Can non-convergence of a model be taken as proof of its inferiority compared to another converged model?

No worries @Bob Carpenter. I’ll take any help I can get. "For what?" Enough information for you to advise me how to improve this model. I just wondered if you’d need loo-ecdf or any of those diagnostic plots. Doesn’t sound like you do.

What do you mean by "if you set the coefficient to zero"?`. Do you mean set the prior on the cubic term to zero? I realised i probably should have included the model itself

fit_zibetabinomial_cubic_ats <- brm(formula = outcome | trials(set) ~ ats_baseline*yearsFromStart + ats_baseline*I(yearsFromStart^2) + ats_baseline*I(yearsFromStart^3) + (1 | encID),
                                data = workingDF,
                                family = zero_inflated_beta_binomial(),
                                prior = c(prior(normal(0, 3),
                                                class = Intercept),
                                          prior(normal(0, 4),
                                                class = b),
                                          prior(cauchy(0, 3),
                                                class = sd)),
                                save_pars = save_pars(all=TRUE),
                                seed = 1234,
                                refresh = 0,
                                cores = 4)

Pretty generic prior setting I realise. I could go more specific for different coefficients but haven’t had to up to this stage (i.e. through all the iterations of Gaussian, Binomial, Beta-Binomial, Zero-inflated Beta-Binomial, Zero-inflated Beta Binomial with a quadratic).

Not much I can do about the amount of data I have. Can you suggest a better prior for the cubic, assuming that’s what you mean by setting coefficients to zero?

p.s. Thanks for your help
p.p.s. More puns please, and emojis