Comment by nxobject
1 day ago
I just needed to stop and say: as a biostatistician, boy do I love a beautiful complex longitudinal design: I remember my old professor asking us how at this point we would decompose into cross-sectional and longitudinal effects, Lord's paradox, etc... and I still don't fully understand Lord's paradox as well as I should.
This is a very important idea. For example, one issue with accelerated longitudinal designs, see image [1], is that while they efficiently cover a larger age range, the fixed effects of age are largely driven by cross-sectional differences between who is samples are younger and older ages. One method that can be used to test whether the pattern seen in the fixed effects represents the pattern within subjects is to decompose within and between effects of age. For example, you can create a non-time-varying variable like age at first visit (starting_age), and then a within subject variable change in age since first visit, which would be zero at the first visit (age1-age1=0, age2-age1 for change of age between visit 2 and visit 1, age3-age1, for change in age between 3rd visit and first visit), calling it dage. Then in the mixed model, test for an interaction between starting_age:dage. If you have an interaction, then you know that the within subject effect of change in age is different depending on how old you were when you started. I got this from Lesa Hoffman's freely available lectures [2], particularly [3][4], and now I discovered she recently published [5], which I should read.
[1] https://e-m-mccormick.github.io/static/longitudinal-primer/l... [2] https://www.lesahoffman.com/ [3] https://www.lesahoffman.com/PSYC944/944_Lecture11_Alt_Time.p... [4] https://www.lesahoffman.com/Workshops/SMiP_Presentation_June... [5] https://www.tandfonline.com/doi/full/10.1080/00273171.2025.2...
And thank you for the reminder of Lord's paradox. I should refresh myself.