How to conduct a multilevel model/regression for panel data in Python?

Question

I have yearly data over time (longitudinal data) with repeated measures for many of the subjects. I think I need multilevel modeling/regressions to deal with sure-to-be correlated clusters of measurements for the same individuals over time. The data currently is in separate tables for each year.

I was wondering if there was a way that was built into scikit-learn, like LinearRegression(), that would be able to conduct a multilevel regression where Level 1 is all the data over the years, and Level 2 is for the clustered on the subjects (clusters for each subject's measurements over time). And if so, if it's better to have the longitudinal data laid out length-wise (where the each subject's measures over time are all in one row) or stacked (where each measure for each year is it's own row).

Is there a way to do this?

Answer 1

Linear regression will not be suitable for a multilevel model.

A mixed effects model is a good way to fit most multilevel models.

In python you can use mixedlm in statsmodels. For example:

In [1]: import statsmodels.api as sm

In [2]: import statsmodels.formula.api as smf

In [3]: data = sm.datasets.get_rdataset("dietox", "geepack").data

In [4]: md = smf.mixedlm("Weight ~ Time", data, groups=data["Pig"])

In [5]: mdf = md.fit()

In [6]: print(mdf.summary())
         Mixed Linear Model Regression Results
========================================================
Model:            MixedLM Dependent Variable: Weight    
No. Observations: 861     Method:             REML      
No. Groups:       72      Scale:              11.3669   
Min. group size:  11      Log-Likelihood:     -2404.7753
Max. group size:  12      Converged:          Yes       
Mean group size:  12.0                                  
--------------------------------------------------------
             Coef.  Std.Err.    z    P>|z| [0.025 0.975]
--------------------------------------------------------
Intercept    15.724    0.788  19.952 0.000 14.179 17.268
Time          6.943    0.033 207.939 0.000  6.877  7.008
Group Var    40.394    2.149                            
========================================================