I am modeling data from an experiment with a mixed model. The outcome variable is a percentage. There are three fixed effects, Condition: diseased and healthy, Time point: 1, 2 and 3 , Drug: A,B,C,D,E. Subject is taken as the random effect. I need to perform three tests:
- Check for a significant difference between disease and healthy for time point 1 and drug A, and so on for all the combinations of time points and drugs
- Check for significant difference between Time point 1 and 2 for all the combinations of drugs and conditions
- Check for a significant difference between Drug A and B for all the combinations of time points and conditions.
The data is unbalanced
This is what I did:
1. Build a linear mixed model
fit_1 <- lmer(y~Condition*Drug*Timepoint+(1|Subject))
lsmeans to perform tests
lsmeans(fit_1,pairwise~Condition | Drug * Timepoint,adjust="none") lsmeans(fit_1,pairwise~Timepoint | Drug * Condition,adjust="none") lsmeans(fit_1,pairwise~Drug | Condition * Timepoint,adjust="none")
However, none of the p-values were less than the nominal 0.05 alpha-level. The inference on these values was significant when Wilcoxon test was used. So I went back to check the residuals and they seemed to violate the assumptions of normal distribution and homoscedasticity. Should I use GLMM instead? If so, which family will be applicable when $y$ variable is a percentage of counts data?