I want to decide about whether a parameter of my linear Bayesian regression model (log-normal family, fitted in R with brms) has a “significant” influence on the response, i.e. the data scale.
I am using Kruschke’s HDI+ROPE rule in R with the sjstats package by @strengejacke (
equi_test function). The function tests the HDI+ROPE rule for each of the fitted posterior distributions of the parameters in the model, i.e. returns whether to accept/reject/leave undecided the null hypothesis. Now, since I am using a log-normal distribution, this is done on the log scale, i.e. it tests if a parameter has some influence on the predictor (mean of the log-normal distribution), if I understand correctly. Does this imply that this result about the parameter is also valid with respect to the model response, i.e. on the data scale, or is it necessary to predict those values first and then evaluate their distribution?