1. ## Addressing Heteroskedasticity: OLS (robust), OLS [aweight], VWLS (w/omega)

Hello dear forum member,

Your recent help with my model specification has been invaluable. I also followed your advise on reading the book by Berry (1993), which led me to additional explorations so I can have BLUE estimates in case of violation of assumption of constant variance of the error term.

So, all my assumptions are met (as supported by the specification tests). Breusch-Pagan test rejects null of constant variance. I attribute that to the intentionally retained outliers (Cook's Ds and DFBETAs are within threshold of 1 for 99% of the data points). I decided to examine if the error variance increases as some variable increases. This notion found support in the attached plot (residual vs. dependent variable (Y), predictors look fine).

#1 My initial remedy was to use robust SE (White), but they don't allow me to "go BLUE"
#2 I ran the OLS estimation of the model with analytic weight [aweight=Y] (following a document I found by Kousser from UCSD), which gave me (a) consistent (with #1) coefficient estimates and more efficient (i.e. smaller) SE and confidence intervals, (b) 10%(!) higher R squared, and (c) even better distribution of the fitted residuals (best one so far).
#3 Additionally, I followed recommendation by Berry (1993) to use GLS for BLUE estimators. So, I calculated omega as follows (using STATA):
- ran regression, saved residuals, sorted Y;
- by Y: egen omega=mean(r1^2)

Then I used variance-weighted least squares (vwls) with the newly created omega as conditional SD. The new coefficients estimates were very close to those in #1 and #2 and the SEs were the most efficient (small) out of all 3 estimations.

Please let me know if my logic and procedures are correct in all this. Thank you in advance

No ideas?

3. ## Re: Addressing Heteroskedasticity: OLS (robust), OLS [aweight], VWLS (w/omega)

Seems like you did more than I can come up with. I would be interested and it would be beneficial to others, if when you are all done if you could list out all of the general steps you took to test model assumptions. This could serve to provide a guidance tool for others.

4. ## Re: Addressing Heteroskedasticity: OLS (robust), OLS [aweight], VWLS (w/omega)

Is your response constrained in some range?

5. ## Re: Addressing Heteroskedasticity: OLS (robust), OLS [aweight], VWLS (w/omega)

Originally Posted by Dason
Is your response constrained in some range?
Sir, do you mean the DV? Yes, it is - 0 - 100 (rating score).

6. ## Re: Addressing Heteroskedasticity: OLS (robust), OLS [aweight], VWLS (w/omega)

Originally Posted by hlsmith
Seems like you did more than I can come up with. I would be interested and it would be beneficial to others, if when you are all done if you could list out all of the general steps you took to test model assumptions. This could serve to provide a guidance tool for others.
I will surely share my methodological approach with others once submit the paper. Hopefully, the reviewers will be convinced.

7. ## Re: Addressing Heteroskedasticity: OLS (robust), OLS [aweight], VWLS (w/omega)

That seems fairly apparently in the residual plot. When you have constrained data you see that diagonal threshold that the residuals don't pass over a lot. I take it you have predictions that aren't too far away from the upper limit. I guess your approach of allowing the variance to be non-constant can somewhat account for this. A beta regression might be interesting to look at though...

8. ## The Following User Says Thank You to Dason For This Useful Post:

kiton (02-03-2015)

9. ## Re: Addressing Heteroskedasticity: OLS (robust), OLS [aweight], VWLS (w/omega)

Originally Posted by Dason
That seems fairly apparently in the residual plot. When you have constrained data you see that diagonal threshold that the residuals don't pass over a lot. I take it you have predictions that aren't too far away from the upper limit. I guess your approach of allowing the variance to be non-constant can somewhat account for this. A beta regression might be interesting to look at though...
If I understood you correctly ("you have predictions that aren't too far away from the upper limit"), you are absolutely correct - plots of Xn against Yhat do have a diagonal trend. Yet, I'd say that only 15-20% of points are in the upper limit.

And thank you very much for a beta regression suggestion, Sir. I'd surely explore it.

10. ## Re: Addressing Heteroskedasticity: OLS (robust), OLS [aweight], VWLS (w/omega)

Good eye Dason.

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