# Hierarchical modelling in Python with statsmodels

I have a dataset with random effects at different hierarchies and now I want to analyze how they influence my target variable. Somehow I'm looking into statsmodels Linear Mixed Effect Models to solve my issue. Though I can't figure out through the documentation how to achieve my goal.

To pick up the example from statsmodels with the dietox dataset my example is:

import statsmodels.api as sm
import statsmodels.formula.api as smf

data = sm.datasets.get_rdataset("dietox", "geepack").data
# Only take the last week
data = data.copy().query("Time == 12")
# Convert Vitamin E to number
data["Evit"] = data["Evit"].map(lambda s: int(s.replace("Evit", "")))
md = smf.mixedlm("Weight ~ Feed + Evit", data, groups=data["Evit"])
mdf = md.fit()
print(mdf.summary())


I want to predict the pigs weight in week 12 from the cumulated food intake Feed and vitamin E dosage Evit. The hierarchy is supposed to be groups sharing a vitamin E dose that have multiple pigs assigned to them.

I would expect to have a model that for every $$Weight$$ in the groups $$i = 1...N$$ and for every pig $$j = 1...M$$ $$Weight_{ij} = \beta_0 + \beta_1 Evit_{i} + \gamma_{0i} + \gamma_{1i} Feed_{ij}$$ then $$\beta_0$$ should be the common intercept shared among all Pigs. $$\beta_1$$ would be the slope that shows the effect of vitamin E. $$\gamma_{0i}$$ is the intercept for the group receiving the same vitamin E injections (this does not make much sense with this dataset, but it's required for my actual problem). $$\gamma_{1i}$$ is the groups slope for the Feed, so that it shows if vitamin dosis lead to different weight gain with the same amount of food.

I would also be interested in how to remove the intercept.

In my actual dataset the group (Evit) determines more variables (for example $$Light$$) that are the same within the group but different between the groups. I would also like to include these. Also there are more variables that are individual (for example $$Hairiness$$). So that the final model could look more like this: $$Weight_{ij} = \beta_0 + \beta_1 Evit_{i} + \beta_2 Light_{i} + \gamma_{0i} + \gamma_{1i} Feed_{ij} + \gamma_{2i} Hairiness_{ij}$$

The question is how do I model this in statsmodels or another Python library.

model = sm.MixedLM.from_formula("weight ~ evit+light", groups="pig", re_formula="feed + hairiness")

• Thank you for the answer! To remove the intercept in the random effects I could use re_formula="0 + feed + hairiness". To get the random effects you can use model.fit().random_effects which contains the intercept and slope for every parameter and group. If you extend your answer by this I will accept it. – Benjamin Jul 7 '20 at 7:37