Modelling a continuous covariate measured at every observation time point

Question

I have a within-subjects design where I measure the dependent variable at 4 time points, repeated measures, in a number of participants (say 30).

To use an analogy (without getting into the specifics of my research), say I want to measure performance on a jump test (a continuous variable), but the covariate I want to control for is another continuous variable, such as a biomarker of fatigue that is measured immediately before each test is performed.

Therefore, it is not like usual covariates of sex, age etc that are static across all observations. Instead, my “covariate” changes at every measurement point, but the dependent variable might be affected by it.

Can anyone come up with a good suggestion as to how to model this? I have a reasonable amount of experience using frequentist and multivariate methods, in jamovi, R, Prism or (if I must) SPSS.

Answer 1

Having a covariate that changes across individual values shouldn't change the modelling approach. You can model that like with any other covariate. In fact, if a covariate had the same value across all observations, it would have no predictive power (associated with no change in the outcome) and be automatically discarded from the model.

Here I am assuming that you have a covariate that changes for observations within the same subject and across subjects, and when you refer to other covariates like sex, that they are constant within the same subject but differ across subjects. This additional covariate should not require a different modelling approach apart from including the new covariate.

Given that your dependent outcome is continuous, a linear mixed model or generalised estimating equations (with one or multiple covariates), mixed-design ANOVA (one covariate) or mixed-design ANCOVA (multiple covariates) should be valid approaches. This assumes that the model assumptions with each test are held, such as the residuals being approximately normally distributed. You have generalised linear mixed models (GLMMs) in your tags. That may also be suitable (note that a linear mixed model is a special type of GLMM). GLMM allows for further modelling distributions compared to a simple linear mixed model. Given that the jump test outcome is continuous, a linear mixed model should probably suffice, although it is impossible to confirm without reviewing the data and model fit.