Generalized Linear Models (Formula)
This notebook illustrates how you can use R-style formulas to fit Generalized Linear Models.
To begin, we load the Star98
dataset and we construct a formula and pre-process the data:
In [1]:
from __future__ import print_function import statsmodels.api as sm import statsmodels.formula.api as smf star98 = sm.datasets.star98.load_pandas().data formula = 'SUCCESS ~ LOWINC + PERASIAN + PERBLACK + PERHISP + PCTCHRT + \ PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF' dta = star98[['NABOVE', 'NBELOW', 'LOWINC', 'PERASIAN', 'PERBLACK', 'PERHISP', 'PCTCHRT', 'PCTYRRND', 'PERMINTE', 'AVYRSEXP', 'AVSALK', 'PERSPENK', 'PTRATIO', 'PCTAF']] endog = dta['NABOVE'] / (dta['NABOVE'] + dta.pop('NBELOW')) del dta['NABOVE'] dta['SUCCESS'] = endog
Then, we fit the GLM model:
In [2]:
mod1 = smf.glm(formula=formula, data=dta, family=sm.families.Binomial()).fit() mod1.summary()
Out[2]:
Finally, we define a function to operate customized data transformation using the formula framework:
In [3]:
def double_it(x): return 2 * x formula = 'SUCCESS ~ double_it(LOWINC) + PERASIAN + PERBLACK + PERHISP + PCTCHRT + \ PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF' mod2 = smf.glm(formula=formula, data=dta, family=sm.families.Binomial()).fit() mod2.summary()
Out[3]:
As expected, the coefficient for double_it(LOWINC)
in the second model is half the size of the LOWINC
coefficient from the first model:
In [4]:
print(mod1.params[1]) print(mod2.params[1] * 2)
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