Tolerable Heteroskedasticity/ Variance Inhomogenity


a long time ago I have read somewhere, that a regression can overcome heteroskedasticity/ variance inhomogenity up to certain amount.

It might have been working something like the variance is calculated for certain target variable intervals. If the highest variance was maximal m-times larger the lowest variance, on could suppose, that the calculated regression coefficients are still usable, or something like this. Unfortunately I do not find it again.

Do you know this over the thumb rule regarding deviating variances?


Omega Contributor
No source, but the residuals don't have to be perfectly homoskedastic and sometimes people use robust estimators. Not sure if it would matter if they are heteroskedastic, but appear to have a random element and not a distinct underlying pattern??

Would be interested in seeing a citation for this as well. Have not heard of a rule of thumb.
Maximum minimum quotient criterion

I have found it again.

It is the maximum minimum quotient criterion.

Following Ryan (1997, S. 61) there is no need to be afraid of heteroskedacity, till the quotient out of maximum and minimum standard deviation is below 1.5, while quotient above 3.0 are inacceptable. That means, translated to variances, variance quotients above 9.0 are critical. Similar tell Cohen et al. (2003, S. 120) und Fox (1997, S. 306f), who state 10 as critical ratio between the maximal and minimal variance.

Ryan, T.S. (1997). Modern Regression Methods. New York: Wiley.

Cohen, J., Cohen, P., West, S.G. & Aiken, L. (2003). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (3rd ed.). Mahwah: Lawrence Erlbaum Associates.

Fox, J. (1997). Applied Regression Analysis, Linear Models, and related Methods. Thousand Oaks: Sage.