Disaggregating Between and Within Person Effects
created on 3/22/24 by Maria Perica
While cross-sectional data is able to tell us about between-person effects, only longitudinal data can provide information about within-person effects. It is important to note that between-person effects do not necessarily generalize to within-person effects - classic example: at the between-person group level, people are more likely to have a heart attack if they exercise less, but at the within-person level, you are more likely to have a heart attack while exercising than just chillin'.
Two important things to consider when building these models: variable centering and detrending. Centering is important here, even when variables do not vary over time, but if variables vary over time then detrending also becomes important.
Centering
Centering is usually a straightforward thing - subtract the mean from your values! But it becomes complicated in multi-level models because there are multiple means you can be referring to (grand mean vs group/person-centered mean)
Generally three options re: centering in multi level models with longitudinal data. Option 1: don't. Option 2: grand-mean center aka average across the whole group/all timepoints and subtract from every variable datapoint. Option 3: person-mean center aka average across a person's timepoints and subtract their person-specific mean from their data.
Detrending aka controlling for the effect of time
Couple ways to do this depending on which variables you think could be varying with time
Option 1: detrend nothing, Option 2: detrend only the predictor, Option 3: detrend predictor and outcome
There appears to be much debate on how to do this properly and whether you should detrend predictor, outcome or both.
At least one paper recommends just including a 'time' representing variable in your model and that does about as well as multi-step detrending processes (Wang & Maxwell,2015)
In our data, one way to do this is could be add 'visit number' into models as covariate (this would detrend your outcome variable)
Sources: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3059070/, https://pubmed.ncbi.nlm.nih.gov/25822206/, https://centerstat.org/centering/