Reproduce posterior_predict from posterior_linpred for a neg binom spline model

[jonah]

@Angelo_D_Ambrosio

I would like to understand better the difference between posterior_predict and posterior_linpred,

Hi Angelo, here’s a brief explanation of the difference. Suppose you have a negative binomial regression with a log link:

\eta_i = a + bx_i \\ \lambda_i = \exp(\eta_i) \\ y_i \sim {\rm NegBinom}(\lambda_i, \phi)

• posterior_linpred() gives you posterior draws of \eta.
• posterior_linpred(transform=TRUE), or equivalently posterior_epred(), gives you posterior draws of \lambda, that is, it does the inverse link transformation for you.
• posterior_predict() gives you draws from {\rm NegBinom}(\lambda, \phi), that is it uses a NegBinom random number generator and includes the dispersion information in \phi.

@Angelo_D_Ambrosio

if I compare the medians of the posterior_linpred with transform = TRUE and posterior_predict

What do you get if you compare the means instead of the medians?