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I am wondering whether you can assume two different functional relationships that differ based on a group-based predictor in a mixed effects (or any) statistical model. The goal is a predictive model.

For example, group A is assumed to have a linear increase across a continuous time variable up to an asymptote/leveling off based on prior observations, whereas group B might have something like an inverted U-shaped function at first across time (also based on prior observations). I'd like to analyze the two groups together in the same analysis.

My first thought was a polynomial MLM and the parameter estimate for the quadratic component would just end up being close to or at 0 for group A. But the quadratic function would continue to increase exponentially over time (as parabolas of this orientation do) and this is not what my data would eventually do.

Eventually both groups would level off, but assumptions about where the leveling off would occur are not very specific (making reduction of knots in something like a spline difficult). It would be best if the timing of this asymptote-like leveling off could also be variable within the model, but it is not 100% necessary.

Any help or thoughts on the matter are greatly appreciated.

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There is no fundamental reason that disallows you to define two different functional forms for the evolution over time in the two groups. Though depending on the specific details behind the definition of these functions, different software could be more/less flexible in allowing to do this.

Again even though we don’t know the details, I would still be in favor of a spline-based approach.

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  • $\begingroup$ Thanks, I was leaning towards the spline approach. I am thinking that a 3-6 knot spline may get me where I need to be if I have the data for it. I am only familiar with spline regression at a surface level and wondered if you have any literature that has been helpful for digging into the weeds of it a bit. I use R and JMP Pro primarily. $\endgroup$ Aug 5, 2019 at 21:02

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