Hi LMR
If the interaction
term is not statistically significant then there is no evidence of
the existence of two different groups in your sample (as far as the
longitudinal trajectory is concerned they are all controls, the
groups might be different at baseline though). This is why main
effects are only tested after the interactions have been previously
tested. In your model a common “base time slope” is assumed for
both groups (the second coefficient) but you are also explicitly
modeling the possibility of the case-group slope being exceeding the
control/common base slope by an extra quantity. That quantity is the
interaction term.
Hope this makes
sense
Best
-Jorge
>________________________________
> De: Lars M. Rimol <lari...@gmail.com>
>Para: FS maling list <freesurfer@nmr.mgh.harvard.edu>
>Enviado: Miércoles 18 de junio de 2014 8:57
>Asunto: Re: [Freesurfer] Linear Mixed Models in FS?
>
>
>
>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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