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.
- 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.
- See Marginal Effects in Nonlinear Regression for more details on the different kinds of marginal effects.
# 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
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 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)
* Load auto data sysuse auto.dta * Logit Estimation logit foreign mpg weight headroom trunk * Recover the Marginal Effects (Beta Coefficient in OLS) margins, dydx(*)