# Can I estimate a "bidirectional" monotonic effect?

I am working with some spatial location data from a localization experiment where sounds are presented from discrete sources (loudspeakers) at fixed combinations of horizontal and vertical coordinates.

Currently, I am estimating population-level effects (betas) and varying effects (correlations) for each discrete location of which there are 40.

I’m wondering if there is anything I can do that would represent/estimate continuous effects. For example, if I have target horizontal locations at -90, -60, -30, 0, 30, 60, 90 and I expect errors to be larger as the location moves away from zero, can I estimate a “Gaussian-like” effect of target on error?

the monotonic effects in `brms` do this for ordinal, increasing, categorical predictors. Would one monotonic effect of -90, -60, -30, 0 and another for 30, 60, 90 be a valid approach?

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Sorry for not getting to you earlier, your question is relevant and well written.

There are the smooth terms - either splines (Defining smooths in brms formulas — s • brms) or Gaussian processes (Set up Gaussian process terms in brms — gp • brms) AFAIK currently GPs in brms don’t support 2D data, but 2D splines are supported and I’ve seen people use the `t2` term for this goal succesfully (never used them myself, so can’t help much beyond that).

There are also ways to force splines to be monotonic, but I don’t think I’ve seen anyone do 2D and monotonic (and in the particular way you need). It seems like it should be possible to build a spline basis that does what you need, but it will likely be a tiny research project on its own.

Yes, that sounds like a reasonable way to get something without much hassle. Note that `mo` effects are 0 for the reference category, so you can setup that when the actual value is positive the predictor for the negative side is at its reference category and this should work.

Best of luck with the model!