Python Statsmodels Mixedlm (Mixed Linear Model) random effects

Question

I am a bit confused about the output of Statsmodels Mixedlm and am hoping someone could explain.

I have a large dataset of single family homes, including the previous two sale prices/sale dates for each property. I have geocoded this entire dataset and fetched the elevation for each property. I am trying to understand the way in which the relationship between elevation and property price appreciation varies between different cities.

I have used statsmodels mixed linear model to regress price appreciation on elevation, holding a number of other factors constant, with cities as my groups category.

md = smf.mixedlm('price_relative_ind~Elevation+YearBuilt+Sale_Amount_1+LivingSqFt',data=Miami_SF,groups=Miami_SF['City'])

mdf = md.fit()

mdf.random_effects

Entering mdf.random_effects returns a list of coefficients. Can I interpret this list as, essentially, the slope for each individual city (i.e., the individual regression coefficient relating Elevation to sale price appreciation)? Or are these results the intercepts for each City?

Answer 1

I'm currently trying to get my head around random effects in MixedLM aswell. Looking at the docs, it seems as though using just the groups parameter, without exog_re or re_formula will simply add a random intercept to each group. An example from the docs:

# A basic mixed model with fixed effects for the columns of exog and a random intercept for each distinct value of group:

model = sm.MixedLM(endog, exog, groups)
result = model.fit()

As such, you would expect the random_effects method to return the city's intercepts in this case, not the coefficients/slopes.

To add a random slope with respect to one of your other features, you can do something similar to this example from statsmodels' Jupyter tutorial, either with a slope and an intercept:

model = sm.MixedLM.from_formula(
    "Y ~ X", data, re_formula="X", groups=data["C"])

or with only the slope:

model = sm.MixedLM.from_formula(
    "Y ~ X", data, re_formula="0 + X", groups=data["C"])

Looking at the docs for random_effects, it says that it returns the mean for each groups's random effects. However, as the random effects are only due to the intercept, this should just be equal to the intercept itself.

MixedLMResults.random_effects()[source]
    The conditional means of random effects given the data.

    Returns:    
        random_effects : dict
        A dictionary mapping the distinct group values to the means of the random effects for the group.

Some useful resources to look further at include:

• Docs for the formula version of MixedML
• Docs for the results of MixedML
• This Jupyter notebook with examples for using MixedML (Python)
• Stanford tutorial on mixed models (R)
• Tutorial on fixed and random effects (R)