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!
LMR
-------------------------------------------------------------------
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
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