Prediction with latent variables in brms multivariate models

[ViktorR]

Thanks Paul for bringing multi-variate models to brms! I'd like to use a multivariate model to infere a latent variable to make predictions when no observations of this latent variable is available. However, I'm struggling of finding a good implementation of such a model. The idea is to fit a model that can predict a latent variable and then use draws from the posterior predictive distribution of this model as input for another model to incorporate the uncertainties of the previous prediction. 

Here's a small toy example to show what I'd like to do:

library(brms)
data(mtcars)


#Multi-variate model
bf_hp<-bf(hp ~ cyl, family = gaussian())
bf_mpg<-bf(mpg ~ hp, family = gaussian)
fit<-brm(bf_mpg+bf_hp, data=mtcars)


newdata_NA<-data.frame(hp=c(NA,NA),
                       cyl=c(10,4))

#Fails because of missing input data
post_pred<-posterior_predict(fit, newdata = newdata_NA)

My idea for now would be to fit the first model, take draws of the posterior predictive distribution and use these as input data for the next model. However, this leads either to huge sample sizes when taking all samples from the  posterior predictive distribution or I have to take again a sample of the full sample. I'm neither sure if this is at all the right way to do it nor if there is a more elegant way for such a problem in brms. 

library(brms)
library(reshape2)


#Init
data(mtcars)
chains<-4
iter<-2000
warmup<-iter/2
samples<-(iter-warmup)*chains


#Fit model to predict latent variable horse power (hp) by the number of cylinders (cyl)
fit_hp<-brm(hp~cyl, data=mtcars, family=gaussian(), chains=chains, iter=iter, warmup=warmup)
fit_mpg<-brm(mpg ~ hp, data = mtcars, chains=chains, iter=iter, warmup=warmup)


# Draws from posterior predictive distribution of latent variable
post_pred_hp<-posterior_predict(fit_hp, newdata=data.frame(cyl=c(10,4)))


#Create input data from predictions of latent variable
newdata_mpg<-data.frame(hp=c(post_pred_hp[,1],post_pred_hp[,2]),
                    cyl=c(rep(10,samples),rep(4,samples)))


#Draws from posterior predictive distribution for all samples from posterior predictive distribution of the previous model
post_pred_mpg<-posterior_predict(fit_mpg,newdata=newdata_mpg)
post_pred_mpg<-cbind(melt(post_pred_mpg[,1:samples])$value,melt(post_pred_mpg[,(samples+1):ncol(post_pred_mpg)])$value)

Thanks, Viktor

[Paul Buerkner]

Hi Viktor,

maybe my last post in https://github.com/paul-buerkner/brms/issues/303 can help you.

Best

Paul

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