This is a bit ambiguous that what does predictions mean here. The final predictive distribution is the (linear) weighted average of the predictive distributions from each model. But we don’t have access directly to predictive distributions, but usually only to posterior draws from them- To get posterior predictive draws from the model average do this
yrep1 <- posterior_predict(fit1, draws=round(wts[1]*S))
yrep2 <- posterior_predict(fit2, draws=round(wts[2]*S))
...
yrep <- c(yrep1, yrep2, ...)
where S is the number of draws from each posterior predictive distribution. Then from yrep you can compute what you need. @nels, is this what you have done?
This is wrong. 1 ) You can’t average log-likelihoods directly, 2) the importance sampling ratio r_i^{(s)} is not anymore proportional to 1/p(y_i|\theta^{(s)}), and 3) you can’t use psis-loo for checking the effect of the weight computation. 3 would require cross.validation over the weight computation, but if we ignore that then you could compute log of average of loo-predictive densities (which have been computed for each model). I don’t think there is an easy way to do 3.