I want to compare how fast children from 2 countries [Country] run on a treadmill [Speed] at two time points [Time]. Specifically, I wanto to see whether the change over time is different in those two countries. Moreover, I want to control for the fixed effects of age at baseline [Ageb], weight at baseline [Weightb], and height at baseline [Heightb]. I wanto to allow children of different ages to have different slopes (older children should gain more speed compared to younger children). Finally, I want to control for the random effects of examination date [Date] and treadmill used to measure the speed [TreadmilId]. Date and Treadmill are time-varying.
I thought a repeated measures mixed effects model would be appropriate for this research question. What should be the notation in lme4 then?
Would the below notation be good?
Speed ~ Time*Country + Ageb + Heightb + Weightb + (1+Ageb|SubjectId) + (1|Date) + (1|TreadmillId)
Alternatively, if I treated Age, Weight, and Height as time varying covariates, could I use the following notation:
Speed ~ Time*Country + Age + Height + Weight + (1+Ageb|SubjectId) + (1|Date) + (1|TreadmillId)
I would be greatfull for alternate approaches to the problem as well.