# Comparing models with different functional forms of the same y variable using loo\_compare

**URL:** <https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161>\
**Category:** Modeling\
**Tags:** brms\
**Created:** [February 19, 2024, 10:03am UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161 "2024-02-19T10:03:29Z")\
**Posts on this page:** 16\
**Page:** 1

<div class="post-metadata">

**Author:** ![llewmills](https://avatars.discourse-cdn.com/v4/letter/l/4da419/32.png) [@llewmills](https://discourse.mc-stan.org/u/llewmills)\
**Post date:** [February 19, 2024, 10:03am UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/1 "2024-02-19T10:03:29Z")

</div>

I have modelled the effect of a cannabis agonist drug on number of days of cannabis use during a 12-week clinical trial. It is a mixed effects model for repeated measures regression, with group (time invariant categorical predictor: placebo vs active) as the primary predictor and time as the repeated measure (levels: baseline, Week 4, Week 8, Week 12). The outcome is number of days of illicit cannabis in the previous 28 days (measured four times as stated).

I can treat the outcome as either continuous, for which I would use a standard gaussian regression _or_ as a bounded count in which case i would use an aggregated binomial. In brms the models looked like this

Gaussian

```no-highlight
brm(formula = cu ~ group*week + (1|id),
 	  data = cu,
  	  family = gaussian(),
          prior = c(prior(normal(14, 1.5), class = Intercept),
 			  prior(normal(0, 11), class = b),
 			  prior(cauchy(1,2), class = sd)),
	 iter = 1e4,
 	 warmup = 1e3,
 	 chains = 3,
 	 cores = 3,
 	 control = list(adapt_delta = .99),
	 save_pars = save_pars(all=T),
 	 seed = 1234) -> modCont

```

Aggregated binomial

```no-highlight
brm(formula = cu | trials(set) ~ group*week + (1|id),
	data = cu,
	binomial(link = logit),
	prior = c(prior(normal(0, 1.5), class = Intercept),
			  prior(normal(0, 1), class = b),
		      prior(cauchy(0,2), class = sd)),
    iter = 1e4,
	warmup = 1e3,
	chains = 3,
	cores = 3,
	control = list(adapt_delta = .99),
	save_pars = save_pars(all=T),
	seed = 1234) -> modAggBinom

```

Now I used `loo` with moment matching on each model and hence was able to compare the two models with `loo_compare` and got the following output and warning message

```no-highlight
            elpd_diff se_diff
modCont 0.0 0.0 
modAggBinom -813.4 142.6 
Warning message:
Not all models have the same y variable. ('yhash' attributes do not match) 

```

Now to me this makes sense; you _shouldn’t_ be able to compare models where the outcome variables are in a different form.

BUT the reason I did this is that I have a memory from either a lecture on youtube or a paper where Aki Vehtari suggested that with loo-cv it _is_ possible to compare models where the outcome has different functional form. Did I dream that? Is there a way to compare the performance of my aggregated binomial vs gaussian models? If so what is the procedure? Also if so, where could I find some guidance on how to achieve such a comparison?

---

<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:** [February 20, 2024, 12:50pm UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/2 "2024-02-20T12:50:34Z")

</div>

It is possible to compare continuous and discrete if you are careful, se [CV-FAQ: Can cross-validation be used to compare different observation models / response distributions / likelihoods?](https://users.aalto.fi/~ave/CV-FAQ.html#13_Can_cross-validation_be_used_to_compare_different_observation_models __response_distributions__ likelihoods)

It would be useful to see posterior predictive check plots, too

---

<div class="post-metadata">

**Author:** ![llewmills](https://avatars.discourse-cdn.com/v4/letter/l/4da419/32.png) [@llewmills](https://discourse.mc-stan.org/u/llewmills)\
**Post date:** [February 21, 2024, 4:10am UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/3 "2024-02-21T04:10:14Z")

</div>

Thank you @avehtari. So if I understand what it says in the link correctly

(1) What I did in the example I gave is not correct, i.e. directly comparing the continuous vs discrete models via loo\_compare?

(2) In order to compare the two I would need to discretise the continuous outcome? If this is the case (a) in what sense are they being compared given that iby discretising the continuous outcomes it will no longer be continuous (b) do you know of an online tutorial where this is done so I can follow along and learn how to do it?

---

<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:** [February 21, 2024, 8:00am UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/4 "2024-02-21T08:00:48Z")

</div>

I have in my to-do list to make a case study illustrating the discretization. The easiest case is when the target is integer counts and the target is not scaled for the continuous model, as then in the discretization the width of each bin is 1, and the approximate probability of bin is the density at the target value times the bin width 1. In that case the density value is also (approximate) probability value and the models can be compared directly. Based on that, it seems like your models should be comparable if the data cu is the same. It is possible that the hash is different if brms stores the data in one model as doubles and in another one as integers. As the elpd\_diff is very big, I’m suspicious of the results, but if you post also a plot of the distribution of y and some posterior predictive plots, I might be able to say more. The explanation and the code you posted is not clear on what do you mean by aggregated.

---

<div class="post-metadata">

**Author:** ![llewmills](https://avatars.discourse-cdn.com/v4/letter/l/4da419/32.png) [@llewmills](https://discourse.mc-stan.org/u/llewmills)\
**Post date:** [February 21, 2024, 9:32am UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/5 "2024-02-21T09:32:04Z")

</div>

I can’t edit my original post but here is the data. It is real data (already plublished [here](https://jamanetwork.com/journals/jamainternalmedicine/fullarticle/2737918)) from a 12 week clinical trial testing efficacy of a cannabis agonist drug nabiximols on cannabis use among people with cannabis dependence.

- `id` is participant id. 128-level factor.

- `cu` is the outcome, days of illicit cannabis use in the previous 28 days. It was measured four times, at weeks 0 (baseline), 4, 8, and 12. Not all participants stayed in the trial the whole 12 weeks so some have missing data. In the two models I described in the original post this was treated as either a continuous variable (in the model `modCont`) or as a bounded count (in the model `modAggBinom`).

- `set` is the possible number of days of cannabis use. All values are therefore 28. This variable is used in the binomial regression syntax for the `modAggBinom` model described in the original post, i.e. `cu | trials(set)`

- `group` is the group participants were randomised to, a binary categorical (placebo vs nabiximols).

- `week` is a four-level factor indicating which stage of the trial the measure of cannabis use `cu` was taken: 0, 4, 8, or 12.

If you wanted to use this data for your case study I would be honoured (your to-do list permitting). This is real data from a published clinical trial and is simple.

Here is the data

```no-highlight
id <- factor(c(1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 13, 14, 15, 16, 16, 17, 18, 18, 18, 18, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 26, 27, 27, 28, 28, 28, 28, 29, 30, 30, 30, 30, 31, 31, 32, 32, 32, 32, 33, 33, 33, 34, 34, 34, 35, 35, 36, 36, 37, 37, 37, 37, 38, 39, 39, 39, 39, 40, 40, 40, 41, 42, 42, 42, 42, 43, 43, 43, 43, 44, 44, 45, 45, 46, 46, 46, 46, 47, 47, 47, 47, 48, 48, 49, 49, 49, 50, 50, 50, 50, 51, 51, 51, 52, 52, 52, 52, 53, 53, 53, 53, 54, 54, 55, 55, 55, 55, 56, 57, 57, 57, 57, 58, 58, 58, 58, 59, 59, 59, 59, 60, 60, 60, 60, 61, 61, 61, 62, 63, 63, 64, 64, 64, 65, 65, 65, 65, 66, 66, 66, 66, 67, 67, 67, 67, 68, 68, 68, 69, 69, 69, 69, 70, 70, 70, 70, 71, 71, 71, 71, 72, 73, 73, 73, 73, 74, 74, 74, 75, 76, 76, 76, 76, 77, 77, 77, 77, 78, 78, 78, 79, 79, 79, 79, 80, 80, 80, 80, 81, 81, 81, 81, 82, 82, 83, 83, 84, 84, 84, 85, 85, 85, 86, 86, 86, 86, 87, 87, 87, 87, 88, 88, 88, 88, 89, 89, 89, 89, 90, 90, 90, 90, 91, 91, 91, 91, 92, 92, 92, 92, 93, 93, 93, 93, 94, 94, 94, 94, 95, 95, 95, 95, 96, 96, 96, 96, 97, 97, 97, 98, 98, 98, 98, 99, 99, 99, 99, 100, 101, 101, 101, 102, 102, 102, 102, 103, 103, 103, 103, 104, 104, 105, 105, 105, 105, 106, 106, 106, 106, 107, 107, 107, 107, 108, 108, 108, 108, 109, 109, 109, 109, 110, 110, 111, 111, 112, 112, 112, 112, 113, 113, 113, 113, 114, 115, 115, 115, 115, 116, 116, 116, 116, 117, 117, 117, 117, 118, 118, 119, 119, 119, 119, 120, 120, 120, 120, 121, 121, 121, 122, 123, 123, 123, 123, 124, 124, 124, 125, 125, 125, 125, 126, 126, 126, 126, 127, 127, 128))

group <- factor(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0),
				levels = 0:1,
				labels = c("placebo", "nabiximols"))

week <- factor(c(0, 4, 8, 12, 0, 4, 8, 0, 4, 8, 0, 4, 8, 12, 0, 4, 0, 4, 8, 12, 0, 4, 0, 4, 8, 12, 0, 4, 8, 0, 4, 8, 12, 0, 4, 8, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 8, 12, 0, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 0, 4, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 0, 4, 0, 4, 8, 12, 0, 0, 4, 8, 12, 0, 4, 0, 4, 8, 12, 0, 4, 8, 0, 4, 12, 0, 8, 0, 4, 0, 4, 8, 12, 0, 0, 4, 8, 12, 0, 4, 8, 0, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 0, 4, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 0, 4, 12, 0, 4, 8, 12, 0, 4, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 0, 4, 8, 12, 0, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 12, 0, 0, 4, 0, 4, 8, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 0, 4, 8, 12, 0, 4, 8, 0, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 0, 4, 0, 4, 8, 0, 4, 8, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 0, 4, 8, 12, 0, 4, 8, 12, 0, 0, 4, 8, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 0, 4, 0, 4, 8, 12, 0, 4, 8, 12, 0, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 12, 0, 0, 4, 8, 12, 0, 4, 12, 0, 4, 8, 12, 0, 4, 8, 12, 0, 4, 0))

cu <- c(13, 12, 12, 12, 28, 0, NA, 16, 9, 2, 28, 28, 28, 28, 28, NA, 28, 28, 17, 28, 28, NA, 16, 0, 0, NA, 28, 28, 28, 28, 17, 0, NA, 28, 27, 28, 28, 26, 24, 28, 28, 28, 25, 28, 26, 28, 18, 16, 28, 28, 7, 0, 2, 28, 2, 4, 1, 28, 28, 16, 28, 28, 24, 26, 15, 28, 25, 17, 1, 8, 28, 24, 27, 28, 28, 28, 28, 28, 27, 28, 28, 28, 28, 20, 28, 28, 28, 28, 12, 28, NA, 17, 15, 14, 28, 0, 28, 28, 28, 0, 0, 0, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 21, 24, 28, 27, 28, 28, 26, NA, 28, NA, 20, 2, 3, 7, 28, 1, 19, 8, 21, 7, 28, 28, 20, 28, 28, 28, 24, 20, 17, 11, 25, 25, 28, 26, 28, 24, 17, 16, 27, 14, 28, 28, 28, 28, 28, 28, 14, 13, 4, 24, 28, 28, 28, 21, 28, 21, 26, 28, 28, 0, 0, 28, 23, 20, 28, 20, 16, 28, 28, 28, 10, 1, 1, 2, 28, 28, 28, 28, 18, 22, 9, 15, 28, 9, 1, 20, 18, 20, 24, 28, 28, 28, 19, 28, 28, 28, 28, 28, 28, 28, 28, 28, 4, 14, 20, 28, 28, 0, 0, 0, 28, 20, 9, 24, 28, 28, 28, 28, 28, 21, 28, 28, 14, 24, 28, 23, 0, 0, 0, 28, NA, 28, NA, 28, 15, NA, 12, 25, NA, 28, 2, 0, 0, 28, 10, 0, 0, 28, 0, 0, 0, 23, 0, 0, 0, 28, 0, 0, 0, 28, 0, 0, 0, 28, 2, 1, 0, 21, 14, 7, 8, 28, 28, 28, 0, 28, 28, 20, 18, 24, 0, 0, 0, 28, 15, NA, 28, 1, 1, 2, 28, 1, 0, 0, 28, 28, 14, 21, 25, 19, 16, 13, 28, 28, 28, 28, 28, 28, 28, 27, 19, 21, 18, 1, 0, 0, 28, 28, 28, 28, 28, 24, 27, 28, 18, 0, 3, 8, 28, 28, 28, 9, 20, 25, 20, 12, 19, 0, 0, 0, 27, 28, 0, 0, 0, 20, 17, 16, 14, 28, 7, 0, 1, 28, 24, 28, 25, 23, 20, 28, 14, 16, 7, 28, 28, 26, 28, 28, 26, 28, 28, 28, 24, 20, 28, 28, 28, 28, 28, 8, 6, 4, 28, 20, 28)

set <- rep(28, length(cu))

cu <- data.frame(id, group, week, cu, set)

```

The `brms` code I provided in the original post should work on this dataset without need of any alteration.

---

<div class="post-metadata">

**Author:** ![llewmills](https://avatars.discourse-cdn.com/v4/letter/l/4da419/32.png) [@llewmills](https://discourse.mc-stan.org/u/llewmills)\
**Post date:** [February 21, 2024, 9:36am UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/6 "2024-02-21T09:36:53Z")

</div>

I use the term aggregated binomial regression but I am starting to realise few other people use this term. It is simply a binomial regression where the outcome is a bounded count (days’ illicit cannabis use out of 28) rather than a bernoulli [0,1] outcome.

I’m not sure I have the skills to implement your discretization suggestion without some guidance, not without a few days’ or weeks` reading and some practice at the very least. Personally I would find it incredibly useful to be able to do this. Days of substance use data is almost never distributed normally (most often bimodal, with modes at 0 days used/28 and 28 days used/28). It makes analysis quite challenging.

---

<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:** [February 21, 2024, 10:06am UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/7 "2024-02-21T10:06:29Z")

</div>

> [@llewmills](#):
>
> `set <- rep(28, length(daysCannUse))`

daysCannUse is not defined, is it the same as cu?

---

<div class="post-metadata">

**Author:** ![llewmills](https://avatars.discourse-cdn.com/v4/letter/l/4da419/32.png) [@llewmills](https://discourse.mc-stan.org/u/llewmills)\
**Post date:** [February 21, 2024, 10:30am UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/8 "2024-02-21T10:30:26Z")

</div>

Yes that’s right. i’m sorry about that. Have edited the post with the data (on my phone while walking the dog). Should work now.

---

<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:** [February 21, 2024, 10:56am UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/9 "2024-02-21T10:56:24Z")

</div>

Based on a quick experiment, you should have used `family=beta_binomial()`. I’ll get back to you with more details and explanation of comparison to continuous model.

---

<div class="post-metadata">

**Author:** ![llewmills](https://avatars.discourse-cdn.com/v4/letter/l/4da419/32.png) [@llewmills](https://discourse.mc-stan.org/u/llewmills)\
**Post date:** [February 21, 2024, 11:22am UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/10 "2024-02-21T11:22:06Z")

</div>

Amazing thank you!

---

<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:** [February 26, 2024, 6:40pm UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/11 "2024-02-26T18:40:08Z")

</div>

Here’s a link to a case study that illustrates the discretization and I couldn’t resist to add additional workflow for model and prior checking [https://users.aalto.fi/~ave/casestudies/Nabiximols/nabiximols.html](https://users.aalto.fi/~ave/casestudies/Nabiximols/nabiximols.html)

Let me know if the explanation is clear enough, and I can add more if needed

---

<div class="post-metadata">

**Author:** ![llewmills](https://avatars.discourse-cdn.com/v4/letter/l/4da419/32.png) [@llewmills](https://discourse.mc-stan.org/u/llewmills)\
**Post date:** [February 26, 2024, 9:40pm UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/12 "2024-02-26T21:40:42Z")

</div>

Absolutely increible @avehtari! So thorough. You never need to resist the urge to go into greater depth. A total honour to have you analyse our data. Thank you so much! I must say I feel very relieved that the results you found with the beta-binomial substantively match those we found in the original study. Best of all, you have given me a roadmap for how to model the data in a study we are currently setting up with essentially the exact same outcome but with a different drug. I feel like I should send you a bottle of scotch to thank you.

---

<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:** [February 27, 2024, 7:46am UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/13 "2024-02-27T07:46:13Z")

</div>

You can thank me in acknowledgments and send me a link to the paper. Feel free to ask questions about the other parts of the workflow, too

---

<div class="post-metadata">

**Author:** ![llewmills](https://avatars.discourse-cdn.com/v4/letter/l/4da419/32.png) [@llewmills](https://discourse.mc-stan.org/u/llewmills)\
**Post date:** [February 27, 2024, 10:12am UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/14 "2024-02-27T10:12:26Z")

</div>

Deal, though I must say I came out ahead in this arrangement. I don’t anticipate a paper coming out till 2026-27; addiction trials take a LONG time. Thank you so much again. I haven’t had a chance to absorb everything yet but I will follow up with questions as they inevitably occur to me.

---

<div class="post-metadata">

**Author:** ![llewmills](https://avatars.discourse-cdn.com/v4/letter/l/4da419/32.png) [@llewmills](https://discourse.mc-stan.org/u/llewmills)\
**Post date:** [February 28, 2024, 12:37am UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/15 "2024-02-28T00:37:46Z")

</div>

I noticed a typo in your notebook. In the ‘Comparison of discrete and continuous models section’ is a sentence that reads ‘The normal model predictions are not constrained between 0 and 28 (or −0.5 and 28.5), and thus the probabilities for `cu` ∈(0,1,2,…,28) do not necessarily sum to 1’. Now when I copied the text into this reply the numbers appeared but in the html document itself they are invisible. Just thought you might like to know. :)

---

<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:** [February 28, 2024, 8:41am UTC](https://discourse.mc-stan.org/t/comparing-models-with-different-functional-forms-of-the-same-y-variable-using-loo-compare/34161/16 "2024-02-28T08:41:26Z")

</div>

This shows fine in my browser

 ![image](https://canada1.discourse-cdn.com/flex030/uploads/mc_stan/original/3X/3/4/34da286d8d821fb03af79b84e701bc43c3c26918.png)

I did notice that it can take up to 10s that they come up. The html is self-contained, and with all the figures quite big, and mathjax can then be slow, too