# Multilevel analysis or separate analysis for each level - group / individual analysis

I collected muscle activity levels from 4 different leg muscles on each lower limb over a 20 jump test in 2 groups of athletes. One group has ACL injury (n=11) and there is a control group (n=11). Additionally, there are 4 separate jump phases for each individual jump. Finally, I break the 20 jumps down into 4 clusters of 5 jumps to evaluate the fatigue effects (cluster 1 = rested, cluster 4 = fatigued). You can think of the 4 clusters of jumps as a time series.

My first analysis plan was to subset my data down to each level of interest. I planned to filter out a single muscle first, and then a single jump phase. I then planned to assess equality of variance and normality and to transform my data as needed to compare the left limb to the right limb for each group separately using a paired t-test. Then, I planned to make group comparisons by comparing the injured limb of the ACL subjects to a limb average for the controls, and the uninjured limb of the ACL subjects to the limb average for the controls using a one-way anova. I would repeat this process for each muscle and each jump phase.

My second plan was to delve into something more complex like a multilevel model. Note that I would plan to build this model up to include interaction terms and the appropriate contrasts to get at my 2 primary research questions: do muscle activity levels differ between limbs and between groups w/ fatigue for ACL subjects and controls as measured over the four different jump clusters.

Here is my first attempt at this model without the interaction terms included (I wanted to save space).

Muscle.Activity.lme = lme(muscle.activity~group+limb+muscle+jump.cluster+jump.phase, random = ~1 | subject/limb/muscle/jump.cluster/jump.phase, data = EMG, method = "ML")


My questions:

1. Is it wrong to separate out the various levels to perform between group and within group comparisons as indicated in my first analysis plan?

2. Is a multilevel model feasible for my data set and is this approach reasonable? I think my sample size might be too small but I'm wondering if this is a significant limitation or one that needs to be managed.

3. Are there any other analysis approaches that might work better?

Thank you for any insight you can provide.

Matt

• Preliminary query: do you have an idea of what sampling distribution your muscle activity data may follow? Is it indeed approximately normally distributed? This will help me tailor my answer below to your specific situation. – Brash Equilibrium Jul 21 '15 at 2:40

I recommend starting with a model that includes an athlete-level intercept to account for the repeated measures within athlete, which is probably the most important hierarchical aspect of this system. I would then include population-level effects for jump (or jump cluster of you prefer to group jumps as you mentioned), ACL-injury indicator, and limb. Limb and ACL you would treat as factor variables. Limb would effectively be a set of dummy variables, with one limb chosen as the reference group. I don't know if you tested all four limbs separately, but if you did, you might consider having limb instead coded as upper-lower and left-right indicators, which you may want to interact with both each other and the handedness of the athlete if available. You might even consider a second order interaction between handedness, limb, and side of body. And then of course there are the possibilities of interaction effects among handedness, body side, upper/lower, and jump order (your fatigue measure). With all of these possible interactions you may want to use a modeling framework that will provide some automated variable selection and regularization to reduce the effects of multicollinearity and to ameliorate the curse of dimensionality. If you are looking for a regularized regression-modeling framework that allows for random effects and is really good for balancing the need for good predictions against the accessibility of easily-interpretable parameters, I suggest you try mboost (for a boosted option) or possibly MCMCglmm for a fully Bayesian option. The mboost package has the added advantage of allowing for smoothing splines to be included in the model as well as linear effects and individual level intercepts.