# Simple Multinomial Logistic Regression Performance

**URL:** <https://discourse.mc-stan.org/t/simple-multinomial-logistic-regression-performance/18277>\
**Category:** Modeling\
**Tags:** performance\
**Created:** [September 29, 2020, 7:59pm UTC](https://discourse.mc-stan.org/t/simple-multinomial-logistic-regression-performance/18277 "2020-09-29T19:59:43Z")\
**Posts on this page:** 6\
**Page:** 1

<div class="post-metadata">

**Author:** ![nhiananto](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/nhiananto/32/9460_2.png) [@nhiananto](https://discourse.mc-stan.org/u/nhiananto)\
**Post date:** [September 29, 2020, 7:59pm UTC](https://discourse.mc-stan.org/t/simple-multinomial-logistic-regression-performance/18277/1 "2020-09-29T19:59:43Z")

</div>

Hello,

I’m new to Stan and I’m trying to fit a simple multinomial logistic model using rstan and I want to know if I have coded the model efficiently and/or that the performance I’m seeing is normal. I’m using a Windows machine and the Stan version is 2.21.0.

I’ve looked around the forums for a bit and I came across this [post](https://discourse.mc-stan.org/t/improving-performance-on-logistic-regression-with-informative-priors/14707), and my problem is kind of similar in that the performance that I’m seeing is not that great and I’m not sure if there is something wrong with the way I coded the model up. I’ve also enabled parallel cores using:

```stan
options(mc.cores = parallel::detectCores())

```

and configured the C++ toolchain as suggested in the getting started page of RStan.

The data I’m trying to fit is fairly small, it’s a conjoint survey data of about ~340 units each doing 16 tasks of 5 choices each task. The choices include an outside option of all zeros and there are a total of 10 number of variables.

The data is organized as such that the rows corresponds to: the number of units x the number of tasks each unit does x the number of choices (n \* t \* p) and I’ve collapsed the number of units x the number of tasks to (n \* t = N), and so the dimension for x is (N x na) where na is the number of variables.

The stan model code for it is given below:

```stan
model_code = "
data {
  int p; //number of choice alternatives
  int na; //number of alternative-specific vars
  
  int N; //data length
  int y[N]; //n x 1 multinomial outcomes
  matrix[N * p, na] x; //dataset
}
parameters {
  vector[na] beta;
}
model {
  vector[N * p] x_beta = x * beta;

  matrix[N, p] x_beta2;
  x_beta2 = to_matrix(x_beta, N, p, 0); //convert to matrix N x p
  
  beta ~ normal(0, 100); //specify prior
  
  for (n in 1:N)
    y[n] ~ categorical_logit(x_beta2[n]');
}
"

```

From what I’ve seen from the documentation, the categorical\_logit has not been vectorized and I have to resort to the use of loops. I ran the model to draw 20,000 draws of the beta parameters and, I tried running the model a couple of times and I’m seeing that it takes me, on average, ~30 minutes to complete 20,000 draws and currently I’m just using 1 chain. I’ve tried using a more reasonable prior for logistic regression \mathcal{N}(0, 1), but I’m seeing similar performance (just very slightly better) after doing so.

Thanks,  
Niko

---

<div class="post-metadata">

**Author:** ![mike-lawrence](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/mike-lawrence/32/59_2.png) [@mike-lawrence](https://discourse.mc-stan.org/u/mike-lawrence)\
**Post date:** [September 29, 2020, 9:07pm UTC](https://discourse.mc-stan.org/t/simple-multinomial-logistic-regression-performance/18277/2 "2020-09-29T21:07:02Z")

</div>

Any reason you’re trying to obtain so many samples? The defaults of 1000 post-warmup samples are sufficient for inference even in the tails of the distribution, especially if there are multiple chains. Are you not getting a good effective sample size at the default?

---

<div class="post-metadata">

**Author:** ![mike-lawrence](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/mike-lawrence/32/59_2.png) [@mike-lawrence](https://discourse.mc-stan.org/u/mike-lawrence)\
**Post date:** [September 29, 2020, 10:34pm UTC](https://discourse.mc-stan.org/t/simple-multinomial-logistic-regression-performance/18277/3 "2020-09-29T22:34:52Z")

</div>

Also, folks [have reported recently](https://discourse.mc-stan.org/t/large-cmdstan-performance-differences-windows-vs-linux/14415/34) that best performance on Windows is achieved by [using WSL](https://support.rstudio.com/hc/en-us/articles/360049776974-Using-RStudio-Server-in-Windows-WSL2).

---

<div class="post-metadata">

**Author:** ![nhiananto](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/nhiananto/32/9460_2.png) [@nhiananto](https://discourse.mc-stan.org/u/nhiananto)\
**Post date:** [September 30, 2020, 5:24pm UTC](https://discourse.mc-stan.org/t/simple-multinomial-logistic-regression-performance/18277/4 "2020-09-30T17:24:43Z")

</div>

There’s not really a reason for the number of samples I’m trying to obtain. Since, I’m new to Stan, I just want to gauge how fast Stan is for producing samples and/or if I’m doing something ineffective in my model code.

---

<div class="post-metadata">

**Author:** ![mike-lawrence](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/mike-lawrence/32/59_2.png) [@mike-lawrence](https://discourse.mc-stan.org/u/mike-lawrence)\
**Post date:** [September 30, 2020, 6:40pm UTC](https://discourse.mc-stan.org/t/simple-multinomial-logistic-regression-performance/18277/5 "2020-09-30T18:40:27Z")

</div>

Ok, then you should definitely stick with the default of 1000 post-warmup samples and only explore more if you are getting low effective sample sizes. Look into using WSL, and if your system has `2*N` or more CPU cores (where `N` is the number of chains desired, usually 4), take a look at `reduce_sum()` for within-chain parallelization. Oh, and certainly don’t use that `normal(0, 100)` prior.

---

<div class="post-metadata">

**Author:** ![mike-lawrence](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/mike-lawrence/32/59_2.png) [@mike-lawrence](https://discourse.mc-stan.org/u/mike-lawrence)\
**Post date:** [September 30, 2020, 7:58pm UTC](https://discourse.mc-stan.org/t/simple-multinomial-logistic-regression-performance/18277/6 "2020-09-30T19:58:28Z")

</div>

Now, it does look like you’re doing a bunch of transformations (casting to matrix, transpose) that might be affecting computation speed, but I get out of my depth very quickly in that realm. @Bob_Carpenter could you take a peek at the OP and comment on whether those transformations are going to be very costly?