Include an example of a random slope model as a way to demonstrate how to use this aspect of statsmodels

[aezarebski]

aas-extended-examples/example-6/example-6-answers.md

Line 274 in f57c16d

If we were to add `years_post_phd` as a covariate, what sort of model would this

There is an example on the following page of the the statsmodels documentation:

https://www.statsmodels.org/dev/examples/notebooks/generated/mixed_lm_example.html

Basically, you use the re_formula in addition to the existing formula (which specifies fixed effects) and group to specify a random slope (and intercept) model.

Here is an example of fitting a random intercept model

data = sm.datasets.get_rdataset("dietox", "geepack").data
md = smf.mixedlm("Weight ~ Time", data, groups=data["Pig"])
mdf = md.fit(method=["lbfgs"])
print(mdf.summary())

and here it is with the random slope for each pig through time as well as the random intercept:

md = smf.mixedlm("Weight ~ Time", data, groups=data["Pig"], re_formula="~Time")
mdf = md.fit(method=["lbfgs"])
print(mdf.summary())