nlme::lme() 中随机术语语法的解释

Question

I am trying to determine whether there is a significant effect of treatment on microbiome diversity between two timepoints (two timepoints x three treatments).
Can somebody please explain how to model this using linear mixed models using the nlme library in R ?
Particularly how to handle repeated sampling of the same subject over time.

I have seen the three following syntaxes used but don't really understand the difference between them.

model1 <- lme(diversity ~ treatment * timepoint,
               random = ~ 1 | mouseID,
               data = alpha_df)

model2 <- lme(diversity ~ treatment * timepoint,
               random = ~ timepoint | mouseID,
               data = alpha_df)

model3 <- lme(shannon ~ treatment * timepoint,
               random = ~ 1 + timepoint | mouse,
               data = alpha_df)

I think model3 is the correct one for my use but I am not sure.

Thanks in advance!

Answer 1

~ 1 | mouse ~ 1 | mouse means "one intercept per mouse". There is a main, fixed intercept (actually there are three intercepts, one per treatment), and the random intercepts of the mice are normally distributed around the main intercept.

~ timepoint | mouse ~ timepoint | mouse is the same as ~ 1 + timepoint | mouse ~ 1 + timepoint | mouse . It means "one regression line (ie an intercept and a slope) per mouse". There is a main slope (actually three main slopes because of the interaction term with the treatments) and the random slopes are normally distributed around the main slope.

So the "biggest" model is ~ 1 + timepoint | mouse ~ 1 + timepoint | mouse . If there is a biological justification that the mice have the same diversity value at time 0, you can drop the intercept: random = ~ 0 + timepoint .