# Hierarchical model

**URL:** <https://discourse.pymc.io/t/hierarchical-model/7883>\
**Category:** Questions\
**Created:** [August 13, 2021, 5:23pm UTC](https://discourse.pymc.io/t/hierarchical-model/7883 "2021-08-13T17:23:24Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![Ludovic\_Ferrer](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/ludovic_ferrer/32/3973_2.png) [@Ludovic\_Ferrer](https://discourse.pymc.io/u/Ludovic_Ferrer)\
**Post date:** [August 13, 2021, 5:23pm UTC](https://discourse.pymc.io/t/hierarchical-model/7883/1 "2021-08-13T17:23:24Z")

</div>

Hello everyone,  
I am new to pymc3 and I’d like to model some time series data with a hierarchical model.  
Basically, I used pymc3 to derive parameters of a sum of exponential functions that describe my observed data over time. This part is working correctly if i provide one data set at a time.

```auto
with pm.Model() as model_biexpo:
    ke = pm.Exponential('ke', lam=1)
    ka = pm.Exponential('ka', lam=50)
    c = pm.Exponential('c', lam=1e-4)
    epsilon = pm.HalfNormal('epsilon',sigma=5)
    measures = pm.Deterministic('measures', bi_exponential(ke, ka, c, t))
    y_like = pm.Normal('y_like', mu=measures, observed=observed, sd=epsilon)
    dec_trace = pm.sample(15000, progressbar=False, tune=8000)
    burned_dec_trace = dec_trace[8000:]

```

where  
`observed` & `t` are measured data and time of measurement respectively. So far so good. results are great.

Following [this document](http://docs.pymc.io/notebooks/GLM-hierarchical.html) & [this one](http://docs.pymc.io/pymc-examples/examples/generalized_linear_models/GLM-hierarchical.html), I try to implement a hierarchical model to fit several dataset at the same time.

For my first try, i don’t want to look after hyperparameters in my model, I want to stick to the unpooled model like in [radon example](http://docs.pymc.io/notebooks/GLM-hierarchical.html).

My data (as a pandas Dataframe) are arranged like so:

| | hours | measures |
| --- | --- | --- |
| code | | |
| --- | --- | --- |
| 0 | 3.95 | 6.044405e-06 |
| 0 | 22.25 | 2.673205e-06 |
| 0 | 46.07 | 1.961030e-06 |
| 0 | 70.81 | 1.262165e-06 |
| 0 | 142.49 | 7.512900e-07 |
| 1 | 2.00 | 1.355847e-05 |
| 1 | 26.04 | 1.151494e-06 |
| 1 | 49.77 | 8.385432e-07 |
| 2 | to continue with some other data... |

For each code, several time and measurements. Note that the number of time points are not necessary the same.

I don’t how to organize my data to fit into the model derived from [here](http://docs.pymc.io/pymc-examples/examples/generalized_linear_models/GLM-hierarchical.html):

```auto
with pm.Model() as unpooled_model_biexpo:
    ke = pm.Exponential('ke', lam=1, shape=nb_sbjct)
    ka = pm.Exponential('ka', lam=50, shape=nb_sbjct)
    c = pm.Exponential('c', lam=1e-4, shape=nb_sbjct)
    t = theano.tensor.dcol('t')
    epsilon = pm.HalfNormal('epsilon',sigma=5)
    tps_measures =data.loc[:,'hours'].values.reshape(len(idx_pat),1).astype('double')
    measures = pm.Deterministic('measures', tt.function([ke, ka, c, t],
                                            bi_exponential(ke, ka, c, tps_measures), on_unused_input='warn'))
    y_like = pm.Normal('y_like', mu=measures, observed=data.loc[:,'measures'], sd=epsilon)
    dec_trace = pm.sample(15000, progressbar=False, tune=8000)
    burned_dec_trace = dec_trace[8000:]

```

if I understand correctly `nb_subjct` should be the number of different code in my dataset, say: `nb_suject=len(data.index.unique())`.

I don’t figure out how to handle the measurements properly as the number of data point vary from subject to subject. Despite my several attempts, I didn’t find a way to properly encode this information for each subject.

Any help would be greatly appreciated.  
Best regards  
LF