Hi! I’m currently working on a meta analysis about the relationship between sleep and memory. Specifically, one aspect of my study involves analyzing the circular-linear correlation between a circular variable (EEG phase) and a linear variable (memory index). The data I will be using is about circular-linear partial r (distributed from 0 to 1) instead of the usual Pearson’s r. So after converting these values to Fisher’s z, the resulting distribution approximates a half-normal distribution rather than a normal distribution.
What I would like to ask is when I use a half-normally distributed data to build a Bayesian hierarchical model, would it be appropriate to set the μ prior to a half-normal distribution using the code below, or are additional steps necessary?
priors <- c(prior(“normal(0,1)”, class = "b", coef = "Intercept", lb = 0), prior(“cauchy(0,0.5)”, class = “sd”))
I would greatly appreciate any insights or guidance on this question!