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Stepwise regression as a robustness test after an OLS?
Would it be accepted to use the same variables, but switch from OLS to stepwise in Stata?
Or what other test would you recommend after having used an OLS?
Thomas:
after an OLS, you shoud usually check for:
- heteroskedasticity of the residuals distribution (see -estat hettest-);
- model misspecification (-estat ovtest-), that may well include endogeneity of one or more regressors;
- correctness of the functional form of the regressand (see -linktest-), that is a more general test for model misspecification;
- quasi-extreme multicollinearity (see -estat vif-). Please note that quasi-extreme multicolinearity is way oversold/overblown (the usual reference for this topic is https://www.hup.harvard.edu/catalog....=9780674175440, Chapter 23).
Eventually, stepwise mechanism proves the existence of devil (see why at https://www.stata.com/support/faqs/s...sion-problems/).
Thomas:
the issue is that -stepwise- is not a robustness test, as you usually end up with a model specification that, at best, shows a tenuous relatioship with the original one,
In addition, whenever we talk about "robustness", we are required to define against with nuisances we want our OLS to be robust to (heteroskedasticity?else?).
Thomas:
short answer: do those test reject the null? If yes, you might have something to inspect more carefully.
Long(er) answer: doubts on OLS building blocks are obviously legal, but I would recommend you to take a look at any decent textbook on statistics/econometrics textbook to be 100% aware of what postestimation routines are for.
Also did the "ovtest", but this is above the significance level, hence I imagine it means that there are no latent omitted variables in the model. So I can proceed with it.
. estat ovtest
Ramsey RESET test using powers of the fitted values of PercentageOfIntVolume
Ho: model has no omitted variables
F(3, 86) = 2.00
Prob > F = 0.1205
Thomas:
your postestimation tests highlight that you have heteroskedastcity in the residual dustribution; just invoke the -robust- option for your standard error.
After that, resist the temptation to run -hettest- again, because it will tell you that you still have heteroskedasticity (and you should ignore it), as the -robust- option affects standard errors to account for heteroskedasticity, but does not hqve any effect on the residual distribution (that remains as it was before invoking the -robust- option).
The -ovtest- is, unfortunately, less powerful that I hoped it to be when I was taught on statistics at the university (tons of years ago, my bad): it simply investigates whether power of the fitted values make any sense as regressors: if that is the case, there's something wrong with the functional form of the regressand; to9 have a more comprehensive idea, see -linktest- entry in Stata .pdf manual).
Thomas:
yes, the -linktest- outcome shows no evidence of abnormalities in the functional form of the regressand.
Hence, you're only issue is heteroskedasticity, that you can manage with the -robust- option.
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