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I'm trying to analyse a potential carryover effect from a study with a crossover design 3x3, three treatments and three periods. My data has a latin square design with the treatment sequences CBA, ACB, BAC. Therefore, it is not completely balanced, all six sequences are not included. But the study is uniform. I'm using baseline as a covariate. I have found information on how to get the likelihood of a carryover effect with a crossover design 2x2 but less for 3x3. The same problem seem to have been discussed earlier:

repeated measures ANOVA, crossover trial, R

But with no clear solution. Does anyone know how to do this? In a 2x2 design I have seen it is possible to get the sequence effect by adding the period and the sequence to the model or to add the interaction, trt*period:

https://ethz.ch/content/dam/ethz/special-interest/math/statistics/sfs/Education/Advanced%20Studies%20in%20Applied%20Statistics/course-material-1719/Repeated/3_crossover.pdf

I don't know if this applies to a 3x3 design. In the anova below I have tried this but I don't get the same results. Maybe it means its the wrong solution for a 3x3 design. Or maybe the problem is that the design is not completely balances? Does anyone have a solution for this? Thanks! :)

ibslm1 <- lmer(formula= diettrt[,i] ~ BL+ trt+period+ randseq + (1|id) , data=diettrt)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: diettrt[, i]
          Chisq Df Pr(>Chisq)    
BL      70.7333  1  < 2.2e-16 ***
trt     15.7889  2  0.0003728 ***
period   0.6983  2  0.7052894    
randseq  0.0802  2  0.9606988    
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ibslm1 <- lmer(formula= diettrt[,i] ~ BL+ trt*period + (1|id) , data=diettrt)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: diettrt[, i]
             Chisq Df Pr(>Chisq)    
BL         68.4161  1  < 2.2e-16 ***
trt        16.0165  2  0.0003327 ***
period      0.7084  2  0.7017481    
trt:period  5.3143  4  0.2565389    
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