Issues with cholesky_factor_corr Matrices: Estimated as 1 During Model Fitting, Exceeding [-1,1] in Predictive Sampling

Modeling
1

Hi everyone,

We are working with a Bayesian model in Stan that includes two sets of Cholesky factorized correlation matrices:

parameters {
  array[M-1] cholesky_factor_corr[how_many_factors_in_random_design[1]] sigma_correlation_factor;
  array[M-1] cholesky_factor_corr[how_many_factors_in_random_design[2]] sigma_correlation_factor_2;
}

model {
  for (m in 1:(M-1)) {
    sigma_correlation_factor[m] ~ lkj_corr_cholesky(2.0);
    sigma_correlation_factor_2[m] ~ lkj_corr_cholesky(2.0);
  }
}

The model fits without divergence issues (only 2 divergent transitions out of ~4000 draws), but we noticed unexpected behavior in the correlation structures:

  1. Both correlation matrices are consistently estimated as identity matrices (all correlations ≈ 1.0). : The sampled values of sigma_correlation_factor and sigma_correlation_factor_2 do not vary—they are always 1.0.
  2. rhat and ess_bulk for both matrices return NA.
fit$summary('sigma_correlation_factor_2')
# A tibble: 13,068 × 10
   variable                            mean median    sd   mad    q5   q95  rhat ess_bulk ess_tail
   <chr>                              <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>    <dbl>    <dbl>
 1 sigma_correlation_factor_2[1,1,1]      1      1     0     0     1     1    NA       NA       NA
 2 sigma_correlation_factor_2[2,1,1]      1      1     0     0     1     1    NA       NA       NA
 3 sigma_correlation_factor_2[3,1,1]      1      1     0     0     1     1    NA       NA       NA
 4 sigma_correlation_factor_2[4,1,1]      1      1     0     0     1     1    NA       NA       NA
 5 sigma_correlation_factor_2[5,1,1]      1      1     0     0     1     1    NA       NA       NA
 6 sigma_correlation_factor_2[6,1,1]      1      1     0     0     1     1    NA       NA       NA
 7 sigma_correlation_factor_2[7,1,1]      1      1     0     0     1     1    NA       NA       NA
 8 sigma_correlation_factor_2[8,1,1]      1      1     0     0     1     1    NA       NA       NA
 9 sigma_correlation_factor_2[9,1,1]      1      1     0     0     1     1    NA       NA       NA
10 sigma_correlation_factor_2[10,1,1]     1      1     0     0     1     1    NA       NA       NA
# ℹ 13,058 more rows
# ℹ Use `print(n = ...)` to see more rows
  1. When performing predictive sampling (generated quantities block), some correlation values exceed [-1,1], leading to numerical errors.
Loading model from cache...
Running standalone generated quantities after 1 MCMC chain, with 1 thread(s) per chain...

Chain 1 Exception: lub_free: Correlation variable is 1.00006, but must be in the interval [-1, 1] (in '/tmp/RtmpXRypuf/model-44b176a8d7478.stan', line 184, column 1 to column 144)
Warning: Chain 1 finished unexpectedly!

Error: Generating quantities for all MCMC chains failed. Unable to retrieve the generated quantities.

Questions for the Community

  1. Why are both correlation matrices being estimated as identity matrices (1.0 everywhere)?
  2. What could be causing rhat and ess_bulk to return NA for these parameters?
  3. Why does sigma_correlation_factor_2 exceed [-1,1] in predictive sampling when it was estimated as 1?

Any insights, debugging suggestions, or best practices would be greatly appreciated!

Thanks in advance for your help

1 Like
2

Hi, @zhanchen, and welcome to the Stan forums.

Hard to say anything without knowing what the rest of the model is.

It’s hard to say much more without seeing the rest of the model.

3

Usually this errors are because not enough significant figures were requested in the initial run, so the checks in generated quantities fail. Usually changing to 9 (from the default of 6) is enough. We’re considering changing the default because of this