Hi Livia,
yes, 0 0 0 1 is the interaction (if longitudinal slopes = atrophy rates, differ across groups).
When interpreting these, it makes sense to look at your model:
Y_ij = b0 + b1 t_ij + b2 g_i + b3 t_ij g_i where t is time, g is group. For group=0 you have Y_ij = b0 + b1 t_ij so b0 is the intercept of group_0, and b1 the slope
For group=1 you have Y_ij= ( b0 + b2 ) + (b1 + b3) t_ij so (b0 + b2) is the intercept for group_1 and (b1 + b3) the slope.
So slope difference across groups is (b1 + b3) - b1 = b3 so c=( 0 0 0 1 ) (this is group_1 minus group_0) and intercept difference is (b0 + b2 ) - b0 = b2, so c = ( 0 0 1 0 )
Average slope across both groups is:
0.5 * (b1 + b3 + b1) = b1 + 0.5 b3 so c =( 0 1 0 0.5 )
Best, Martin
On 6. Jun 2017, at 07:44, Livia Liu livialiu333@gmail.com wrote:
Dear FS experts, I want to add some in my early mail. If the contrast CM.C= [0 0 0 1] is designed for the interaction effect(time and group). How to design contrasts to do the main effect about the time and group? CM.C=[0 1 0 1] and CM.C=[0 0 1 1]? Or other? I wonder I may be wrong in designing matrix X in early mail. Please help me.Looking forward to reply, and thanks very much. Kind regards, Livia
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