# Vectorized \`ordered\_logistic\` compiles but then does not sample correctly

**URL:** <https://discourse.mc-stan.org/t/vectorized-ordered-logistic-compiles-but-then-does-not-sample-correctly/10843>\
**Category:** Modeling\
**Tags:** specification\
**Created:** [September 5, 2019, 3:18pm UTC](https://discourse.mc-stan.org/t/vectorized-ordered-logistic-compiles-but-then-does-not-sample-correctly/10843 "2019-09-05T15:18:45Z")\
**Posts on this page:** 1\
**Showing post:** 4

<div class="post-metadata">

**Author:** ![Solomon](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/solomon/32/2495_2.png) [@Solomon](https://discourse.mc-stan.org/u/Solomon)\
**Post date:** [August 18, 2024, 2:26pm UTC](https://discourse.mc-stan.org/t/vectorized-ordered-logistic-compiles-but-then-does-not-sample-correctly/10843/4 "2024-08-18T14:26:27Z")

</div>

Hey all. I have a somewhat related issue with these data. I’m fitting a simplified version of a model from the 2nd edition of [_Statistical Rethinking_](https://xcelab.net/rm/). In Section 12.4, McElreath introduced an ordered categorical predictor, education, which has 8 levels ranging from `"Elementary School"` to `"Graduate Degree"`. In McElreath’s style of notation, the full version of the model was

\begin{align} R\_i & \sim \operatorname{Ordered-logit} (\phi, \kappa) \\ \phi\_i & = \beta\_E \sum\_{j=0}^{E\_i - 1} \delta\_j + \beta\_A A\_i + \beta\_I I\_i + \beta\_C C\_i \\ \kappa\_k & \sim \operatorname{Normal}(0, 1.5) \\ \beta\_A, \beta\_I, \beta\_C, \beta\_E & \sim \operatorname{Normal}(0, 1) \\ \delta & \sim \operatorname{Dirichlet}(\{ 2, 2, 2, 2, 2, 2, 2 \}), \end{align}

where R is the ordinal response variable, E is our new ordered categorical predictor, and A through C are other predictors. I’m dropping those other predictors here to streamline the model and the code, which simplifies my model for \phi\_i to

\phi\_i = \beta\_E \sum\_{j=0}^{E\_i - 1} \delta\_j.

I’m currently working through the **rstan** code, with this version running successfully:

```no-highlight
library(tidyverse)
library(tidybayes)
library(rstan)

data(Trolley, package = "rethinking")

edu_levels_vec <- c("Elementary School", "Middle School", "Some High School", "High School Graduate",
                    "Some College", "Bachelor's Degree", "Master's Degree", "Graduate Degree")

stan_data <- Trolley |> 
  mutate(edu_new = factor(edu, levels = edu_levels_vec)) |> 
  select(response, edu_new) |> 
  compose_data(alpha = rep(2, times = 7))

model_code <- '
data {
  int n;
  array[n] int response;
  array[n] int edu_new;
  vector[7] alpha; // For the `delta` prior
}
parameters {
  ordered[6] kappa;
  real bE;
  simplex[7] delta;
}
model {
  vector[n] phi;
  vector[8] delta_j;
  delta_j = append_row(0, delta);
  
  for (i in 1:n) phi[i] = bE * sum(delta_j[1:edu_new[i]]);
  response ~ ordered_logistic(phi, kappa);
  
  kappa ~ normal(0, 1.5);
  bE ~ normal(0, 1);
  delta ~ dirichlet(alpha);
}
'

fit1 <- stan(
  model_code = model_code, 
  data = stan_data,
  cores = 3, chains = 3, seed = 12)

```

Now we get to the heart of my problem. I’m trying to vectorize the code for the `phi`, and can’t seem to get it right. Here’s my current attempt:

```no-highlight
'
model {
  vector[n] phi;
  vector[8] delta_j;
  delta_j = append_row(0, delta);
  
  phi = bE * sum(delta_j[1:edu_new]); // Only this line has chaged.
  response ~ ordered_logistic(phi, kappa);
  
  kappa ~ normal(0, 1.5);
  bE ~ normal(0, 1);
  delta ~ dirichlet(alpha);
}
'

```

When I try running the model this way, I get this error message:

```no-highlight
Error in stanc(file = file, model_code = model_code, model_name = model_name, : 
  0
Semantic error in 'string', line 17, column 27 to column 34:
   -------------------------------------------------
    15: delta_j = append_row(0, delta);
    16:  
    17: phi = bE * sum(delta_j[1:edu_new]); // Only this line has chaged.
                                    ^
    18: response ~ ordered_logistic(phi, kappa);
    19:  
   -------------------------------------------------

Range bound must be of type int. Instead found type array[] int.

```

I don’t understand what this is prompting me to do. Is there a way to vectorize `phi`?

---

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