Comparison using WAIC

 P(Model 1 better than Model 2)=Φ(elpd_diff​/se_diff)

prob_model_better <- function(elpd_diff, se_diff) {

  z <- elpd_diff / se_diff

  p <- pnorm(z)

  return(p)

}

elpd_diff <- 5
se_diff   <- 3

prob_model_better(elpd_diff, se_diff)

Result:

[1] 0.952

So there is approximately 95% probability that model 1 predicts better than model 2.

It is not the probability that the model is better — only that its predictive accuracy is higher.

You can use also the function Probability_Best_Model_WAIC() in HelpersMG packages that uses original loo results to compare the predictive accuracy of several models.



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