[R-sig-ME] Mixed models with dependent compositional data

[Dot Dumuid]

We are analysing data from a randomised controlled trial for an exercise
intervention.

We have 106 participants, in three groups:
(1) control (n=34)
(2) moderate exercise (n=36)
(2) intensive exercise (n= 36)

We want to know if participants' use of time changed differently depending
on which group they were in.

Our outcome measure is participants' 24-hour time-use composition
(minutes/day spent in 4 domains: sleep, sitting, standing and physical
activity).

Time use is measured at 3 time points:
(1) baseline
(2) post-intervention
(3) 12-month follow-up

Time in all four domains always adds to 24 hours, therefore if all
components are included in the model there would be perfect
multicollinearity. So we have expressed the time-use compositions as sets
of three isometric log-ratio (ilr) coordinates created using an orthonormal
basis. These ilr coordinates contain all relative information regarding the
time-use compositions and can be used to represent the compositions in
multivariate statistical models.

So, the variables for our model look like this:
ID = participant ID
gp = a factor variable ("I", "M, "C"), for intense, moderate or control
group
time = a factor variable (1, 2, 3) for time point of measurement
ilr1, ilr2 and ilr3 = three isometric log ratios (the dependent variables).

We would like to run a model like this:

fit=lmer(cbind(ilr1, ilr2, ilr3) ~gp * time + (1|ID)),
car::Anova(fit)  # this does a Type II MANOVA Test (Pillai)

(ignoring for the moment that participants may have random slopes).

But the lme4 regression command (lmer) does not allow more than one
dependent variable. We cannot work out how to compute a statistic for the
interaction effect between group and time point for all the log ratios
together (i.e., the set of log ratios).

Thanks in advance!
Dot

	[[alternative HTML version deleted]]