rstanarm does the wrong thing with collinear predictors, fails to include the prior when doing some setup

[andrewgelman]

Summary:

A simple model runs fast (as expected) in Stan but runs extremely slowly in rstanarm.

Description:

It's a regression model with collinear predictors and a proper and reasonably strong prior. The posterior is fine and well behaved, but rstanarm mistakenly does some computations with the likelihood (rather than the posterior, or prior-augmented likelihood), causing major problems.

Reproducible Steps:

Here's the R code.

Ilibrary("rstanarm")
library("rstan")
library("cmdstanr")
x1 <- 1:5
x2 <- 1:5
y <- c(1,5,2,3,4)

stan_data <- list(N=length(y), y=y, x1=x1, x2=x2, mu_b=c(0,0,0), sigma_b=c(1,1,1))
model <- cmdstan_model("linear.stan")
fit_1 <- model$sample(data=stan_data, num_chains=4)
fit_1$diagnose()
fit_1$summary()

fake <- data.frame(x1, x2, y)
fit <- stan_glm(y ~ x1 + x2, data=fake, prior_intercept=normal(0, 1, autoscale=FALSE), prior=normal(0, 1, autoscale=FALSE))

And here's the Stan program, linear.stan:

data {
  int N;
  vector[N] x1;
  vector[N] x2;
  vector[N] y;
  vector[3] mu_b;
  vector<lower=0> [3] sigma_b;
}
parameters {
  vector[3] b;
  real<lower=0> sigma;
}
model {
  y ~ normal(b[1] + b[2]*x1 + b[3]*x2, sigma);
  b ~ normal(mu_b, sigma_b);
}

RStanARM Version:

Version 2.19.2

R Version:

R version 3.6.1

Operating System:

macOS Catalina, 10.15.1 (but the problem occurs under other operating systems as well)