Why does this brms-generated model not compile after 15 minutes?

Modeling
,
1

(Moving this over from a brms issue at @paul.buerkner recommendation)

I am trying to fit this multilevel model using brms 2.22.0 and backend cmdstanr 2.36.0:

y ~ x_1 +... x_K + (x_1 + ... + x_K || g1 * g2)

However, when K = 32 the model does not compile after 15 minutes. Note the following cases do compile:

  • replace || with |. However with K=32 I do not want to fit a 32 x 32 covariance matrix
  • K = 2
  • replacing g1 * g2 with just g1

Looking at the generated stan code-- when switching from | to ||, things that were vectorized get unvectorized. For example the priors on the random effects involve 32+1 calls to std_normal_lpdf

It’s not clear to me why this takes forever. It is complicated but not that complicated? Even the vectorized | model is slow to compile as @paul.buerkner points out. And why is the ||g1 model fine?

Here’s a script to generate fake data, print the model, and compile:

N = 100 # number of observations
K = 32 # number of predictors
J1 = 2 # number of groups g1
J2 = 2 # number of groups g2

df = as.data.frame(matrix(rnorm(N*K), nrow=N))
x_names = paste0("x_", 1:K)
colnames(df) = x_names

df$g1 = factor(sample(1:J1, N, replace=TRUE))
df$g2 = factor(sample(1:J2, N, replace=TRUE))

# y has no relationship to x and g, just fake data for compiling model
df$y = rnorm(N) 

sum_x_str = paste(x_names, collapse="+")
formula = as.formula(sprintf("y ~ %s + (%s||g1*g2)", sum_x_str, sum_x_str))

brms::make_stancode(formula, df, backend="cmdstanr", chains=0)
brms::brm(formula, df, backend="cmdstanr", chains=0)
2

What platform are you running on? This compiles for me in 2mins on an M1 Mac:

   user  system elapsed 
128.401   2.382 133.564

Definitely on the slow side though

3

Thanks! Admittedly my machine is old (Intel i5-3320M).

I’m curious, when you switch the formula from ||g1*g2) to ||g1) how much faster is it? That was the thing that was confusing to me-- why would one compile in 2 minutes (on my hardware) and the other not compile after 10 minutes.

4

PS I am using debian linux, I can pull some compiler info if you are interested and tell me what command to run in shell/R.