# Am I doing the right model?

**URL:** <https://discourse.pymc.io/t/am-i-doing-the-right-model/16982>\
**Category:** v5\
**Tags:** modeling, hierarchical\
**Created:** [May 9, 2025, 8:12pm UTC](https://discourse.pymc.io/t/am-i-doing-the-right-model/16982 "2025-05-09T20:12:25Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![rodrigotakming](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/rodrigotakming/32/9124_2.png) [@rodrigotakming](https://discourse.pymc.io/u/rodrigotakming)\
**Post date:** [May 9, 2025, 8:12pm UTC](https://discourse.pymc.io/t/am-i-doing-the-right-model/16982/1 "2025-05-09T20:12:25Z")

</div>

In my dataset there is 4 columns (project\_id, responsible\_id, date\_reference, acquisitiontypes, number\_of\_tasks\_finished). What we call project is an client that has contract with us, and the responsible is the person from that project that is doing the n\_tasks on an given day of an specific acquisitiontypes (somethink like the type of task). The ideia is to model number\_of\_tasks\_finished so we can estimate an realistic goal for an employer taken into account the historic of the specific project and the task\_type, since different projects are more dinamic and work intensive than others and some type of tasks are more common than others.

About the dataset, there is 11k rows with 167 projects, 7 types of tasks. Since the ideia is to generalize for any kind of person, we chose to not consider the responsible\_id.

The model it self is hierarchical and we wanted to estimate project\_random\_effects, the task\_type\_beta and an project\_task\_type\_interaction. The thing is that this model trains really slowly, but when we consider another model with only the interaction parameter, the model trains really fast. But we want to estimate some task\_type because the ideia is that when another project comes in we can make an prediction based on the type.

Am I doing something wrong?

The model code:

```py
import pymc as pm
import pandas as pd
import numpy as np
import arviz as az

project_categories = pd.Categorical(train_df['project'], train_df['project'].unique())
acquisitiontype_categories = pd.Categorical(train_df['acquisitiontype'], train_df['acquisitiontype'].unique())

coords = {
    "projects": project_categories.categories, 
    "acquisitiontypes": acquisitiontype_categories.categories
}
with pm.Model(coords=coords) as model:
    project_codes = pm.Data("project_codes", project_categories.codes)
    acqtype_codes = pm.Data("acqtype_codes", acquisitiontype_categories.codes)
    y_data = pm.Data("y_data", train_df['tasks_finished'])
    
    alpha = pm.Normal("interaction_mean", 0, 0.5)

    project_sd = pm.Exponential("project_sd", 3)
    project_effect = pm.Normal("project_effect", 
                                 0, project_sd, 
                                 dims=('projects'))

    channel_sd = pm.Exponential("channel_sd", 3)
    channel_effect = pm.Normal("channel_effect", 
                                 0, channel_sd, 
                                 dims=('acquisitiontypes'))

    interaction_deviation = pm.Exponential("interaction_deviation", 3)
    interaction_effect = pm.Normal("interaction_effect", 
                                 0, interaction_deviation, 
                                 dims=('projects', 'acquisitiontypes'))

    mu = pm.math.exp(
            alpha + project_effect[project_codes] + channel_effect[acqtype_codes] + interaction_effect[project_codes, acqtype_codes]
        )
    y = pm.Poisson("y", mu, observed=y_data, shape=project_codes.shape)

    trace = pm.sample(target_accept=0.9)

```

---

<div class="post-metadata">

**Author:** ![tbosois](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/tbosois/32/8683_2.png) [@tbosois](https://discourse.pymc.io/u/tbosois)\
**Post date:** [May 11, 2025, 9:42pm UTC](https://discourse.pymc.io/t/am-i-doing-the-right-model/16982/2 "2025-05-11T21:42:08Z")

</div>

If you like your model but are concerned about it being slow, try the following:

```auto
trace = pm.sample(target_accept=.9, nuts_sampler = 'nutpie',nuts_sampler_kwargs={'backend':'jax')

```

You’ll need to pip install jax and nutpie but this should give you a very large speedup.

---

<div class="post-metadata">

**Author:** ![bob-carpenter](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/bob-carpenter/32/8124_2.png) [@bob-carpenter](https://discourse.pymc.io/u/bob-carpenter)\
**Post date:** [May 15, 2025, 7:32pm UTC](https://discourse.pymc.io/t/am-i-doing-the-right-model/16982/3 "2025-05-15T19:32:30Z")

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> [@rodrigotakming](#):
>
> ```auto
> project_sd = pm.Exponential("project_sd", 3)
> project_effect = pm.Normal("project_effect", 
> 0, project_sd, 
> dims=('projects'))
> 
> ```

I think this is going to give you the centered parameterization of the hierarchical model. You might want to rewrite to draw `channel_effect_std` from a standard normal and then let `channel_effect = channel_sd * channel_effect_std`. Whether the centered or non-centered will be more efficient will determine on the how informative the data and prior are about the parameter values—the more data and stronger prior you have, the more likely the centered parameterization is to be better.

The exponential distribution in PyMC uses a rate (inverse) scale parameterization, so the prior on your standard deviations has a mean of 1/3 and a standard deviation of 1/3 (see [pymc.Exponential — PyMC 5.22.0 documentation](https://www.pymc.io/projects/docs/en/stable/api/distributions/generated/pymc.Exponential.html)).