How does the formula for the lmer function work?
Some examples:
library('lmer')
lmer(Yield~(1|Batch),Dyestuff)
lmer(Yield~(Batch)*(1|rep(c(1,2,3),10)),Dyestuff)
lmer(Reaction ~ Days + (1|Subject) + (0+Days|Subject), sleepstudy)
On the left of ~ sign is the dependent variable and on the right comes all the independent variables separated by the + sign.
Is there any difference between + and *?
What does 1|Batch mean? Does it have to do with the intercept? With being a random or a fixed effect?
What does Day|Subjects mean?
(1|Batch)means "one intercept per batch". $\endgroup$(Days|Subject)means a random intercept and a random slope for each subject.(1|Subject)would mean only a random intercept but a common slope across subjects. $\endgroup$