I have an experiment where we have 3 covariates: subject, treatment and time. I want to examine the effect of treatment, the effect of time, and their interaction, while controling for subject effect (there is substantial subject effect)

An abbreviated explanation of my experiment is:

sbj_A | tr_1 | time_0

sbj_B | tr_1 | time_0

sbj_C | tr_1 | time_0

sbj_A | tr_2 | time_0

sbj_B | tr_2 | time_0

sbj_C | tr_2 | time_0

sbj_A | tr_1 | time_1

sbj_B | tr_1 | time_1

sbj_A | tr_2 | time_1

sbj_B | tr_2 | time_1

sbj_C | tr_2 | time_1

Note that one of the conditions contains one less sample (`sbj_C | tr_1 | time_1`

) which was removed since it showed some sequencing issues with it. However, I now want to perform different comparisons so I consider `~treatment + time + treatment:time + subject`

. I then want to perform all relevant comparisons (`effect of treatment`

, `effect of time`

, and `effect of treatment * time`

), but get an error that the matrix is not full rank. I believe this is because of the sample number difference. How would you tackle this issue?

Many thanks in advance