# Topic model with an outcome variable

**URL:** <https://discourse.mc-stan.org/t/topic-model-with-an-outcome-variable/12377>\
**Category:** Modeling\
**Created:** [December 19, 2019, 7:45am UTC](https://discourse.mc-stan.org/t/topic-model-with-an-outcome-variable/12377 "2019-12-19T07:45:23Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![Youjiajia](https://avatars.discourse-cdn.com/v4/letter/y/d6d6ee/32.png) [@Youjiajia](https://discourse.mc-stan.org/u/Youjiajia)\
**Post date:** [December 19, 2019, 7:45am UTC](https://discourse.mc-stan.org/t/topic-model-with-an-outcome-variable/12377/1 "2019-12-19T07:45:23Z")

</div>

I am interested in relating LDA to an outcome variable (building the outcome into the generative model rather than working LDA outputs as features for another classification/regression task).

The generative process I am thinking of is:  
for each topic k:  
draw \phi\_k \sim Dir(\beta)  
for each document d:  
for each topic k:  
draw \theta\_d \sim Dir(\alpha)  
for each word i,  
draw z\_i \sim Cat(\theta\_d)  
draw w\_i \sim Cat(\theta\_{z\_i})  
draw outcome y\_d \sim bernoulli\_logit(a + \lambda \* \theta\_d)

I get an error in the last line of the model part.

And also it seems that in my model part, the last loop of going over 1 to M is unnecessary. However, for the text data, I followed the format of the stan reference manual where [https://mc-stan.org/docs/2\_18/stan-users-guide/naive-bayes-classification-and-clustering.html](https://mc-stan.org/docs/2_18/stan-users-guide/naive-bayes-classification-and-clustering.html)

> The relevant variables for the program are `N` , the total number of words in all the documents, the word array `w` , and the document identity array `doc` .

So, I am not entirely sure how I should modify the last line of my model.

My code is the following:

```no-highlight
data {
  int<lower=2> K; // num topics
  int<lower=2> V; // num words
  int<lower=1> M; // num docs
  int<lower=1> N; // total word instances
  int<lower=1,upper=V> w[N]; // word n
  int<lower=1,upper=M> doc[N]; // doc ID for word n
  int y[M]; // outcome variable 
  vector<lower=0>[K] alpha; // topic prior
  vector<lower=0>[V] beta; // word prior
}
parameters {
  simplex[K] theta[M]; // topic dist for doc m: 169
  simplex[V] phi[K]; // word dist for topic k :827
  real a;
  real lambda[K];
}
model {
  for (m in 1:M)
    theta[m] ~ dirichlet(alpha); // prior
  for (k in 1:K)
    phi[k] ~ dirichlet(beta); // prior
  for (n in 1:N) {
    real gamma[K];
    for (k in 1:K)
      gamma[k] = log(theta[doc[n], k]) + log(phi[k, w[n]]);
    target += log_sum_exp(gamma); // likelihood;
  }
  for (m in 1:N)
    y[m] ~ bernoulli_logit(a + lambda * theta[m]); // issue here
}

```

---

<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:** [January 3, 2020, 12:34pm UTC](https://discourse.mc-stan.org/t/topic-model-with-an-outcome-variable/12377/2 "2020-01-03T12:34:46Z")

</div>

Please always post the full error message, it makes things easier for us to investigate. In any case this looks like a type mismatch, note that Stan is picky about vector/matrix arithmetics and differentiates between row and column vectors. At first glance it seems you want lambda to be a `row_vector`, then the `*` operator would mean a dot-product. Some more info can be found at [https://mc-stan.org/docs/2\_19/reference-manual/arithmetic-expressions-section.html](https://mc-stan.org/docs/2_19/reference-manual/arithmetic-expressions-section.html)

Best of luck with your model!