Formulas: Fitting models using R-style formulasΒΆ
Since version 0.5.0, statsmodels allows users to fit statistical models using R-style formulas. Internally, statsmodels uses the patsy package to convert formulas and data to the matrices that are used in model fitting. The formula framework is quite powerful; this tutorial only scratches the surface. A full description of the formula language can be found in the patsy docs:
Loading modules and functions¶
from __future__ import print_function
import numpy as np
import statsmodels.api as sm
Import convention¶
You can import explicitly from statsmodels.formula.api
from statsmodels.formula.api import ols
Alternatively, you can just use the formula namespace of the main statsmodels.api.
sm.formula.ols
Or you can use the following conventioin
import statsmodels.formula.api as smf
These names are just a convenient way to get access to each model's from_formula classmethod. See, for instance
sm.OLS.from_formula
All of the lower case models accept formula and data arguments, whereas upper case ones take endog and exog design matrices. formula accepts a string which describes the model in terms of a patsy formula. data takes a pandas data frame or any other data structure that defines a __getitem__ for variable names like a structured array or a dictionary of variables.
dir(sm.formula) will print a list of available models.
Formula-compatible models have the following generic call signature: (formula, data, subset=None, *args, **kwargs)
OLS regression using formulas¶
To begin, we fit the linear model described on the Getting Started page. Download the data, subset columns, and list-wise delete to remove missing observations:
dta = sm.datasets.get_rdataset("Guerry", "HistData", cache=True)
df = dta.data[['Lottery', 'Literacy', 'Wealth', 'Region']].dropna()
df.head()
Fit the model:
mod = ols(formula='Lottery ~ Literacy + Wealth + Region', data=df)
res = mod.fit()
print(res.summary())
Categorical variables¶
Looking at the summary printed above, notice that patsy determined that elements of Region were text strings, so it treated Region as a categorical variable. patsy's default is also to include an intercept, so we automatically dropped one of the Region categories.
If Region had been an integer variable that we wanted to treat explicitly as categorical, we could have done so by using the C() operator:
res = ols(formula='Lottery ~ Literacy + Wealth + C(Region)', data=df).fit()
print(res.params)
Patsy's mode advanced features for categorical variables are discussed in: Patsy: Contrast Coding Systems for categorical variables
res = ols(formula='Lottery ~ Literacy + Wealth + C(Region) -1 ', data=df).fit()
print(res.params)
Multiplicative interactions¶
":" adds a new column to the design matrix with the interaction of the other two columns. "*" will also include the individual columns that were multiplied together:
res1 = ols(formula='Lottery ~ Literacy : Wealth - 1', data=df).fit()
res2 = ols(formula='Lottery ~ Literacy * Wealth - 1', data=df).fit()
print(res1.params, '\n')
print(res2.params)
Many other things are possible with operators. Please consult the patsy docs to learn more.
Functions¶
You can apply vectorized functions to the variables in your model:
res = smf.ols(formula='Lottery ~ np.log(Literacy)', data=df).fit()
print(res.params)
Define a custom function:
def log_plus_1(x):
return np.log(x) + 1.
res = smf.ols(formula='Lottery ~ log_plus_1(Literacy)', data=df).fit()
print(res.params)
Any function that is in the calling namespace is available to the formula.
Using formulas with models that do not (yet) support them¶
Even if a given statsmodels function does not support formulas, you can still use patsy's formula language to produce design matrices. Those matrices
can then be fed to the fitting function as endog and exog arguments.
To generate numpy arrays:
import patsy
f = 'Lottery ~ Literacy * Wealth'
y,X = patsy.dmatrices(f, df, return_type='dataframe')
print(y[:5])
print(X[:5])
To generate pandas data frames:
f = 'Lottery ~ Literacy * Wealth'
y,X = patsy.dmatrices(f, df, return_type='dataframe')
print(y[:5])
print(X[:5])
print(sm.OLS(y, X).fit().summary())