Contrasts for distributional parameters in a shifted log normal distrbution

Hi,
some of the response depends on the exact formula (and potentially other code) you used to fit your model, could you share those, as well as the complete model output?

Not really. First, focusing too much on the estimate can be misleading, the reported uncertainty is also important. Second, if I am guessing correctly, sigma_Intercept is just the intercept of the linear model for sigma, the interpretation of the intercept cannot be made without understanding how the other covariates interact with it.

Generally, with such complex models, there will be a ton of interactions between the model parameters and I am not sure emmeans will handle it well. If you are interested only in the log mean (i.e. you don’t care about sampling variability), then focusing only on the main formula for mean might be enough and you can ignore sigma (as that just represents the sampling variability and that it is not the same for all groups). If you need to do anything more complex, I usually find it better to just use posterior_predict, posterior_linpred or posterior_epred to generate predictions for a suitably chosen data, representing a hypothetical future experiment (say all combinations of trial and bias with average age). And then look at the comparisons of interest in those predictions. This is a bit harder as it forces you to think about a lot of details, but those details can matter, so being explicit about them is IMHO beneficial

I wrote about this elsewhere, i.e Inferences marginal of random effects in multi-level models - #3 by martinmodrak and Multivariate model interpreting residual correlation and group correlation - #6 by martinmodrak , but that was in a quite different context so feel free to ask for clarifications!

Best of luck with your model!