longitudinal disease progression study where it did matter (maybe this example is more clear than Ogle & Barber)
- lgpr: an interpretable non-parametric method for inferring covariate effects from longitudinal data
- R package build on top of Stan: Longitudinal Gaussian Process Regression • lgpr
Whether it matters computationally depends on the amount of data and parameterization.
Whether it can change the implied prior, depends on how strong the likelihood is.
Whether it matters when reporting the results depends on what you want to report.