# Linear mixed effects model with time series

I have been reading through the different posts here on linear mixed effects models, but am still very unsure whether I have understood the task correctly, therefor I am reaching out for help by the community, any point in the right direction will be greatly appreciated!

The task I was given is described as follows:

The mean difference between treatment and placebo in terms of symptoms core values at Day1, Day2, Day3, Day4 will be estimated with a repeated linear mixed effect model (LMM) with an unstructured covariance matrix. Treatment and time will be used as fixed effects, and baseline symptoms severity as a covariate.

• Dependent variable: Severity at given time
• Fixed effect: Treatment + Timepoint
• Covariate: Baseline measure

Example data:

mydata <- data.frame(
Subject  = c(rep(c("F1", "F2", "F3", "F4"), each=4)),
Timepoint = c(rep(c("1", "2", "3", "4"), each=4)),
Treatment = c(rep(c("B", "A", "C", "B"), each = 4)),
Severity_at_given_time = c(6.472687, 7.017110, 6.200715, 6.613928,6.829968, 7.387583, 7.367293, 8.018853, 7.527408, 6.746739, 7.296910, 6.983360, 6.816621, 6.571689, 5.911261, 6.954988))


And then fitting the model as follows:

severity.model = lmer(Severity_at_given_time ~ Treatment + Timepoint + (1|Baseline_measure), data=my.data)
summary(severity.model)


(In my full data that gives an R2 of 0.02)

Now I have to say I dont understand the part about "repeated LMM", why is that? From talking to the experimentalists they want to know whether there is a significant difference between treatment and placebo over time, which should already be captured by a single LMM?

Many thanks for feedback!

If understand correctly, you want to fit a multivariate regression model (aka marginal model) with an unstructured covariance matrix. This can be done, for example, using function gls() from package nlme. In your case, you could use something like:
fm <- gls(Severity ~ Timepoint * Treatment + baseline, data = your_data,