I have biomass data (continuous response variable). If sufficient data is collected, the log(Biomass) follows a normal distribution. However, I am separating the overall biomass by family (i.e., biomass for each family) and in some sites no families were recorded, and the biomass of that family is 0.
Up to now I have log + 1 transformed the family biomass data. This gives me positive values for the non-zero biomasses and 0´s where the family biomass was 0. The non-zero transformed values follow a normal distribution. If I use stan_glmer model only considering the non-zero values,the pp_check and residuals look fine (in R). But that is excluding my 0's! (which is excluding part of the reality)
I wanted to account for the 0's and I was suggested a hurdle model: one which uses a binomial distribution to specify the probability of getting a 0 or a positive value, and then fits another distribution to the non-zero data. I have been investigating a bit more about this model and reached the brms package (where you have the hurdle_lognormal function). My question is, is there a similar function that does hurdle_normal or hurdle_gaussian? If I fit the hurdle_lognormal to my transformed family biomass data the predictive fit underestimates the observed data (e.g., residuals are scattered around 2.5 instead of around 0) (comment: this also happens with my non-transformed data). I think the reason why this is happening is because it is using a lognormal distribution for the non-zero values; if it used a normal distribution I think the model fit would improve tremendously.
I really want to do this using bayesian techniques (e.g., stan). However, I did look at other packages that have the hurdle function (e.g., hurdlr or pscl) and I still couldn't specify the normal distribution for the non-zero values.
Any comments or suggestions about how to proceed? Thank you very much in advance! :)