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Level II

Mixed model: which specifications for cross-over designs?

I ran a cross-over trial where healthy volunteers came to the lab twice (separated by a wash-out period) and underwent sensory testing at both arm and foot, before and after one of two neuromodulation interventions. Each participant underwent both conditions in a randomly assigned order. We want to see if the neuromodulation interventions affected the outcomes differently for the arm and the foot.


I would like to analyze the (continuous) outcomes with a mixed model (I use JMP Pro 16.2). My fixed effects are Time (baseline and poststim), Stimulation (two levels), Limb (arm and foot), and all their interactions. I added Subject as a Random effect (intercept only).

I have questions on two levels:


1. Accounting for baseline values

  • It has been suggested to me that I adjust for baseline values of the outcome by including them as a fixed effect. This obviously improves the model's fit (lower AIC) and reduces the SE of the parameter estimates, but I worry about including the same values both as outcome and predictor.
  • Moreover, doesn't the inclusion of Subject as a random effect already account for the different baseline values (with the big caveat that the baseline is different for arm and foot and for each stimulation level).
  • To account for that, should I cross Subject(intercept) with Limb and Stimulation, to account for the different baselines for the two limbs in the two sessions? And if yes, how do I specify that correctly in the model?
  • Another option is to calculate change scores (post–baseline), use them as the outcome, and then include baseline as a fixed effect to adjust for them.


2. Covariance structure

  • I have also been pondering the need to specify a Covariance structure. Since I have only two time points, I guess I have only one pair of covariances to estimate, and therefore, do I really need to specify a covariance structure at all? Doesn't the inclusion of Subject as a random effect account for the correlation in the observations from the same subject?
  • If I try to specify Covariance structure (called Repeated Structure in JMP), I run into problems. In JMP, the default is set to Residual. But, as described in the JMP manual: "The Residual structure specifies that there is no covariance between observations, namely, the errors are independent." This is obviously not the case here. When I try more appropriate structures, I get into trouble. Because I have four values for each time-point for each subject (e.g. timepoints before: for each limb and for each stimulation), I get error messages, like so: The XXX covariance model requires that no subjects have duplicate values of the Repeated input variable.


Sorry for the long post. Any help pointing me to the best specification for this model would be greatly appreciated.