Heteroskedasticity detection - Multiple linear regression

[sumah]

I selected my final multiple linear regression model and wanted to test for heteroskedasticity. It seems that I can do that using "white option" in the model statement using PROC REG but not PROC GLM.

What's the difference between white and welch tests?

What is the correct way to test for heteroskedasticity using PROC GLM?

[Rick_SAS]

PROC REG assumes that the explanatory variables are continuous. White's test uses the variance of the residuals to determine whether the data are heteroskedasticity.

PROC GLM was originally designed for the analysis of variance. The Welch test analyzes a CLASS variable (that is, categorical) and tests for equal variances across the levels of a specified CLASS variable. It is only applicable to a simple one-way model.  

I don't think PROC GLM supports a formal hypothesis test, but you can use diagnostic plots to inspect the distribution of the residuals and a Q-Q plot to inspect their approximate normality. Put PLOTS=ALL on the PROC GLM statement, which will create a panel of diagnostic plots and a panel of residual plots. You can inspect the diagnostic plots to get a fee for whether heteroskedasticity is a problem.  For more about the diagnostic panel, see https://blogs.sas.com/content/iml/2021/03/24/regression-diagnostic-plots-sas.html 

[sbxkoenk]

Hello,

• You can fit a model in which the residual variance is proportional to a power of the mean (a PoM-model).
• I am under the impression you might be interested in a model in which the residual variance differs according to the level of some categorical predictor variable(s).

Such models (both above!) can be handled quite easily with the MIXED procedure (or HPMIXED if you have a large dataset or LMIXED if you have Viya). 
PROC NLMIXED is also an option.

PROC MIXED, by default, uses the generalized least squares (GLS) method as the default estimation method for fixed effects.
The generalized least squares (GLS) - method is a good start when you want to deal with heteroskedasticity.

Koen

[SteveDenham]

For GLM: To test for homogeneity of variance across CLASS levels in a one-way ANOVA setting, use the MEANS statement with the HOVTEST option. There are a variety of tests available. I prefer the Brown-Forsythe method.

For mixed models (GLIMMIX being preferred); Include a RANDOM statement with the following syntax:

RANDOM _residual_/group = <class variable>;

And add the following COVTEST statement:

COVTEST 'common variance' homogeneity

This conducts a likelihood ratio test. One nice thing about this approach is that even for moderate sized datasets, you can ignore the testing part, and rely on convergence in distribution of the variance components if, in fact, there is no heteroscedasticity. You do this at the cost of degrees of freedom, so if you are in a situation where power of the test is at a premium, you can remove the statements if the test is non-significant.

For a situation where you have a main linear regression and you are looking for the influence of fixed categorical covariates, the GLIMMIX approach is quite handy.

SteveDenham