- Operating System: macoS High Sierra, 10.13.4
- brms Version: 2.4.0
I have three main questions:
- There seems to be a difference between people’s descriptions of ‘multinomial’ and ‘categorical’ multilevel models on internet forums, mc-stan posts, and stack exchange posts. I thought that a categorial variable is equivalent to a multinomial variable, meaning a variable with multiple, unordered categories. Surely, I’m missing a piece of the puzzle. Can someone please explain whether there is actually a difference between the two terms in theory and in brms, and if so, explain what the difference is?
I have two more questions about the priors of my particular multilevel model. Before that, here is some background information on the type of data I have:
- Outcome variable (1): categorical, 6 categories, N=168
- Predictor variable (2): both categorical, 3 and 4 categories, N=25
- Control variable (1): categorical, 25 categories, N=25
- There are levels (a hierarchy) in my data: the outcome variable is at level 1 and the predictors and the control variable are at level 2.
Goal : Is there a correlation between the predictor variables and the outcome variable, taking the control variable into account?
For example , 168 students responded to a question that had 6 possible answers (outcome var.). These 168 students are unequally distributed across 25 schools (control var.). Each of these 25 schools has 2 characteristics (predictor var.). Do students’ answers correlate with the kind of school they attend, controlling for the school itself?
ex.prior <- c(prior_string(“normal(0,1)”, class=“b”))
fit <- brm(
formula= GS ~ IS + SS + (1|School),
family= categorical (link=“logit”),
control = list(adapt_delta = 0.9)
When running get_prior() on my potential model, there are 52 priors that I have to set. I’ve read that it is more efficient to create priors in strings (i.e. with prior_string() ), but I am unsure of whether I should set priors on all 52 of the parameters or not. The Bayesian part of my brain shouts “yes!”, but in terms of doing this practically, the priors that I set often return errors. I would just like to use weak, regularizing priors, and I am a bit confused as to how to do this for the different kinds of parameters. Do I set priors on all of the classes, the coefs, the groups, or the dpars?
I mentioned in question 2 that I want to use weak, regularizing priors, as I’m still trying to understand priors for categorical variables. From what I’ve read on different forums and papers, it seems that “normal(0,1)” for coef b, and “cauchy(0,1)” for coef sd, are used quite often as weak, regularizing priors for categorical models. Does anyone have any recommendations for literature on priors for categorical variables?