Textbooks say to not adjust group means for a covariate when their
regression
lines are not parallel, since mean differences depend upon the value of the
covariate.
But, what exactly are adjusted group means in the presence of interaction?
And don't they sometimes make sense?
Take the example of age adjusted means for 3 groups: regression with 2
indicator variables for the groups and age a continuous variable.
Say, there is an interaction between groups and age and we ignore it and fit
the above "adjusting" model with only the 3 main effect variables.
It seems to me that the age-adjusted group mean differences are the averages
of group mean differences over all values of the covariate in the sample.
Isn't this right?
If it is right, then I'd think that sometimes it would be exactly what you'd
want to know, eg say your sample included the age range of your population
and
you just wanted to show that your crude group mean differences weren't due
to
age differences between groups.
Just some late night ramblings...
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