Normality and Homoscedasticity Residuals

[Nouschka Snijders]

Dear all,

The residuals of my regression have been tested for normality and homoscedasticity. It turns out they are not normally distributed and heteroscedasticity.

How can I adapt the OLS regression such that the residuals act as if they are normally distributed and homoscedastic (such that the estimating and testing remains valid)? I know I can use the command "robust". Does this command ensures that the residuals are not normally distributed or that they become homoscedastic?

Best regards

[Nick Cox]

With absolutely no details here about your data or your specific model, it is hard to give specific advice.

Usually, or at least often, the answer is not to use OLS and/or to work on a different scale (e.g. transform one or more variables or use a non-identity link for the response). (It is kind of odd that people name a regression model by the estimation method used, here OLS, but that seems common in various social sciences.)

Good regression texts and courses explain that residuals (more precisely, errors) being normal is the least important assumption or (as I prefer to say) ideal condition for regression. That being so, junk your textbook if it tells you otherwise. (Taking a different course if the teacher tells you otherwise may not be so practical.)

Similarly residuals being homoscedastic is great if it is approximated but lack of it is sometimes something one just accepts.

The most important thing to worry about is whether the regression does a good job on capturing the systematic structure in your data. This one judges in the usual ways from regress output but even with multiple predictors added variable plots can always be plotted. With one predictor nothing beats a scatter plot with added regression line as diagnostic.

It's a really good idea to look at the residuals to see what is wrong about the model but the most important assumption (again, ideal condition) is Y = Xb.

[Carlo Lazzaro]

Nouschka:
have you also checked that -estat ovtest- and -estat vif- outcomes do not spot something more worrysome than heteroskedasticity?