I found this helpful article, so I will try to answer this myself. Hopefully someone like @ucfagls will chime in if I am wrong.
sds(stime_1) is the sd of the smooth weights (spline coefficients). This determines the amount of ‘wiggliness’, in an analogous way to how the sd of group-level effects in a varying slopes and intercepts model determine the amount of variability among groups in slopes and intercepts. However, the actual numeric value of the sds() is not very practically interpretable, because thinking about the variance of smooth weights for any given data and model seems abstract to me. However, if the
value is around zero, then this is like ‘complete-pooling’ of the basis functions, which means that there isn’t much added value of more than a single basis function.
stime_1 is the unpenalized weight (ie coefficient) for one of the “natural” parameterized basis functions. The rest of the basis functions are like varying effects. Again, because the actual numeric value of stimes_1 is the value for the unpenalized coefficient for one of the basis functions, this wouldn’t seem to have a lot of practically interpretable meaning just from viewing this number.
Follow-up question - what if I have longitudinal data for 300 participants, with multiple data points per participant, where I would like to fit a spline. Does doing something like brm(outcome ~ s(time) + (time|id) make any sense? If so, how does the varying linear slope for time relate to the s(time)? I would like a varying slopes model, but if it isn’t linear, is there a varying splines model? I don’t think (s(time)|id) can be fit in brms, if I remember, and I am also not sure it makes much sense…
Again, any help is appreciated, and hopefully I have answered my original question correctly and don’t lead anyone else astray! Please correct if I am wrong.
Edit - also, still not sure about the y-axis on the conditional_smooths() plot…