Hi Jesper, thanks for your answer. A short follow up question. I'm
still a bit unsure about the Variance of a contrast. I know that
Variance is the Sum of the Squared Deviations from the Mean. However I
just don't get if for contrasts and I guess my question really is: How
is the VARCOPE calculated?
Here is what I think it is with a simple example:
Let's say I have a voxel with the following 25 values over time.
1 1 8 9 2 1 1 2 9 8 1 2 1 2 8 8 1 1 2 2 9 9 1 2 1
my EV1 is
0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0
my EV2 is
0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0
taken together
1 1 8 9 2 1 1 2 9 8 1 2 1 2 8 8 1 1 2 2 9 9 1 2 1
0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0
0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0
one can clearly see that EV1 covariates with the data while EV2 doesn't.
I set ev1 and ev2 up as a model matrix and got the inverse (Moore-
Penrose-Pseudoinverse) of it and then multiplied the inverse with the
data.
My parameter estimate for EV1 is 8.50 and for EV2 is 1.33.
I specified a contrast - Contrast1 EV1>EV2: 1 -1
COPE in this case is the same as PE1 minus PE2. Right?
So COPE1 would be (8.5*1) + (-1*1.33) = 7.2
Now I multiply my PEs with my contrast and get [8.50, -1.33]
then I multiply [8.50, -1.33] with my model matrix and see what the
model predicts. In my case that would be:
0.00 0.00 8.50 8.50 0.00 -1.33 -1.33 0.00 8.50 8.50 0.00 -1.33 -1.33
0.00 8.50 8.50 0.00 -1.33 -1.33 0.00 8.50 8.50 0.00 0.00 0.00
When I calculate the difference between predicted_data and actual data
I get
1.00 1.00 -0.50 0.50 2.00 2.33 2.33 2.00 0.50 -0.50 1.00 3.33 2.33
2.00 -0.50 -0.50 1.00 2.33 3.33 2.00 0.50 0.50 1.00 2.00 1.00
then I square every element and sum it up - in my case 72. I think
that is VARCOPE1 - is that right?
Now I could calculate e.g. a t-test:
t = Parameter_Estimate / Standard_Error
t = PE / ((VARCOPE)^0.5 / (degrees_of_freedom)^0.5)
t = 7.2 / (72^0.5 / 23^0.5) = 4.07
That seems a rather low t-value for this made up data so I think I'm
doing something wrong here.
Sorry for these basic questions but I at least want to get the basics
right. Thanks, Michael
On 19-Jun-09, at 12:14 PM, Jesper Andersson wrote:
> Very simple answer,
>
>> Hi, I have a very simple question.
>> I know that PE means parameter estimate.
>> What does COPE and VARCOPE stand for?
>
> COPE=COntrast of Parameter Estimates.
> VARCOPE=VARiance of COntrast of Parameter Estimates.
>
> Jesper
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