Marginal Effects and Hypothesis Tests via marginaleffects

PyFixest integrates with the excellent marginaleffects package. Among many other things, marginaleffects allows you to compute:

• average marginal effects,
• subgroup marginal effects,
• linear and non-linear hypothesis tests.

import numpy as np
from marginaleffects import avg_slopes, hypotheses

import pyfixest as pf

data = pf.get_data()
data["Y_bin"] = np.where(data["Y"] > 0, 1, 0)

fit = pf.feglm("Y_bin ~ X1 + X2 | f1", data=data, family="logit")
fit.tidy()

	Estimate	Std. Error	t value	Pr(>|t|)	2.5%	97.5%
Coefficient
X1	-1.016344	0.109323	-9.296712	0.000000e+00	-1.230613	-0.802075
X2	-0.165899	0.028449	-5.831409	5.496138e-09	-0.221659	-0.110140

Average marginal effects

To compute the average marginal effect of X1 on the response scale:

avg_slopes(fit, variables="X1")

shape: (1, 3)

term	contrast	estimate
str	str	f64
"X1"	"dY/dX"	-1.016344

You can also report group-specific average marginal effects:

avg_slopes(fit, variables="X1", by="f1")

shape: (30, 4)

f1	term	contrast	estimate
f64	str	str	f64
0.0	"X1"	"dY/dX"	-1.016344
1.0	"X1"	"dY/dX"	-1.016344
2.0	"X1"	"dY/dX"	-1.016344
3.0	"X1"	"dY/dX"	-1.016344
4.0	"X1"	"dY/dX"	-1.016344
…	…	…	…
25.0	"X1"	"dY/dX"	-1.016344
26.0	"X1"	"dY/dX"	-1.016344
27.0	"X1"	"dY/dX"	-1.016344
28.0	"X1"	"dY/dX"	-1.016344
29.0	"X1"	"dY/dX"	-1.016344

Linear hypothesis tests

Suppose we want to test the linear restriction \(X_1 = X_2\). The hypotheses() function uses the model’s estimated covariance matrix, so it works naturally with PyFixest objects.

hypotheses(fit, "X1 - X2 = 0")

shape: (1, 8)

term	estimate	std_error	statistic	p_value	s_value	conf_low	conf_high
str	f64	f64	f64	f64	f64	f64	f64
"X1-X2=0"	-0.850445	0.1086	-7.830952	4.8850e-15	47.540568	-1.063297	-0.637592

Non-linear hypothesis tests

For non-linear transformations, marginaleffects applies the delta method automatically. This is useful for ratio-style summaries or uplift calculations.

Here is a simple OLS example:

fit_ols = pf.feols("Y ~ X1 + X2", data=data)

hypotheses(fit_ols, "(X1 / Intercept - 1) * 100 = 0")

shape: (1, 8)

term	estimate	std_error	statistic	p_value	s_value	conf_low	conf_high
str	f64	f64	f64	f64	f64	f64	f64
"(X1/Intercept-1)*100=0"	-211.719067	8.478682	-24.970752	0.0	inf	-228.336978	-195.101155

Notes

For broader functionality / the full capability of marginaleffects, see the marginaleffects book.