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I'm faced with analyzing the following design:

In a longitudinal study, the muscle tissue of about 25 subjects are analyzed at 8 timepoints. Specifically, 7 measurements are taken during a race during multiple days (I don't know the spacing of the measurements). The 8th measurement is several weeks after the race. At each time point, muscle measurements in 4 separate muscle groups in both legs (left and right) are assessed. There is one observation per subject/leg/muscle group/time point. As I see it, this is a crossed design, because both legs and all muscle groups are analyzed for each participant.

I have tried to graphically summarize the (simplified) design (just for 2 subjects and 2 muscle groups for simplicity):

enter image description here

Information about the model:

  • Time points will be treated categorically and not continuously.
  • Fixed effects will include time point (categorical), age (continuous), sex (cateogrical), leg (categorical), muscle group (cateogrical) and another muscle parameter (continuous).
  • Random effects will at minimum include a random intercept per subject (i.e. (1 | subject) in lmer).
  • The goal is i) assess the relationship between the outcome and the other muscle parameter that is also measured at each time point.

My questions:

  • What are possible/sensible random effects for such a study design?
  • What are the "maximal" random effects for this study design?

I'm using lmer from the lme4 package in R and would appreciate suggestions in this regard (also the software is not crucial).

COOLSerdash
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  • Please add some information regarding fixed effects and which question you plan to answer with this model. I could imagine scenarios where leg and muscle group would be fixed effects/random slopes and subject and time grouping variables of crossed random effects. Time could also be a fixed effect/random slope (maybe even use a mgcv GAM?) and temporal auto-correlation might have to be considered (--> package nlme). – Roland Jan 29 '18 at 07:31
  • @Roland Thanks for your suggestions. I've added some information to the question. I would like to refrain from modelling time as continuous and possibly even nonlinear. Please ask if you need more information. – COOLSerdash Jan 29 '18 at 11:56
  • In your diagram there is no arrow from Right leg to Muscle group 1. Is that intended or an oversight? Why do you want time as a categorical fixed effect? I would have suggested something like y ~ age * sex * leg * mgroup * mparam + (leg * mgroup * mparam | subject) + (leg * mgroup * mparam | time) as a start for model development. – Roland Jan 29 '18 at 12:04
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    What's the idea behind treating leg as fixed? Are all subjects same-handed and so you expect systematic differences between left and right legs? If not, then leg should rather be a nested random effect (nested within subject). This reminds me of this thread https://stats.stackexchange.com/questions/120964, see in particular my answer there. (cc to @Roland) – amoeba Jan 29 '18 at 12:08
  • @Roland The missing arrow is indeed an error. I corrected the picture. – COOLSerdash Jan 29 '18 at 16:51
  • @amoeba Thanks, these are exactly the hints I'm after. – COOLSerdash Jan 29 '18 at 16:51
  • You should clarify what your time points are. Is it something like before intervention, after intervention, 24h after? Or just several repetitions of the measurement? Or smth else? How many time points do you have? – amoeba Jan 29 '18 at 16:56
  • @amoeba I've added a description of the time points to the question. – COOLSerdash Jan 29 '18 at 17:00
  • You might also want to clarify how many observations you have per subject/leg/muscleGroup/timePoint -- is it only one? – amoeba Jan 29 '18 at 20:06
  • @amoeba I've added the information. Thank you very much. – COOLSerdash Jan 29 '18 at 20:08
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    OK, I think the experimental design is clear now. So what you can theoretically consider is something like y ~ age * sex * mgroup * mparam * time + ((mgroup + time) * mparam | subject/leg). But note that this is a very complicated model that you cannot fit unless you have a huge amount of subjects, so realistically you will have to simplify it quite drastically. – amoeba Jan 29 '18 at 21:45
  • @amoeba Thank you very much for this suggestions. The number of subjects is indeed extremely limited (less than 30!). – COOLSerdash Jan 30 '18 at 05:07

0 Answers0