I have an ordinal response variable and a bunch of predictors, some of them are ordinal.

What is the best way to model the interaction between two ordinal variables, taking into account the monotonic effect?

I would use `brms`

because the monotonic effect is already built-in thanks to the `mo()`

function

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If I understand it correctly, what you want is a matrix of coefficients that increase in all rows and columns. That actually sounds like a quite complex structure and I am not sure how I would go about implenting it. I would expect brms to not support this directly, but I am on mobile and canâ€™t check. I think something like `mo(a) + mo(b) + a:mo(b)`

should work and is the closest you can get easily to the desired structure.

Tagging @paul.buerkner to check my reasoningâ€¦

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I `a`

is also monotonic, we should probably use `mo(a) + mo(b) + mo(a):mo(b)`

or equivalenlty just `mo(a)*mo(b)`

.

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