Hello,
I have noted contradictory advice from statisticians on how to model time-varying covariates in a repeated measures mixed effect model. For instance, you may have BMI measured every month as the exposure and a blood biomarker measured at the same time (or maybe different times) every month as the outcome. If you wanted to determine the effect of BMI throughout the follow-up period then how would you do this?
Some statisticians say you don't do anything differently (at least not in STATA coding) because in long format STATA can determine which variables are level 1 and level 2 by whether or not they vary by time-point. Other statisticans state that you need to create new variables that equate to the between- and within-person effect on the outcome.
Just wondering what you all thought of this.
Thank you,
Spencer
Spencer,
As far as I understand it both advices are correct, depending on what you want to know. In the classic mixed-effects model, you can simply include your time-varying predictor variable as usual. In this model, however, the fixed (within) and the random (between) effects are entangled with each other and cannot be interpreted in a differentiated way. For example, you cannot separate the effects for individuals whose BMI has changed and those whose BMI remained constant over time. This is only possible by using so-called hybrid models that split the effects of cluster-varying covariates on the outcome into within-cluster and between-cluster effects. The terms for these effects would have to be formed beforehand and taken into the model together: the centered predictor forms the fixed effect and the mean of the predictor forms the random effect. Both effects can then be interpreted independently. However, by doing so you would assume that fixed and random effects are uncorrelated; the question is how realistic that is. The user-specific Stata command xthybrid automates the term formation and estimates the effects separately. To my knowledge, xthybrid also allows the estimation of correlated effects (i.e. the Mundlak model).
In short, if the average effect of BMI on the biomarker across all persons is sufficient for you, take the normal mixed model. If you are specifically interested in the difference between BMI-invariant and BMI-variant persons - and I think that's the more interesting approach here - take the hybrid model.
Hope this helps.
Regards,
Alex
Here is some Stata Code for demonstration:
mixed blood bmi || id:, mle /* classic model with entangled effects */
bys id: center bmi, prefix(z_) mean(m) /* fixed effect by hand */
egen m_bmi=mean(bmi), by(id) /* random effect by hand */
mixed blood z_bmi m_bmi || id:, mle /* hybrid model by hand */
ssc install xthybrid
xthybrid blood bmi, clusterid(id) family(gaussian) link(identity) /* automated hybrid model */
xthybrid blood bmi, clusterid(id) family(gaussian) link(identity) cre /* Mundlak model */
the different forms of the model are discussed here
Article Fixed and Random effects models: making an informed choice
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