# How to implement Zero-Inflated Multinomial?

**URL:** <https://discourse.pymc.io/t/how-to-implement-zero-inflated-multinomial/3961>\
**Category:** Questions\
**Created:** [October 12, 2019, 6:00pm UTC](https://discourse.pymc.io/t/how-to-implement-zero-inflated-multinomial/3961 "2019-10-12T18:00:57Z")\
**Posts on this page:** 1\
**Showing post:** 25

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**Author:** ![AlexAndorra](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/alexandorra/32/9142_2.png) [@AlexAndorra](https://discourse.pymc.io/u/AlexAndorra)\
**Post date:** [November 10, 2019, 11:50am UTC](https://discourse.pymc.io/t/how-to-implement-zero-inflated-multinomial/3961/25 "2019-11-10T11:50:51Z")

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Just realized I can mark this as solved thanks to @junpenglao’s suggestion of considering that non-available categories have probability 0 – this implies we know in advance which categories are absent. Of course, I’m curious about @aseyboldt thoughts on profiling and speed-ups if he’s got any!  
Here is a simplified version of the model, for the sake of readability and understanding how to implement the idea with PyMC:

```python
with pm.Model() as m_multi:
    a_cluster = pm.Normal("a_cluster", -1.8, 0.5, shape=(Nclusters, Ncategories - 1))
    a_pivot = tt.as_tensor_variable(np.full(shape=(Nclusters, 1), fill_value=-2.2))
    a_cluster_f = tt.horizontal_stack(a_cluster a_pivot)

    lat_p = tt.nnet.softmax(a_cluster_f[cluster_id])

    # zero-inflation process:
    # keep only preferences for available categories:
    slot_p = cats_available * lat_p
    # normalize preferences:
    slot_p = slot_p / tt.sum(slot_p, axis=1, keepdims=True)
    R = pm.Multinomial("R", n=N, p=slot_p, observed=sim_R)

    trace_multi = pm.sample(2000, tune=3000, init="adapt_diag")

```

Hope this will help future users!  
For the curious out there, the real model is much more complicated (varying-effects and covariance) but I’ll open source it – as well as real and simulated data – once I’ve had time to clean it up!  
And again, a big thank you to Junpeng 🍾 Couldn’t have done it without your help! Now I owe you a second beer when you come to Paris 😉

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