residuals to make sense? I would like to compare the distribution of residuals from different models. I thought that Studentized residuals would be the best approach to make the residuals comparable.

[Nick Cox]

I guessed wrong what you meant by "robust regression". You meant "regression with robust standard errors" I was following this kind of idea: https://en.wikipedia.org/wiki/Robust_regression

Sorry: My post has no bearing on your question, but only on the rreg command. The lesson for me is not to guess. The lesson for you is to show precise code at the outset to make your question specific.

[Trevor Andrew]

Agreed, I should have posted an example code. Then you think it's not possible to get studentized residuals after running a regression with clustered standard errors? I saw an older post on stackexchange about this topic that you were part of, but there was no final answer.

[Nick Cox]

I don't have the right kind of expertise to answer your real question.

[Joao Santos Silva]

Trevor,

If I am not mistaken, Studentized Residuals are scaled (among other things) by the standard error of the errors of the model. If you use robust standard errors, you are assuming that there is no single standard error of the errors of the model because of the heteroskedasticity, so you do not have a key ingredient to compute what you want. Does it make sense?

Joao

[Trevor Andrew]

Joao Santos Silva not quite. What do you mean by that there is no single standard error of the errors of the model because of the heteroskedasticity?

[Joao Santos Silva]

Dear Trevor Andrew,

If there is heteroskedasticity, each error has potentially a different variance, therefore (conditionally on the regressors) you have one standard error for each error.

Best wishes,

Joao

[Trevor Andrew]

Dear Joao Santos Silva I have a follow up question. I understand that heteroskedasticity implies that each error has potentially a different variance but why does this imply that you have one standard error for each error? And what exactly do you mean by standard error for each error?

[Joao Santos Silva]

Trevor, please check a textbook.

[Trevor Andrew]

I was just confused by your terminology because you refer to residuals and error term both with error. So essentially you are saying that if I use robust standard errors I force my model to have the same standard error for each residual? My final goal is to compare distribution of residuals from two different models with two different outcomes. Since the outcomes have different scales, it is not possible to compare the distribution of the residuals of each model. Couldn't you then just run two robust regressions with different outcomes, obtain the residuals, and divided each residual by the standard deviation of the residuals? That way all residuals would have the same scale and I could compare residuals from the two models?

[Trevor Andrew]

Dear Joao Santos Silva I just wanted to revive the chat. My final goal is to compare distribution of residuals from two different models with two different outcomes. Since the outcomes have different scales, it is not possible to compare the distribution of the residuals of each model. Couldn't you then just run two robust regressions with different outcomes, obtain the residuals, and divided each residual by the standard deviation of the residuals? That way all residuals would have the same scale and I could compare residuals from the two models?

[Joao Santos Silva]

Dear Trevor Andrew,

I presume that by robust regression you mean OLS regression with robust standard errors. Do you understand what is the purpose of using robust standard errors?

Best wishes,

Joao