This is my first attempt with Bayesian statistics. I need to figure out if I have enough information to set more informative priors for a zero-one-inflated beta regression in
brms. Initially I used the default priors (coi: beta(1, 1), Intercept: student_t(3, 0, 10), phi: gamma(0.01, 0.01), sd: student_t(3, 0, 10), zoi: beta(1, 1)), which according to my understanding are uninformative and have no impact on the posterior. I saw that many people in Bayesian statistics encourage researchers to think about using more informative priors, so I wonder if I could derive something from a previous study I did, with the same dependent variables.
The stimulus was a set of 36 clips that had been selected subjectively by experimenters to fit into 9 classes which were combinations of two 3-level categoricals: pleasure (negative, neutral, positive) and intensity (low, medium, high). There were 6 clips in each class. The participants watched the clips and evaluated them in terms of pleasure and intensity on two continuous sliders with values in [0,1].
The stimulus is a set of 18 clips that have been generated from the clips of the previous study, and the generative model was conditioned on the pleasure/intensity continuous scores given by the participants of the previous study. The clips are labeled with 3-level categorical tags, p_cat (negative, neutral, positive) and i_cat (low, medium, high), that were derived from the discretization of conditioning continuous scores in 3 bins. Current participants evaluated them as in the previous study: pleasure and intensity in two continuous sliders with values in [0,1]. Here is my current model:
mvbind(pleasure, intensity) ~ p_cat * i_cat + age + experience + gender + (1|item) + (1 |subject)
where p_cat and i_cat are the 3-level categories for pleasure and intensity.
Can I use information from the distribution of the response in the previous study as a prior to the current study?
In case that would be an acceptable approach, would it make sense to add priors on the coefficients for each level of my categorical variables p_cat and i_cat? For instance, in terms of p_cat and the response pleasure, a prior for the coefficient of Intercept (reference level for negative p_cat), another for the coefficient of neutral p_cat, and a third one for positive p_cat.
If this is acceptable, can I get all the responses from previous study, split them in 3 bins, get the mean and variance of each bin and use this to set the priors mentioned in 2?
- Operating System: Ubuntu 16.04.6 LTS
- brms Version: 2.10.0