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Thread: Regression assumptions

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    Regression assumptions




    this comes from Introduction to Econometrics by Stock and Watson. On page 161 they note in a footnote "....it might be helpful to note that some textbooks add homosedasticity to the list of least squares assumptions. As just discussed, however, this additional assumption is not needed for the validity of OLS regression analysi as long as hetroskedasticty-robust standard errors [White's] are used."

    I was wondering what poster's thought of this. It is a new argument to me.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Regression assumptions

    As far as I recall from Berry, W. D. (1993). Understanding regression assumptions (Vol. 92). Sage Publications., when the assumption of homoroskedasticity is violated the estimates are unbiased, yet they are not BLUE. And the efficiency of standard errors could be improved by using robust SE's, indeed.

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    Re: Regression assumptions

    Berry was actually a professor of mine and he clearly agreed that homoscedasticity was a regression assumption [which only effected the se and thus blue]. This author appears to disagree - I am not sure who is right. I was really wondering how common this second view is [I have seen Berry's views on regression assumptions used often].
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Regression assumptions

    i really don't think it's saying anything different from what's already been said. look closely at the wording they're using:

    Quote Originally Posted by noetsi View Post
    "....it might be helpful to note that some textbooks add homosedasticity to the list of least squares assumptions. As just discussed, however, this additional assumption is not needed for the validity of OLS regression analysi as long as hetroskedasticty-robust standard errors [White's] are used."
    i think what Stock & Watson are saying is that if you default to always use robust standard errors, then homoscedasticity stops being an issue. the key here is to notice that if you have homoscedasticity , the weight matrix used to calculate standard errors becomes an identity matrix and the formula for robust standard errors reduces back to the usual formula to obtain regular standard errors. but if you have heteroskedasticity, then you're already taking care of it because you're always adjusting your standard errors.

    i guess it's an overly-convoluted way of saying "better safe than sorry so always correct your standard errors". or something like that.
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    Re: Regression assumptions

    I think they are both just saying the same thing though one references cautious correction approach.
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    Re: Regression assumptions

    I did not think that the White robust errors actually always got rid of unequal error variance, just some types of it. I agree they mean safe than sorry, that appears to be a common view although I had not realized it to recently.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Regression assumptions

    Awhile back I had a dataset and question where patients could have contributed more than one observation, so independence was broken. When running a multi-level model, it (multilevels) did not explain any additional covariance, so I ran a fixed effects model with sandwich based estimates. I know this does not really pertain to your post, but thought it could provide an example of its usage. So overall, I felt bad that I was not controlling for the meager between group variability, so I took a cautious approach by applying White's Errors.
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    Re: Regression assumptions

    While it does not pertain to my post it does raise a question. Do you use SAS or R for multilevel analysis. I need to do multilevel and while I know SAS does it, I don't know if it does it well enough...
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Regression assumptions

    To my original post this is an awesome resource for knowing about or testing assumptions.

    http://www.statisticalassociates.com/assumptions.pdf
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Regression assumptions


    I use SAS and it seems sound. Multilevel modeling has been around long enough for it to be reliable. Will check out the link tomorrow.
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