On Thu, 2024-07-25 at 09:54 -0400, Dan Levitas wrote:

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I am performing a longitudinal LME analysis in which participants were scanned anywhere from 2-6 times over the course of several years. There are 4 groups denoting participants: Controls (C, coded as 0), group 1 (G1, coded as 1), group 2, (G2, coded as 2), and group 3 (G3, coded as 3). Additionally, I have included two covariates (age and number of previous concussions). With a single random effect (intercept, all 1s), my design matrix is:

Yij = intercept + time + age + numPrevConcussion + G1 + time*G1 +G2 + time*G2 + G3 + time*G3

I am primarily interested in time*group interaction differences between G1 and G2 (G1 - G2) and G1 and G3 (G1 - G3).

I first tried single row contrasts separately (i.e. CM.C = [0 0 0 0 0 1 0 -1 0 0] for G1-G3, and CM.C = [0 0 0 0 0 1 0 0 0 -1] for G1 - G3), which produced no significant results. I then created a multi-row contrast of the two contrasts above (i.e. CM.C = [zeros(2,5) [-1 0 1 0 0;-1 0 0 0 1]]), which also did not reveal significant findings. Only when I created a 3-row contrast (CM.C = [zeros(3,5) [1 0 0 0 0;1 0 -1 0 0;1 0 0 0 -1]]) did I get significant results.

I'm a bit unsure how to properly interpret these contrasts and wanted to get clarification on my thinking. Is the 3-row contrast assessing the null hypothesis of no group differences in the rate of change over time among the four groups? If so, does the lack of findings in the 2-row and single row contrasts indicate that there are no interaction differences between G1 and G2, and between G1 and G3?

Yes, this interpretation seems correct to me, both for the multi- and single-rows contrasts.

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