I was confused by many of the responses to Mike's post... maybe because I'm
not a statistician. But I'm guessing Mike isn't a statistician either, so
maybe he is as confused as I.
My (limited) understanding is that the homogeneity of variances requirement
for a regression is in the response variable. Basically, when you do a
least squares regression, the technique gives a "pooled" estimate for the
variance in the response variable. If the response variance changes across
the range of the regressor variable, this pooled estimate is not
appropriate.
There are many examples in my area of background (analytical chemistry)
where the response variance is not constant, but the %CV ("coefficient of
variation", also called the RSD or "relative standard deviation") is
constant. In cases like this, the analyst often uses a transformation of
the response variable (such as ln(Y) or Y^0.5) to make the variances
homogeneous prior to the regression.
As for tests for homogeneity of variance, I know that in JMP (the low-end
SAS program) there are several tests for homogeneity within the Fit Y by X -
ANOVA platform. (To get this to work in JMP, you need to change the X
variable from a continuous to an ordinal variable). The tests available
include O'Brien, Brown-Forsythe, Levene, and Bartlett. I am unable to
comment on the strengths and weaknesses of these tests, but would be
interested in hearing what the more experienced list-members have to say
with regards to them. (I am also interested to find out how off-the-mark my
comments are!)
- Eric Scharin
-----Original Message-----
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED]]On Behalf Of mike
Sent: Friday, May 12, 2000 12:01 PM
To: [EMAIL PROTECTED]
Subject: homogeneity of variances
First, I'd like to thank all who responded to my first post concerning
normality and regression analysis. However, now this leads me to my next
question.
The error terms in the regression model are required to have normal
distributions with constant variance. I understand how to test for
normality in SAS, but how do you test for homogeneity of variances in SAS?
Do you test the residuals or the orginial data for homogeneity of variance?
I have looked at the SAS manual and there is a test for homogeneity of
variance for Proc GLM using the Means statement. However, this doesn't seem
to be the same as looking at the variance of a linear regression (does
variance increase, decrease, or stay the same with increasing X values).
Any suggestions?
Thanks again. Mike
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