# Results from monotonic effect versus dummy variables in brms

**URL:** <https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537>\
**Category:** Modeling\
**Created:** [March 5, 2020, 9:49am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537 "2020-03-05T09:49:07Z")\
**Posts on this page:** 20\
**Page:** 1

<div class="post-metadata">

**Author:** ![ssalimi](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ssalimi/32/7119_2.png) [@ssalimi](https://discourse.mc-stan.org/u/ssalimi)\
**Post date:** [March 5, 2020, 9:49am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/1 "2020-03-05T09:49:07Z")

</div>

Hi,  
I tried to model the same question with two different models for an ordinal outcome and ordinal predictor:  
fit1: crated 3 dummy variables for an 4 levels ordinal variable and each level was always compared to basic level as 0.

fit 2: Used the ordinal variable in the model but use mo()

Below are the results for fit 1 and 2 and loo\_comparison.  
And marginal graphs for mo.  
It seems fit 1 is better if i am right, but how come these two estimates are too different in fit1 and fit2.  
Fit 1 estimates is more similar to frequentist ordinal regression model!!!

```
fit1: 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept[1] 0.43 0.36 -0.27 1.14 1.00 914 843
Intercept[2] 1.59 0.35 0.93 2.34 1.00 882 812
Intercept[3] 2.63 0.35 2.00 3.33 1.00 850 811
Intercept[4] 3.46 0.35 2.80 4.20 1.00 813 867
Intercept[5] 4.23 0.36 3.54 4.95 1.00 802 811
Intercept[6] 5.01 0.36 4.33 5.75 1.00 804 872
Intercept[7] 5.69 0.37 5.00 6.43 1.00 809 802
Intercept[8] 6.42 0.38 5.73 7.20 1.00 781 842
Intercept[9] 7.24 0.39 6.49 8.01 1.00 851 807
Intercept[10] 8.03 0.40 7.28 8.86 1.00 831 727
Intercept[11] 9.18 0.44 8.36 10.07 1.00 783 892
hearing2cat1 1.35 0.14 1.07 1.61 1.00 904 743
hearing3cat1 1.28 0.24 0.81 1.72 1.00 1272 849
hearing4cat1 1.33 0.30 0.75 1.91 1.00 1113 704
age10int1 0.66 0.05 0.57 0.75 1.00 785 763
sex1 0.30 0.10 0.10 0.48 1.00 1366 912
yrs2 0.04 0.04 -0.03 0.11 1.00 1044 906

fit2:
Population-Level Effects: 
                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept[1] -0.04 0.42 -0.84 0.81 1.00 3046 3209
Intercept[2] 1.17 0.42 0.38 2.03 1.00 3051 2904
Intercept[3] 2.27 0.43 1.48 3.15 1.00 3160 2665
Intercept[4] 3.13 0.43 2.33 4.00 1.00 3096 2837
Intercept[5] 3.91 0.43 3.09 4.78 1.00 3075 2849
Intercept[6] 4.68 0.44 3.85 5.56 1.00 3095 2681
Intercept[7] 5.36 0.44 4.52 6.25 1.00 3110 2781
Intercept[8] 6.08 0.45 5.23 6.99 1.00 3132 2639
Intercept[9] 6.88 0.45 6.03 7.78 1.00 3131 2701
Intercept[10] 7.66 0.46 6.81 8.60 1.00 3167 2741
Intercept[11] 8.79 0.49 7.84 9.80 1.00 3408 2846
sex1 0.31 0.10 0.11 0.51 1.00 7074 3825
yrs2 0.04 0.04 -0.03 0.12 1.00 4747 3722
morec_sevhearing1 0.56 0.07 0.45 0.70 1.00 4011 3279
moage10int1 0.63 0.07 0.51 0.77 1.00 2465 2756

Simplex Parameters: 
                      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
morec_sevhearing11[1] 0.73 0.08 0.56 0.89 1.00 3585
morec_sevhearing11[2] 0.12 0.06 0.02 0.26 1.00 6196
morec_sevhearing11[3] 0.15 0.08 0.03 0.33 1.00 3997
moage10int11[1] 0.13 0.06 0.02 0.26 1.00 3198
moage10int11[2] 0.10 0.05 0.03 0.20 1.00 5083
moage10int11[3] 0.32 0.05 0.22 0.43 1.00 3751
moage10int11[4] 0.16 0.04 0.09 0.24 1.00 4982
moage10int11[5] 0.11 0.03 0.05 0.18 1.00 5265
moage10int11[6] 0.06 0.03 0.01 0.12 1.00 6426
moage10int11[7] 0.11 0.05 0.02 0.22 1.00 2997

 LOO fit 1
Computed from 1000 by 1320 log-likelihood matrix

         Estimate SE
elpd_loo -2832.5 22.8
p_loo 16.4 0.4
looic 5665.0 45.7
------
Monte Carlo SE of elpd_loo is 0.1.

All Pareto k estimates are good (k < 0.5).
See help('pareto-k-diagnostic') for details.

loo fit2
         Estimate SE
elpd_loo -2819.9 23.0
p_loo 19.3 0.5
looic 5639.7 46.1
------
Monte Carlo SE of elpd_loo is 0.1.

All Pareto k estimates are good (k < 0.5).
See help('pareto-k-diagnostic') for details.
 
loo_compare(fit1,fit2)
loo_compare(fit1,fit2)
     elpd_diff se_diff
fit2 0.0 0.0  
fit1 -12.6 5.6  

the marginal graph for fit2 is attached! 
Another question is about yrs(figure is also attached), with a wide variation! Do I need to transform this variable? 
Thanks for your inputs, it will help me move forward! ![hearing1|575x324](upload://kOmTf2SEEPZ2YpGaP3AyRGEaBqY.png) ![time2_bodn2|575x324](upload://kIwkwZkJuKXgpLObhsH3gAaenPq.png)
```

---

<div class="post-metadata">

**Author:** ![ssalimi](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ssalimi/32/7119_2.png) [@ssalimi](https://discourse.mc-stan.org/u/ssalimi)\
**Post date:** [March 5, 2020, 9:50am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/2 "2020-03-05T09:50:01Z")

</div>

![hearing1](https://canada1.discourse-cdn.com/flex030/uploads/mc_stan/original/2X/9/91dd1402fc5c921c436e7aabde8558dfa3e95b4c.png)

Fit monotonic effect

---

<div class="post-metadata">

**Author:** ![ssalimi](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ssalimi/32/7119_2.png) [@ssalimi](https://discourse.mc-stan.org/u/ssalimi)\
**Post date:** [March 5, 2020, 9:50am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/3 "2020-03-05T09:50:56Z")

</div>

> [@ssalimi](#):
>
> I tried to model the same question with two different models for an ordinal outcome and ordinal predictor:  
> fit1: crated 3 dummy variables for an 4 levels ordinal variable and each level was always compared to basic level as 0.
> 
> fit 2: Used the ordinal variable in the model but use mo()
> 
> Below are the results for fit 1 and 2 and loo\_comparison.  
> And marginal graphs for mo.  
> It seems fit 1 is better if i am right, but how come these two estimates are too different in fit1 and fit2.  
> Fit 1 estimates is more similar to frequentist ordinal regression model!!!

![time2_bodn2](https://canada1.discourse-cdn.com/flex030/uploads/mc_stan/original/2X/9/9133dac66fae7352915971cc15439531a6307d00.png)

variable yrs!

---

<div class="post-metadata">

**Author:** ![torkar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/torkar/32/1355_2.png) [@torkar](https://discourse.mc-stan.org/u/torkar)\
**Post date:** [March 6, 2020, 6:38am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/4 "2020-03-06T06:38:37Z")

</div>

Hi,

`fit2` is in a way ‘better’ than `fit1`:

```
> -12.6 + c(-1,1)*1.96*5.6
[1] -23.576 -1.624

```

Have you standardized `Years`, i.e., `scale(yrs2)`?

The uncertainty is there either way, and I don’t understand why this is a problem? Without seeing your models, and the data, it’s hard for me to say why there’s such a large difference in the estimates.

---

<div class="post-metadata">

**Author:** ![ssalimi](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ssalimi/32/7119_2.png) [@ssalimi](https://discourse.mc-stan.org/u/ssalimi)\
**Post date:** [March 6, 2020, 7:26am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/5 "2020-03-06T07:26:20Z")

</div>

> [@torkar](#):
>
> Have you standardized `Years` , i.e., `scale(yrs2)` ?
> 
> The uncertainty is there either way, and I don’t understand why this is a problem? Without seeing your models, and the data, it’s hard for me to say why there’s such a large difference in the estimates.

Hello,

model for fit1:

```no-highlight
if (!file.exists("hearingcat1_2.RData")) {
 
			bodi_w2=read.csv("disease_w_tofu2.csv",check.names=TRUE)
			  
	
			pmulti_w<-get_prior( rec_n_r_bodn2~hearing2cat1+ hearing3cat1+ hearing4cat1+
				age10int1+sex1+yrs2+age10int1,family=cumulative(),data =bodi_w2)
			  
			  
			    pmulti_w$prior[1]<-"normal(0,1)" # sets a N(0,1) on \beta
				pmulti_w$prior[14]<-"normal(0,10)" # for each cutpoint
				
				 fit_hearingcat1_2<-brm( rec_n_r_bodn2~
			  
			   hearing2cat1+ hearing3cat1+ hearing4cat1+age10int1+sex1+yrs2+age10int1
			   ,family=cumulative(),data =bodi_w2,prior=pmulti_w, chains=5,control=list(adapt_delta=0.99,max_treedepth=15),cores=future::availableCores())
			  
			   save(pmulti_w, fit_hearingcat1_2, file="hearingcat1_2.RData")
				} else {
			load("hearingcat1_2.RData")
			}

Model for fit 2:

phear<-get_prior( rec_n_r_bodn2~ mo(rec_sevhearing1)+sex1+age10int1+yrs2,family=cumulative(),
  data =bodi_w2)

phear$prior[1] <- "normal(0,1)" # sets a N(0,1) on \beta
phear$prior[6] <- "normal(0,10)" # for each cutpoint
phear$prior[18] <- "dirichlet(2,2,2)" # sets weakly regularizing dirichlet for 1-3 Likert scale response

fit_hearing2<-brm(
  formula = rec_n_r_bodn2~ mo(rec_sevhearing1)+sex1+age10int1+yrs2,family=cumulative(),
  data =bodi_w2,prior=phear, chains=5,control=list(adapt_delta=0.99,max_treedepth=15),cores=future::availableCores())

```

yrs2 is time interval from first time that varies for each person.  
n\_r\_bodn2 is response at yrs2 and the predictor is measured at yrs1 which is 1 for every person.  
age10int is age categories by 10 years interval.  
[test.csv](https://discourse.mc-stan.org/uploads/short-url/lgbMO0WiQPnoVdMSXGeg5U2Chea.csv) (35.3 KB)

---

<div class="post-metadata">

**Author:** ![torkar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/torkar/32/1355_2.png) [@torkar](https://discourse.mc-stan.org/u/torkar)\
**Post date:** [March 6, 2020, 7:36am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/6 "2020-03-06T07:36:41Z")

</div>

Hi,

maybe someone else can provide more input, but I see you use `adapt_delta` and `max_treedepth` when sampling and that to me indicates you have a misspecified model. Something makes the samples struggle. Check pairs plots.

---

<div class="post-metadata">

**Author:** ![ssalimi](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ssalimi/32/7119_2.png) [@ssalimi](https://discourse.mc-stan.org/u/ssalimi)\
**Post date:** [March 6, 2020, 7:44am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/7 "2020-03-06T07:44:13Z")

</div>

> [@torkar](#):
>
> maybe someone else can provide more input, but I see you use `adapt_delta` and `max_treedepth` when sampling and that to me indicates you have a misspecified model. Something makes the samples struggle. Check pairs plots.

Well! I should have taken them out. First I ran this model for repeated data in long format and with repeated model (1+1|id) I for 10 visits I got the warning to increase adapt\_delta and max\_treedepth, and I assume it was because not every participant had equal number of visits.  
But, with these models I did not need to do it as Rhat =1. My confusion here is to use monotonic effect or dummy variables. I plan to use the estimate as a score!  
Thanks,

---

<div class="post-metadata">

**Author:** ![torkar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/torkar/32/1355_2.png) [@torkar](https://discourse.mc-stan.org/u/torkar)\
**Post date:** [March 6, 2020, 7:51am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/8 "2020-03-06T07:51:57Z")

</div>

Hi Shabnam,

You have two models and one is apparently doing a better job in out of sample prediction. Do posterior predictive checks, i.e., `pp_check()`, to check if the model behaves. You can also simulate data and check if the model recovers all parameters.

---

<div class="post-metadata">

**Author:** ![ssalimi](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ssalimi/32/7119_2.png) [@ssalimi](https://discourse.mc-stan.org/u/ssalimi)\
**Post date:** [March 6, 2020, 7:55am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/9 "2020-03-06T07:55:10Z")

</div>

> [@torkar](#):
>
> Hi Shabnam,
> 
> You have two models and one is apparently doing a better job in out of sample prediction. Do posterior predictive checks, i.e., `pp_check()` , to check if the model behaves. You can also simulate data and check if the model recovers all parameters.

I used pp\_check and both model behaved well, also checked traceplot, they are good as well.  
I need to practice simulation. Thanks for your advice.  
On a differnt note, can i get individual-based posterior estimate? I mean posterior estimate for each person?  
Thanks again.

---

<div class="post-metadata">

**Author:** ![torkar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/torkar/32/1355_2.png) [@torkar](https://discourse.mc-stan.org/u/torkar)\
**Post date:** [March 6, 2020, 7:58am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/10 "2020-03-06T07:58:40Z")

</div>

> [@ssalimi](#):
>
> rec\_n\_r\_bodn2 ~ mo(rec\_sevhearing1) + sex1 + age10int1 + yrs2

If I understand the model above correctly then, no. If you want to model each individual I believe you need to use a varying intercept, i.e., `(1 | individual)`. Perhaps @martinmodrak can provide some insights.

---

<div class="post-metadata">

**Author:** ![ssalimi](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ssalimi/32/7119_2.png) [@ssalimi](https://discourse.mc-stan.org/u/ssalimi)\
**Post date:** [March 6, 2020, 8:07am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/11 "2020-03-06T08:07:14Z")

</div>

> [@torkar](#):
>
> If I understand the model above correctly then, no. If you want to model each individual I believe you need to use a varying intercept, i.e., `(1 | individual)` . Perhaps @martinmodrak can provide some insights.

What I understood about varying intercept is that provides an oveall “sd” for the model, not for each individual.  
In lme4 it is possible to perform post hoc analyses and store individual prediction value or estimate. Not sure if this is possible with brm or other Bayes models.  
Thanks,

---

<div class="post-metadata">

**Author:** ![torkar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/torkar/32/1355_2.png) [@torkar](https://discourse.mc-stan.org/u/torkar)\
**Post date:** [March 6, 2020, 8:20am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/12 "2020-03-06T08:20:21Z")

</div>

Well, if you have a varying intercept then you will be able to look at `ranef(Model)` for each individual.

---

<div class="post-metadata">

**Author:** ![ssalimi](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ssalimi/32/7119_2.png) [@ssalimi](https://discourse.mc-stan.org/u/ssalimi)\
**Post date:** [March 6, 2020, 8:27am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/13 "2020-03-06T08:27:31Z")

</div>

Great. Thanks. I run the model and see how it is and will update here.  
Thanks again for all.

---

<div class="post-metadata">

**Author:** ![martinmodrak](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/martinmodrak/32/133_2.png) [@martinmodrak](https://discourse.mc-stan.org/u/martinmodrak)\
**Post date:** [March 6, 2020, 8:49am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/14 "2020-03-06T08:49:31Z")

</div>

> [@ssalimi](#):
>
> On a differnt note, can i get individual-based posterior estimate? I mean posterior estimate for each person?  
> …  
> In lme4 it is possible to perform post hoc analyses and store individual prediction value or estimate. Not sure if this is possible with brm or other Bayes models.

Yes (if I understand the question correctly), you can use `posterior_predict` or `posterior_linpred` (the former includes the observation nose, the latter only the model uncertainty). You can also predict for new data. One method I’ve found useful in some cases is to make predictions for each person while varying only the factor of interest - see [PPC for ordered\_logistic? - #2 by martinmodrak](https://discourse.mc-stan.org/t/ppc-for-ordered-logistic/8881/2) for a bit more detail and ideas by others.

In Bayesian models it is usually beneficial to work with all the posterior draws instead of just the mean estimate, although this can make the post processing a bit more involved. `predict` and `fitted` methods of `brmsfit` also offer setting `summary = TRUE` to get a single estimate if that’s what you prefer.

I believe @torkar might have interpreted your query as how to _model_ individual-level _variation_, instead of _obtaining_ individual-level _prediction_ which might have led to some confusion (unless I am the one interpreting the conversation wrong :-) )

The difference in the model coefficients themselves is slightly surprising, but hard to interpret on its own as the intercepts have also changed noticeably. As you have correctly noted, using prediction is usually better for comparing differences.

Best of luck with your model!

---

<div class="post-metadata">

**Author:** ![ssalimi](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ssalimi/32/7119_2.png) [@ssalimi](https://discourse.mc-stan.org/u/ssalimi)\
**Post date:** [March 6, 2020, 8:54am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/15 "2020-03-06T08:54:40Z")

</div>

> [@martinmodrak](#):
>
> One method I’ve found useful in some cases is to make predictions for each person while varying only the factor of interest - see [PPC for ordered\_logistic?](https://discourse.mc-stan.org/t/ppc-for-ordered-logistic/8881/2) for a bit more detail and ideas by others.

You got it right. I need individual estimate. The reason for that is I add up estimates of various predictors to create a total score for each person. Thanks for the hints. I need to learn them for first time. Thank you both for your time and help.

---

<div class="post-metadata">

**Author:** ![ssalimi](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ssalimi/32/7119_2.png) [@ssalimi](https://discourse.mc-stan.org/u/ssalimi)\
**Post date:** [March 6, 2020, 9:19am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/16 "2020-03-06T09:19:37Z")

</div>

Still @torkar suggestion may work to consider each individual as a level! Just needs more chains as ids are not repeated!!

---

<div class="post-metadata">

**Author:** ![torkar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/torkar/32/1355_2.png) [@torkar](https://discourse.mc-stan.org/u/torkar)\
**Post date:** [March 6, 2020, 9:22am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/17 "2020-03-06T09:22:06Z")

</div>

Do you have only one measurement/person? If that’s the case I believe it would not work.

---

<div class="post-metadata">

**Author:** ![ssalimi](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ssalimi/32/7119_2.png) [@ssalimi](https://discourse.mc-stan.org/u/ssalimi)\
**Post date:** [March 6, 2020, 9:24am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/18 "2020-03-06T09:24:15Z")

</div>

Yes, in the models above its one measure/person. When we get estimates its mean estimate, I need to get personalized estimate. I will try predict

---

<div class="post-metadata">

**Author:** ![martinmodrak](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/martinmodrak/32/133_2.png) [@martinmodrak](https://discourse.mc-stan.org/u/martinmodrak)\
**Post date:** [March 6, 2020, 10:28am UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/19 "2020-03-06T10:28:20Z")

</div>

While I don’t think you should include varying intercept per person unless you have good reason to (e.g. from PP checks or theory), I think there is a small confusion about how that would work.

> [@ssalimi](#):
>
> Just needs more chains as ids are not repeated!!

> [@torkar](#):
>
> Do you have only one measurement/person? If that’s the case I believe it would not work.

In my experience non-repeating ids are (usually) not a problem for Bayesian models and I have fitted individual-level models succesfully in `brms` on default settings (I don’t think there is any reason to run more chains), although all of them were with different families than `cumulative`.

The theoretical reason is that having a varying intercept for each observation is actually the same as using a more “overdispersed” distribution for observation model. AFAIK the only commonly used distribution where such an “overdispersed” alternative does not exist and the model ceases to be identifiable is the bernoulli (logistic regression). Still it is possible that for your particular dataset and model, varying intercept for each observation will introduce computational issues with the `cumulative` family and it will likely take a much longer time to fit. I however don’t see an a priori reason why it should not be possible. It is also not clear whether it would be actually of any use, in particular if it would be better than changing the `link` parameter to say `cauchit`.

But you have motivated me to do a little experiment of my own using individual-level intercept with cumulative response and it works more often than not, recovering the parameters from simulated data, although it needs slightly increased `adapt_delta` and not very wide prior to avoid computational issues (the effective sample size per iteration is on the low end of acceptable).

Here’s the code:

```no-highlight
library(tidyverse)
library(brms)
options(mc.cores = parallel::detectCores())

set.seed(8964654)
N <- 100
N_levels <- 6
intercepts <- sort(rt(N_levels - 1, 3))
varying_sd <- abs(rnorm(1, 0, 1))
test_data <- data.frame(id = 1:N, varying_effect = rnorm(N, 0, varying_sd)) %>%
  mutate(response_raw = rlogis(N) + varying_effect,
         # The response could probably be simulated in a more clever way
         response_ordinal = case_when(response_raw < intercepts[1] ~ 1,
                                      response_raw < intercepts[2] ~ 2,
                                      response_raw < intercepts[3] ~ 3,
                                      response_raw < intercepts[4] ~ 4,
                                      response_raw < intercepts[5] ~ 5,
                                      TRUE ~ 6))

# Priors matching how I simulated the data
priors <- c(set_prior("normal(0, 1)", class = "sd"), set_prior("student_t(3, 0, 1)", class = "Intercept"))
fit <- brm(response_ordinal ~ 1|id, data = test_data, family = cumulative(), prior = priors, control = list(adapt_delta = 0.95))

summary(fit)

```

---

<div class="post-metadata">

**Author:** ![ssalimi](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/ssalimi/32/7119_2.png) [@ssalimi](https://discourse.mc-stan.org/u/ssalimi)\
**Post date:** [March 6, 2020, 8:33pm UTC](https://discourse.mc-stan.org/t/results-from-monotonic-effect-versus-dummy-variables-in-brms/13537/20 "2020-03-06T20:33:15Z")

</div>

Thanks for all the explanation and the experiment. I play with my data as well accordingly and will update here if anything interesting comes up.  
Thanks again @martinmodrak and @torkar

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