# Large Rhat when predictors not standardized

**URL:** <https://discourse.mc-stan.org/t/large-rhat-when-predictors-not-standardized/39161>\
**Category:** Modeling\
**Tags:** brms\
**Created:** [March 26, 2025, 2:20pm UTC](https://discourse.mc-stan.org/t/large-rhat-when-predictors-not-standardized/39161 "2025-03-26T14:20:38Z")\
**Posts on this page:** 8\
**Page:** 1

<div class="post-metadata">

**Author:** ![ydurr](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ydurr/32/20242_2.png) [@ydurr](https://discourse.mc-stan.org/u/ydurr)\
**Post date:** [March 26, 2025, 2:20pm UTC](https://discourse.mc-stan.org/t/large-rhat-when-predictors-not-standardized/39161/1 "2025-03-26T14:20:39Z")

</div>

Hi, first time brms user. I am trying to run a multilevel model with formula

```no-highlight
log(yield) ~ Item+Year+ pesticides_tonnes +avg_temp+precipitation_mm + (1+Item| Area)

```

see subset of unstandardized data:

```no-highlight
 Area,Item,Year,yield,pesticides_tonnes,avg_temp,precipitation_mm
Albania,Maize,2000,38811,565.82,16.67,994.6187
Albania,Potatoes,2000,141228,565.82,16.67,994.6187
Albania,Wheat,2000,30455,565.82,16.67,994.6187
Albania,Maize,2001,38135,628.79,16.59,1179.969
Albania,Potatoes,2001,148818,628.79,16.59,1179.969
Albania,Wheat,2001,28220,628.79,16.59,1179.969
Albania,Maize,2002,39460,691.75,16.47,1286.1083
Albania,Potatoes,2002,153868,691.75,16.47,1286.1083
Albania,Wheat,2002,31617,691.75,16.47,1286.1083
Albania,Maize,2004,46197,817.68,16.16,1518.797
Albania,Potatoes,2004,149346,817.68,16.16,1518.797
Albania,Wheat,2004,31130,817.68,16.16,1518.797
Albania,Maize,2005,45442,880.64,15.67,1505.5068
Albania,Potatoes,2005,167061,880.64,15.67,1505.5068
Albania,Wheat,2005,31582,880.64,15.67,1505.5068
France,Maize,2000,90766,97878,11.74,1206.9763
France,Potatoes,2000,395987,97878,11.74,1206.9763
France,Wheat,2000,71175,97878,11.74,1206.9763
France,Maize,2001,85711,99694,11.37,1115.8035
France,Potatoes,2001,374385,99694,11.37,1115.8035
France,Wheat,2001,66169,99694,11.37,1115.8035
France,Maize,2002,89751,82448,11.87,1139.3085
France,Potatoes,2002,423804,82448,11.87,1139.3085
France,Wheat,2002,74455,82448,11.87,1139.3085
France,Maize,2004,89907,76099,11.34,982.6951
France,Potatoes,2004,454162,76099,11.34,982.6951
France,Wheat,2004,75788,76099,11.34,982.6951
France,Maize,2005,82539,78265,11.55,935.4893
France,Potatoes,2005,422227,78265,11.55,935.4893
France,Wheat,2005,69887,78265,11.55,935.4893

```

I initially tried fitting the model fit\_brms1 where the continuous predictors pesticides\_tonnes, avg\_temp and precipitation\_mm are unstandardized which lead to large Rhat values.

Example of warning received:

- Warning: There were 929 divergent transitions after warmup.
- Warning: There were 3070 transitions after warmup that exceeded the maximum treedepth. Increase max\_treedepth above 10.
- Warning: There were 2 chains where the estimated Bayesian Fraction of Missing Information was low.
- Warning: Examine the pairs() plot to diagnose sampling problems
- Warning: The largest R-hat is 4.18, indicating chains have not mixed.  
Running the chains for more iterations may help.
- Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.

I tried:

- increasing the number of iterations to 4000
- setting adapt\_delta to larger values like 0.9 and 0.95
- setting prior to N(0,10)

but still obtained large R-hat values.

Finally, I decided to standardize the continuous predictors on fit\_brms2 and the model converges with R-hat values equal to 1.

How can I address the issue with the unstandardized predictors?

Thanks

code and summary of fit below

Code:

```no-highlight
priors <- c(
  prior(normal(0, 1), class = "b")
)

```

```no-highlight
fit_brm1 <- brm(
log(yield) ~ Year+ pesticides_tonnes +avg_temp+precipitation_mm + (1+Item| Area), data=df_yield_eu_train ,cores=4,iter = 2000 ,prior = priors)

fit_brm2 <- brm(
log(yield) ~ Year+ pesticides_tonnes +avg_temp+precipitation_mm + (1+Item| Area) , data=df_yield_eu_nrml_train,cores=4,iter = 2000 ,prior = priors)

```

End Code

Summary fit\_brms1:

```no-highlight
 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log(yield) ~ Area + Item + Year + pesticides_tonnes + avg_temp + precipitation_mm + (1 + Item | Area) - Area 
   Data: df_yield_eu_train (Number of observations: 561) 
  Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup draws = 4000

Multilevel Hyperparameters:
~Area (Number of levels: 11) 
                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 4.12 4.07 0.15 9.60 3.39 4 16
sd(ItemPotatoes) 0.12 0.10 0.01 0.30 3.28 4 11
sd(ItemWheat) 0.46 0.46 0.02 1.28 3.80 4 12
cor(Intercept,ItemPotatoes) 0.39 0.32 -0.01 0.88 3.21 4 11
cor(Intercept,ItemWheat) 0.04 0.88 -1.00 0.92 2.83 5 28
cor(ItemPotatoes,ItemWheat) -0.10 0.68 -0.91 0.99 2.97 5 11

Regression Coefficients:
                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept -17.05 10.36 -33.01 3.47 1.93 6 20
ItemPotatoes 1.34 0.10 1.23 1.53 2.60 5 11
ItemWheat 0.18 0.72 -0.50 1.39 3.05 5 14
Year 0.01 0.00 0.00 0.02 1.54 7 32
pesticides_tonnes 0.00 0.00 -0.00 0.00 1.80 6 12
avg_temp -0.03 0.05 -0.11 0.03 3.05 5 18
precipitation_mm 0.00 0.00 0.00 0.00 2.32 5 16

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.31 0.11 0.22 0.51 2.63 5 28

Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

```

Summary fit\_brms2:

```no-highlight
Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log(yield) ~ Area + Item + Year + pesticides_tonnes + avg_temp + precipitation_mm + (1 + Item | Area) - Area 
   Data: df_yield_eu_nrml_train (Number of observations: 561) 
  Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup draws = 4000

Multilevel Hyperparameters:
~Area (Number of levels: 11) 
                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.53 0.14 0.33 0.89 1.00 1515 2002
sd(ItemPotatoes) 0.28 0.07 0.18 0.45 1.00 1780 2615
sd(ItemWheat) 0.48 0.11 0.31 0.75 1.00 2006 2476
cor(Intercept,ItemPotatoes) -0.20 0.28 -0.70 0.38 1.00 1806 1769
cor(Intercept,ItemWheat) -0.47 0.23 -0.82 0.08 1.00 2332 2411
cor(ItemPotatoes,ItemWheat) 0.68 0.18 0.21 0.92 1.00 2529 2616

Regression Coefficients:
                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept -14.28 2.89 -19.82 -8.60 1.00 4104 2764
ItemPotatoes 1.27 0.09 1.09 1.43 1.00 1629 2222
ItemWheat -0.45 0.15 -0.74 -0.15 1.00 1660 2179
Year 0.01 0.00 0.01 0.02 1.00 4107 2820
pesticides_tonnes 0.03 0.03 -0.03 0.10 1.00 5421 3097
avg_temp -0.17 0.04 -0.25 -0.09 1.00 5710 2767
precipitation_mm 0.07 0.02 0.03 0.10 1.00 6503 2954

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.17 0.01 0.16 0.18 1.00 7227 2679

Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

```

EDIT (Aki): added some ticks for easier reading of code and tables

---

<div class="post-metadata">

**Author:** ![amynang](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/amynang/32/19114_2.png) [@amynang](https://discourse.mc-stan.org/u/amynang)\
**Post date:** [March 26, 2025, 3:15pm UTC](https://discourse.mc-stan.org/t/large-rhat-when-predictors-not-standardized/39161/2 "2025-03-26T15:15:38Z")

</div>

How about mean-centering them without scaling?

Edit: What is the reason you want to avoid standardization?

If you do this inside the formula,

```no-highlight
log(yield) ~ Year+ pesticides_tonnes +scale(avg_temp)+scale(precipitation_mm) + ...

```

brms should give you everything backtransformed.

---

<div class="post-metadata">

**Author:** ![ydurr](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ydurr/32/20242_2.png) [@ydurr](https://discourse.mc-stan.org/u/ydurr)\
**Post date:** [March 26, 2025, 3:35pm UTC](https://discourse.mc-stan.org/t/large-rhat-when-predictors-not-standardized/39161/3 "2025-03-26T15:35:45Z")

</div>

It seems maybe pesticides\_tonnes is causing some issues. I ran the model with mean-centering with and without pesticides\_tonnes.

Without pesticides\_tonnes:  
I obtained Rhat of 1 but warnings with max tree-depth and low ESS which can probably be fixed with more iterations.

With pesticides\_tonnes:  
I obtained large Rhat values of 4.

I’m not against standardization, I was just curious why the chains don’t mix with the unstandardized predictors. Is it maybe something to do with the prior I set?

I am going to try running the unstandardized model without pesticides\_tonnes to see if it changes anything.

edit:  
Indeed, without pesticides\_tonnes, the unstandardized predictor model obtains rhat value of 1, while giving warning about low ESS and reaching treedepth.

---

<div class="post-metadata">

**Author:** ![amynang](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/amynang/32/19114_2.png) [@amynang](https://discourse.mc-stan.org/u/amynang)\
**Post date:** [March 26, 2025, 3:47pm UTC](https://discourse.mc-stan.org/t/large-rhat-when-predictors-not-standardized/39161/4 "2025-03-26T15:47:06Z")

</div>

Hm I totally ignored your prior. Why did you choose this prior? What happens if you run the model without it?

---

<div class="post-metadata">

**Author:** ![ydurr](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ydurr/32/20242_2.png) [@ydurr](https://discourse.mc-stan.org/u/ydurr)\
**Post date:** [March 26, 2025, 4:09pm UTC](https://discourse.mc-stan.org/t/large-rhat-when-predictors-not-standardized/39161/5 "2025-03-26T16:09:32Z")

</div>

I initially didn’t specify a prior and only added it after looking at the diagnostic warnings page, which suggested setting a stronger prior.

The standardized model works with/without setting any priors.

The centered-mean and unstandardized work with/without setting prior when pesticides\_tonnes is not included.

---

<div class="post-metadata">

**Author:** ![mitzimorris](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/mitzimorris/32/29_2.png) [@mitzimorris](https://discourse.mc-stan.org/u/mitzimorris)\
**Post date:** [March 26, 2025, 4:22pm UTC](https://discourse.mc-stan.org/t/large-rhat-when-predictors-not-standardized/39161/6 "2025-03-26T16:22:20Z")

</div>

> [@ydurr](#):
>
> The centered-mean and unstandardized work with/without setting prior when pesticides\_tonnes is not included.

If pesticides\_tonnes is on a very different scale than the rest of your predictors, standardizing the predictor values is necessary. by default, BRMS mean-centers the predictors, but doesn’t standardize them. both make the sampler’s job a whole lot easier - higher effective sample sizes, faster fits.

see the section in the Stan User’s Guide on [standardizing predictors](https://mc-stan.org/docs/stan-users-guide/efficiency-tuning.html#standardizing-predictors).

---

<div class="post-metadata">

**Author:** ![ydurr](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ydurr/32/20242_2.png) [@ydurr](https://discourse.mc-stan.org/u/ydurr)\
**Post date:** [March 26, 2025, 4:30pm UTC](https://discourse.mc-stan.org/t/large-rhat-when-predictors-not-standardized/39161/7 "2025-03-26T16:30:42Z")

</div>

Thank you, that is probably the issue:

| | pesticides\_tonnes | avg\_temp | precipitation\_mm |
| --- | --- | --- | --- |
| min | 121 | 6.66 | 475.23853 |
| max | 114695 | 18.82 | 2026.3944 |
| mean | 15034.91305 | 11.72096257 | 957.1739762 |
| median | 7871.1 | 10.64 | 867.78735 |
| sd | 25194.49011 | 3.395233971 | 308.7355052 |

Pesticide is much larger than the remaining predictors.

---

<div class="post-metadata">

**Author:** ![avehtari](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/avehtari/32/5935_2.png) [@avehtari](https://discourse.mc-stan.org/u/avehtari)\
**Post date:** [March 26, 2025, 7:05pm UTC](https://discourse.mc-stan.org/t/large-rhat-when-predictors-not-standardized/39161/8 "2025-03-26T19:05:58Z")

</div>

With unnormalized predictors `Bulk_ESS` is around 4-7, which is clear indication that chains are stuck in different modes. Looking at the posterior for `fit_brms1`, we see that the varying intercept has expected sd of 4

> [@ydurr](#):
>
> ```no-highlight
> Multilevel Hyperparameters:
> ~Area (Number of levels: 11) 
> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
> sd(Intercept) 4.12 4.07 0.15 9.60 3.39 4 16
> 
> ```

As the target is `log(yield)` it means that the intercepts are likely to explain most of the variation in the data, and chains are stuck in these different local modes where each chain has different varying intercepts.

With normalized data, sd of varying intercepts is more reasonable

> [@ydurr](#):
>
> ```no-highlight
> Multilevel Hyperparameters:
> ~Area (Number of levels: 11) 
> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
> sd(Intercept) 0.53 0.14 0.33 0.89 1.00 1515 2002
> 
> ```