Extract and add to the data values of the probability density function based on a stan linear model

Question

Given the sample data sampleDT and models lm.fit and brm.fit below, I would like to:

estimate, extract and add to the data frame the values of the density function for a conditional normal distribution evaluated at the observed level of the variable dollar.wage_1 .

I can do this using a frequentist linear regression lm.fit and dnorm but my attempt to do the same using a bayesian brm.fit model fails. Therefore, any help would be much appreciated.

##sample data

sampleDT<-structure(list(id = 1:10, N = c(10L, 10L, 10L, 10L, 10L, 10L, 
    10L, 10L, 10L, 10L), A = c(62L, 96L, 17L, 41L, 212L, 143L, 143L, 
    143L, 73L, 73L), B = c(3L, 1L, 0L, 2L, 170L, 21L, 0L, 33L, 62L, 
    17L), C = c(0.05, 0.01, 0, 0.05, 0.8, 0.15, 0, 0.23, 0.85, 0.23
    ), employer = c(1L, 1L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L), F = c(0L, 
    0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 1L), G = c(1.94, 1.19, 1.16, 
    1.16, 1.13, 1.13, 1.13, 1.13, 1.12, 1.12), H = c(0.14, 0.24, 
    0.28, 0.28, 0.21, 0.12, 0.17, 0.07, 0.14, 0.12), dollar.wage_1 = c(1.94, 
    1.19, 3.16, 3.16, 1.13, 1.13, 2.13, 1.13, 1.12, 1.12), dollar.wage_2 = c(1.93, 
    1.18, 3.15, 3.15, 1.12, 1.12, 2.12, 1.12, 1.11, 1.11), dollar.wage_3 = c(1.95, 
    1.19, 3.16, 3.16, 1.14, 1.13, 2.13, 1.13, 1.13, 1.13), dollar.wage_4 = c(1.94, 
    1.18, 3.16, 3.16, 1.13, 1.13, 2.13, 1.13, 1.12, 1.12), dollar.wage_5 = c(1.94, 
    1.19, 3.16, 3.16, 1.14, 1.13, 2.13, 1.13, 1.12, 1.12), dollar.wage_6 = c(1.94, 
    1.18, 3.16, 3.16, 1.13, 1.13, 2.13, 1.13, 1.12, 1.12), dollar.wage_7 = c(1.94, 
    1.19, 3.16, 3.16, 1.14, 1.13, 2.13, 1.13, 1.12, 1.12), dollar.wage_8 = c(1.94, 
    1.19, 3.16, 3.16, 1.13, 1.13, 2.13, 1.13, 1.12, 1.12), dollar.wage_9 = c(1.94, 
    1.19, 3.16, 3.16, 1.13, 1.13, 2.13, 1.13, 1.12, 1.12), dollar.wage_10 = c(1.94, 
    1.19, 3.16, 3.16, 1.13, 1.13, 2.13, 1.13, 1.12, 1.12)), row.names = c(NA, 
    -10L), class = "data.frame")

##frequentist model: this works

lm.fit <-lm(dollar.wage_1 ~ A + B + C + employer + F + G + H,
            data=sampleDT)

sampleDT$dens1 <-dnorm(sampleDT$dollar.wage_1,mean=lm.fit$fitted,
sd=summary(lm.fit)$sigma) 

##bayesian model: this is my attempt - it does not work

//this works
brm.fit <-brm(dollar.wage_1 ~ A + B + C + employer + F + G + H,
            data=sampleDT, iter = 4000, family = gaussian())

//this does not work
 sampleDT$dens1_bayes <-dnorm(sampleDT$dollar.wage_1, mean = fitted(brm.fit), sd=summary(brm.fit)$sigma) 

Error in dnorm(sampleDT$dollar.wage_1, mean = brm.fit$fitted, sd = summary(brm.fit)$sigma) : Non-numeric argument to mathematical function

Thanks in advance for any help.

Answer 1

We have that now fitted(brm.fit) is a matrix, so we want to use only its first column - that of estimates. Also, as there is no reason for the object structure to be the same, summary(brm.fit)$sigma gives nothing. Instead you want summary(brm.fit)$spec_pars[1] . Hence, you may use

sampleDT$dens1_bayes <- dnorm(sampleDT$dollar.wage_1,
                              mean = fitted(brm.fit)[, 1],
                              sd = summary(brm.fit)$spec_pars[1])