Compound glms (bernoulli_logit_glm_lpmf, poisson_log_glm_lpmf, etc) give wrong answer if only intercept

[jgabry]

Description

When X has 0 columns, beta has 0 elements, and alpha has 1 element functions like bernoulli_logit_glm_lpmf (I've checked poisson too but not others yet) ignore alpha and return 0, that is,

bernoulli_logit_glm_lpmf(y | X, alpha, beta) = 0

but it should take into account alpha.

I noticed this problem because of https://github.com/stan-dev/rstanarm/issues/396, where models with only an intercept give the wrong inferences. Turning off using the compound glm functions (bernoulli_logit_glm_lpmf, poisson_log_glm_lpmf) fixes the problem. Below is an example Stan program illustrating the problem.

Example

If I run the following Stan program:

data {
  int<lower=0> N;
  int<lower=0,upper=1> y[N];
}
transformed data {
  matrix[N, 0] X;  // 0 columns
}
parameters {
  real alpha;
  vector[0] beta; // 0 elements 
}
model {
  alpha ~ normal(5, 10);
  target += bernoulli_logit_glm_lpmf(y | X, alpha, beta);
}
generated quantities {
  real test_lpmf = bernoulli_logit_glm_lpmf(y | X, alpha, beta);
}

then test_lpmf always has the value 0.0e+00 (i.e., 0) but it shouldn't be zero due to alpha. I have also tested the poisson case and the same problem occurs.

Expected Output

It should take alpha into account when calculating the lpmf.

Current Version:

v2.20.0 (via CmdStan 2.20.0)

[t4c1]

I think all glms are affected.

[t4c1]

Actually it turns out ordered_logistic_glm_lpmf() was not affected. All others were.

[rok-cesnovar]

Fixed via #1399

[jgabry]

Thanks for fixing so quickly!