# ROPE range for wald/gamma/log-normal distribution regression

Dear Stan/Bayesian experts,

In psychology research, reaction time/response time is highly right-skewed. Inverse-gaussian(wald) distribution/ log-normal distribution are always suggested for modeling the RT.
However, for this kind of regression model, the linkage between predictor and predicted variable is not linear. For instance, in wald regression model, people use square/exponential function (see: Wald and Gamma Regression (Australian insurance claims 2004-2005) — Bambi 0.9.1 documentation) to transform the predictor. From Daniel Habermann’s post(ROPE range specification for binary models - #2 by martinmodrak), it seems for logistic regression, the first derivative of sigmoid function at 0, which is the 0.25 can be used for correct the ROPE range. For instance, if the predictor increase 1 unit, then the predicted variable would increase 0.25 unit, which means the ROPE range has to be corrected by divide the effect size with 4.
However, this method seems inappropriate for exponential function.I can think of several ways to calculate ROPE range in this case. For instance, after the model-fitting, calculate the first derivation of the transform function at the intercept value, using this derivation as the slope. Also, we can replace other transform functions with linear transform functions like RELU or Softplus. Which method is more suitable or is there any butter ideas?

Best,

Hi, I can’t really answer your ROPE question directly because I never used it but I my guess is that it comes down to the same problem everyone has when interpreting non-linear links ie. you can not interpret parameter values by themselves any more but only in the context of the entire model. Conditional effects are one way to look at this. BRMS supports them directly, otherwise you could check out the emmeans or ggeffects packages.

Regarding softplus, just be careful as it only becomes linear for larger values. Close to 0 it looks more like a log link.

And finally, I’d not use an inverse-gamma likelihood in a bayesian model, as the sampling behavior is horrible. The shifted-lognormal and and exponentially modified Gaussian are probably better alternatives for reaction times.

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