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I ran OLS regression in Stata. Based only on the results I got in OLS, is there any way to know if the quantile regression will be a better choice?

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    $\begingroup$ I'd say No, and much though I love Stata, that software is irrelevant here too. Even if you got an excellent-looking result with one method, it could still be better with the other. In any case, what is "better"? Half the point, if not more, is that the methods are based on different ideas of what is appropriate. (What's more, quantile regression for low or high quantiles is a long way from common-or-garden regression.) (I prefer not to conflate models and estimation methods, but that's a different story.) The serious point is why ask, when you can try and find out? $\endgroup$
    – Nick Cox
    Mar 19 '14 at 18:33
  • $\begingroup$ In this specific case I already did, and the quantile regression is better. But I would like to know whether there is any hint I can find in Stata. I have some notes that say that "It's easy to see, based on the OLS estimation results, that the quantile regression is a better choice". I, myself, couldn't see it... Any thoughts? $\endgroup$
    – yarela
    Mar 19 '14 at 18:51
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    $\begingroup$ Sorry, I can't see your notes from here. The statement might make some sense in context. You haven't defined "better". $\endgroup$
    – Nick Cox
    Mar 19 '14 at 18:54
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Two cases where quantile regression may be preferred to OLS are when you have outliers and heteroskedastic data. I know it's not a result in the numerical printout for OLS, but you just look at some residual plots and leverage plots.

What's better? Lower MSE? OLS will almost certainly (guaranteed?) be better according to this metric.

In other cases, you would want to define better as "more correctly models the effect of interest." In that case, quantile regression could be better by allowing you to see trends in the bulk of the data.

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    $\begingroup$ I agree quite strongly with the main points here, but the first sentence is oversimplified. First, outliers can be outliers, but still consistent with even OLS regression, possibly after transformation. Second, it's the same story with heteroscedasticity, where there are various remedies, including also using weighted least-squares. As I remarked earlier in this thread, it is not helpful to conflate models and methods of estimation. $\endgroup$
    – Nick Cox
    Mar 19 '14 at 20:10
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    $\begingroup$ Good point - outliers don't cause OLS to be inconsistent or biased. But, outliers can prevent you from seeing the trend in the bulk of your data and be problematic in that sense. $\endgroup$
    – wcampbell
    Mar 19 '14 at 20:44
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    $\begingroup$ We agree on the important points. Note that I mean "consistent" here in the everyday sense, not the technical sense. Outliers need not be demonised. In environmental data and no doubt other kinds too, an outlier is often just a more extreme value and the main need is to think on logarithmic or reciprocal scale. $\endgroup$
    – Nick Cox
    Mar 19 '14 at 21:02
  • $\begingroup$ I also though that MSE may be the indicator that I'm looking for. But what is "high/low MSE"? Is there any number? $\endgroup$
    – yarela
    Mar 20 '14 at 7:54
  • $\begingroup$ No, the number is relative and depends upon the scale of your data. MSE is going to be lower for the linear reg. Mean absolute error will likely be lower for the quantile reg. $\endgroup$
    – wcampbell
    Mar 20 '14 at 12:02

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