Hi Jorge,
Thank you for your reply!
Again considering the same model from before
intercept(random
effect) + centered age + group + group x centered age + sex
I
think what is confusing me is that I think of the [centered age]
covariate as a column vector which will contain the centered age of both
the control- and the case group. This is how it would be seen in a GLM using the same design matrix.
Therefore it is difficult for me to understand how the contrast [0 1 0 0
0] can inform us about the control group alone. To me it would seem obvious that this contrast tells me something about the effect
of [centered age] on the whole of the sample, regardless of the group
each subject belongs to.
On the other hand, I agree with you that the interaction term could
tell us something about the effect of [centered age] on the case-group
by considering the contrast vector [0 0 0 1 0].
Just for the sake of argument, please consider the following model
intercept(random
effect) + (1-group) x centered age + group + group x centered age + sex
and
compare to the one presented above. Here (1-group) is a column vector
which is 1 where the [group] vector is 0, and vice versa. This
difference ensures that the second term only includes numbers from the
control-group. Applying the contrast [0 1 0 0 0] to this model, would this
not be more appropriate for consider the effect of [centered age]
on the control-group alone?
Given your previous answers I
suspect I'm missing something here, but I would greatly appreciate if
you could please take the time to explain to me how I've gone wrong.
Thanks!
-------------------------------------------------------------------
Hi LMR
1) Yes, you should
use n-1 (0/1) covariates to model n groups. Eg. (Controls, Case 1
and Case 2) the model would be:
intercept(random
effect) + centered age?(might be a random effect too)?+ ?Case1 + Case1 x centered age + Case2 +
Case2 x centered age + sex
2)In model:
intercept(random
effect) + centered age + group + group x centered age + sex
the fourth coefficient is
the interaction term that represents the difference in slope between
the patient and control groups. This is easy to see from your
Question 1 equations. It's also easy to see from those equations
that [0 1 0 0 0] tests the effect of time in the control group since
the group-specific slope is only equal to the coefficient of the time covariate (the
second covariate) when the group covariate is zero (i.e for the
controls).
Hope this makes
sense.
Best
-Jorge
--
yours,
Lars M. Rimol, PhD
St. Olavs Hospital
Trondheim,
Norway