Understanding shifted lognormal parameters and priors

Hey!

Looking at the actual Stan code generated by make_stancode shows that the shifted Log-Normal is parameterized like lognormal_lpdf(Y - ndt | mu, sigma), so, ignoring Jacobians for a moment, this means \log(Y - \text{ndt}) \sim \text{Normal}(\mu, \sigma). With link identity for mu, the coefficients are on the log scale! I know this is a bit confusing – at least for me it was in the beginning. Having a log-link for ndt implies (again, ignoring Jacobian corrections) \log(Y - \exp(\text{ndt})) \sim \text{Normal}(\mu, \sigma), so the ndt coefficients are then also on the log scale as well. You could work out the interpretation for each coefficient, but I’d say the coefficients are not the interesting part of the model – this is especially true for such such non-linear models, or any non-trivial model really. Btw, exp-ing coefficients wont give you the conditional mean of Y, but of its logarithm! Taking the \mu of the above formula, \exp(\mu) is actually an estimate of the (conditional) median of the outcome… and the outcome has ndt in it… well, I’d suggest to look at what group comparisons are meaningful to your analysis an then generate posterior predictions for these outcomes and compare those. This is bit in the spirit of marginal effects (at representative values) which are widely used in frequentist stats as well.

brms is great for that, too! You could try adding truncation to the model… something like trunc(ub = 105), I think. So

bf(RT | trunc(ub = 105) ~ 0 + intercept + A + B + (1 | ID),
   ndt ~  0 + intercept + A + B + (1 | ID))

but I’m not very sure of this one, because I don’t regularly work with brms (although it’s great).

Cheers!
Max

2 Likes