How to have multiple groups in Python statsmodels linear mixed effects model?

Question

I am trying to use the Python statsmodels linear mixed effects model to fit a model that has two random intercepts, e.g. two groups. I cannot figure out how to initialize the m

Answer 1

You are trying to fit a model with crossed random effects, i.e., you want to allow for consistent variation among subjects across scenarios as well as consistent variation among scenarios across subjects. You can use multiple random-effects terms in statsmodels, but they must be nested. Fitting crossed (as opposed to nested) random effects requires more sophisticated algorithms, and indeed the statsmodels documentation says (as of 25 Aug 2016, emphasis added):

Some limitations of the current implementation are that it does not support structure more complex on the residual errors (they are always homoscedastic), and it does not support crossed random effects. We hope to implement these features for the next release.

As far as I can see, your choices are (1) fall back to a nested model (i.e. fit the model as though either scenario is nested within subject or vice versa - or try both and see if the difference matters); (2) fall back to lme4, either within R or via rpy2.

As always, you're entitled to a full refund of the money you paid to use statsmodels ...

Answer 2

Multiple or crossed random intercepts crossed effects can be fit using variance components, which are implemented in a different way from the one-group mixed effects.

I don't find an example, and the documentation seems to be only partially updated.

The unit tests contain an example using the MixedLM formula interface:

https://github.com/statsmodels/statsmodels/blob/master/statsmodels/regression/tests/test_lme.py#L284