Model distribution selection for response variable with peaks

Hi all, I have a response variable that is non-normal and has several peaks. The scale it between 0-1$, with intervals of 0.01. I tried to run a Gaussian model at first but the pp_check plots look quite bad. Based on a previous post here (Gaussian vs. skew-normal model selection), I also tried to run a beta-binomial model after converting my response variable to cents instead of dollars by multiplying it by 100. Gaussian model beta-binomial ppcheck

Here is my model syntax for the two models

brm(ResponseCents | vint(100) ~block*f_transition* f_manner + (1 + block || id , family = beta_binomial2, data = aggrdata, chains = 4, cores = n_cores-1, iter = 4000, warmup = 2000, control = list(adapt_delta = 0.9999, max_treedepth = 15), stanvars = stanvars, inits = "0")  
ResponseModel1 <- lme4::lmer(response ~  block*f_transition* f_manner + (1 + block || id ), data = aggrdata, control = lmerControl(optimizer = "Nelder_Mead", optCtrl=list(maxfun=200000)))

What other types of distributions might fit better?

I think @Guido_Biele (I hope it is ok if I tag you) recently worked on a project where they used a gamma-mixture model for multi-modal data? Maybe that could work. It might also help to mention your independent variables. Is there e.g. a grouping variable that could cause the multi-modality and could be modelled?

Yes I implemented a mixture of gammas, but this wasn’t wit brms and needs coding of the model in Stan directly. The model I used also wasn’t a regression model.

If you want to run a regression, the search term is mixture regression. I am not aware of Bayesian implementations, neither do I know how well non-gaussian likelihoods are supported by the packages that implement it.

Finally, a standard regression could work if you have variables that predict the outcome well. That’s hard to say from your description. (I would recommend to always describe how the data was generated, i.e. what are the measurements, what predictors exist or were manipulated …)

1 Like