# Issues with cholesky\_factor\_corr Matrices: Estimated as 1 During Model Fitting, Exceeding \[-1,1\] in Predictive Sampling

**URL:** https://discourse.mc-stan.org/t/issues-with-cholesky-factor-corr-matrices-estimated-as-1-during-model-fitting-exceeding-1-1-in-predictive-sampling/38744
**Category:** Modeling
**Tags:** rstan
**Created:** [February 11, 2025, 4:11am UTC](https://discourse.mc-stan.org/t/issues-with-cholesky-factor-corr-matrices-estimated-as-1-during-model-fitting-exceeding-1-1-in-predictive-sampling/38744 "2025-02-11T04:11:07Z")
**Posts on this page:** 3
**Page:** 1

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### Author: ![zhanchen](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/zhanchen/32/20002_2.png) [@zhanchen](https://discourse.mc-stan.org/u/zhanchen)
#### Post date: [February 11, 2025, 4:11am UTC](https://discourse.mc-stan.org/t/issues-with-cholesky-factor-corr-matrices-estimated-as-1-during-model-fitting-exceeding-1-1-in-predictive-sampling/38744/1 "2025-02-11T04:11:07Z")

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Hi everyone,

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

```no-highlight
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`.

```no-highlight
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**.

```no-highlight
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

---

<div class="post-metadata">

### Author: ![Bob\_Carpenter](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/bob_carpenter/32/9230_2.png) [@Bob\_Carpenter](https://discourse.mc-stan.org/u/Bob_Carpenter)
#### Post date: [February 11, 2025, 10:08pm UTC](https://discourse.mc-stan.org/t/issues-with-cholesky-factor-corr-matrices-estimated-as-1-during-model-fitting-exceeding-1-1-in-predictive-sampling/38744/2 "2025-02-11T22:08:36Z")

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

> [@zhanchen](#):
>
> We are working with a Bayesian model in Stan that includes **two sets of Cholesky factorized correlation matrices** :

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

> [@zhanchen](#):
>
> Both correlation matrices are consistently estimated as identity matrices

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

---

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### Author: ![WardBrian](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/wardbrian/32/12078_2.png) [@WardBrian](https://discourse.mc-stan.org/u/WardBrian)
#### Post date: [February 11, 2025, 10:13pm UTC](https://discourse.mc-stan.org/t/issues-with-cholesky-factor-corr-matrices-estimated-as-1-during-model-fitting-exceeding-1-1-in-predictive-sampling/38744/3 "2025-02-11T22:13:50Z")

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> [@zhanchen](#):
>
> Why does `sigma_correlation_factor_2` exceed `[-1,1]` in predictive sampling

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