Logit Regressions

A logistical regression (Logit) is a statistical method for a best-fit line between a binary [0/1] outcome variable \(Y\) and any number of independent variables. Logit regressions follow a logistical distribution and the predicted probabilities are bounded between 0 and 1.

For more information about Logit, see Wikipedia: Logit.

Keep in Mind

The beta coefficients from a logit model are maximum likelihood estimations. They are not the marginal effect, as you would see in an OLS estimation. So you cannot interpret the beta coefficient as a marginal effect of \(X\) on \(Y\).
To obtain the marginal effect, you need to perform a post-estimation command to discover the marginal effect. In general, you can ‘eye-ball’ the marginal effect by dividing the logit beta coefficient by 4.

Also Consider

See Marginal Effects in Nonlinear Regression for more details on the different kinds of marginal effects.

Implementations

Gretl

# Load auto data
open auto.gdt

# Run logit using the auto data, with mpg as the outcome variable
# and headroom, trunk, and weight as predictors
logit mpg const headroom trunk weight

Python

There are a number of Python packages that can perform logit regressions but the most comprehensive is probably statsmodels. The code below is an example of how to use it.

# Install pandas and statsmodels using pip or conda, if you don't already have them.

import pandas as pd
import statsmodels.formula.api as smf

df = pd.read_csv('https://vincentarelbundock.github.io/Rdatasets/csv/datasets/mtcars.csv',
                 index_col=0)

# Specify the model, regressing vs on mpg and cyl
mod = smf.logit('vs ~ mpg + cyl', data=df)

# Fit the model
res = mod.fit()

# Look at the results
res.summary()

# Compute marginal effects
marg_effect = res.get_margeff(at='mean', method='dydx')

# Show marginal effects
marg_effect.summary()

R

R can run a logit regression using the glm() function. However, to get marginal effects you will need to calculate them by hand or use a package. We will use the mfx package, although the margins package is another good option, which produces tidy model output.

# If necessary, install the mfx package
# install.packages('mfx')
# mfx is only needed for the marginal effect, not the regression itself
library(mfx)

# Load mtcars data
data(mtcars)

# Use the glm() function to run logit
# Here we are predicting engine type using 
# miles per gallon and number of cylinders as predictors
my_logit <- glm(vs ~ mpg + cyl, data = mtcars,
                family = binomial(link = 'logit'))
# The family argument says we are working with binary data
# and using a logit link function (rather than, say, probit)

# The results
summary(my_logit)

# Marginal effects
logitmfx(vs ~ mpg + cyl, data = mtcars)

Stata

* Load auto data
sysuse auto.dta

* Logit Estimation
logit foreign mpg weight headroom trunk

* Recover the Marginal Effects (Beta Coefficient in OLS)
margins, dydx(*)