Brms: input scaling clarification

[martinmodrak]

Hi,
sorry for not getting to you earlier.

The transformation is described under “Parameterization of the population-level intercept” at the docs for brmsformula

@japhir

I’m trying to understand whether/how brms scales inputs by default. From the generated stan code for a simple model (see below) it looks like by default it does center the inputs, but does not divide them by the standard deviation, is this correct?

That is IMHO correct, but note that it centers only the predictors, not the response data.

@japhir

If I now have the fitted model to the scaled outputs, it seems like I should be able to convert back to the original scale using something like:

Note that centering the design matrix (except for intercept) does NOT change the values of any model coefficients except for the intercept - the coefficients for non-intercept predictors represent change in prediction per unit change in the predictor and thus are invariant to any shifts of the predictor values.

The b_Intercept reported in the model is already shifted back, so it has to be interpreted as if centering did not take place (you can also extract the Intercept parameter which is what the model actually works with)

Also note that for most tasks, you can use posterior_predict/posterior_linpred / posterior_epred that handle a lot of this stuff for you.

@japhir

I tried looking at the docstring for the parameter in brms(..., normalize) but this didn’t clarify this for me.

The normalize option is completely unrelated to data pre-processing (it selects whether normalized or unormalized density functions are used e.g. normal_lpdf vs normal_lupdf).

Best of luck wtih your model!