estimation.api.feglm.feglm

estimation.api.feglm.feglm(
    fml,
    data,
    family,
    vcov=None,
    vcov_kwargs=None,
    ssc=None,
    fixef_rm='singleton',
    iwls_tol=1e-08,
    iwls_maxiter=25,
    collin_tol=1e-09,
    separation_check=None,
    solver='scipy.linalg.solve',
    demeaner=None,
    demeaner_backend=None,
    fixef_tol=None,
    fixef_maxiter=None,
    drop_intercept=False,
    copy_data=True,
    store_data=True,
    lean=False,
    context=None,
    split=None,
    fsplit=None,
    accelerate=True,
)

Estimate GLM regression models with fixed effects.

Supported families: logit, probit, gaussian.

References

Bergé, L. (2018). Efficient estimation of maximum likelihood models with multiple fixed-effects: the R package FENmlm. CREA Discussion Paper.
Correia, S., Guimaraes, P., & Zylkin, T. (2019). ppmlhdfe: Fast Poisson Estimation with High-Dimensional Fixed Effects. The Stata Journal.
Stammann, A. (2018). Fast and Feasible Estimation of Generalized Linear Models with High-Dimensional k-way Fixed Effects. arXiv:1707.01815.

Parameters

Name	Type	Description	Default
fml	str	A two-sided formula string using fixest formula syntax. Syntax: “Y ~ X1 + X2 \| FE1 + FE2”. “\|” separates left-hand side and fixed effects. Special syntax includes: - Stepwise regressions (sw, sw0) - Cumulative stepwise regression (csw, csw0) - Multiple dependent variables (Y1 + Y2 ~ X) - Interaction of variables (i(X1,X2)) - Interacted fixed effects (fe1^fe2) Compatible with formula parsing via the formulaic module.	required
data	DataFrameType	A pandas or polars dataframe containing the variables in the formula.	required
family	str	The family of the GLM model. Options include “gaussian”, “logit” and “probit”.	required
vcov	Union[VcovTypeOptions, dict[str, str]]	Type of variance-covariance matrix for inference. Options include “iid”, “hetero”, “HC1”, “HC2”, “HC3”, “NW” for Newey-West HAC standard errors, “DK” for Driscoll-Kraay HAC standard errors, or a dictionary for CRV1/CRV3 inference. Note that NW and DK require to pass additional keyword arguments via the `vcov_kwargs` argument. For time-series HAC, you need to pass the ‘time_id’ column. For panel-HAC, you need to add pass both ‘time_id’ and ‘panel_id’. See `vcov_kwargs` for details.	`None`
vcov_kwargs	Optional[dict[str, any]]	Additional keyword arguments to pass to the vcov function. These keywoards include “lag” for the number of lag to use in the Newey-West (NW) and Driscoll-Kraay (DK) HAC standard errors. “time_id” for the time ID used for NW and DK standard errors, and “panel_id” for the panel identifier used for NW and DK standard errors. Currently, the the time difference between consecutive time periods is always treated as 1. More flexible time-step selection is work in progress.	`None`
ssc	str	A ssc object specifying the small sample correction for inference.	`None`
fixef_rm	FixedRmOptions	Specifies whether to drop singleton fixed effects. Can be equal to “singleton” (default), or “none”. “singletons” will drop singleton fixed effects. This will not impact point estimates but it will impact standard errors.	`'singleton'`
iwls_tol	Optional[float]	Tolerance for IWLS convergence, by default 1e-08.	`1e-08`
iwls_maxiter	Optional[float]	Maximum number of iterations for IWLS convergence, by default 25.	`25`
collin_tol	float	Tolerance for collinearity check, by default 1e-10.	`1e-09`
separation_check	list[str] \| None	Methods to identify and drop separated observations. Either “fe” or “ir”. Executes “fe” by default (when None).	`None`
solver	SolverOptions, optional.	The solver to use for the regression. Can be “np.linalg.lstsq”, “np.linalg.solve”, “scipy.linalg.solve”, “scipy.sparse.linalg.lsqr” and “jax”. Defaults to “scipy.linalg.solve”.	`'scipy.linalg.solve'`
demeaner	AnyDemeaner \| None	Typed demeaner configuration. Controls the fixed-effects demeaning backend, tolerance, and iteration limits. Accepts a `MapDemeaner`, `WithinDemeaner`, or `LsmrDemeaner` instance. Defaults to `MapDemeaner()` (numba MAP algorithm, tol=1e-6, maxiter=10_000).	`None`
drop_intercept	bool	Whether to drop the intercept from the model, by default False.	`False`
copy_data	bool	Whether to copy the data before estimation, by default True. If set to False, the data is not copied, which can save memory but may lead to unintended changes in the input data outside of `fepois`. For example, the input data set is re-index within the function. As far as I know, the only other relevant case is when using interacted fixed effects, in which case you’ll find a column with interacted fixed effects in the data set.	`True`
store_data	bool	Whether to store the data in the model object, by default True. If set to False, the data is not stored in the model object, which can improve performance and save memory. However, it will no longer be possible to access the data via the `data` attribute of the model object. This has impact on post-estimation capabilities that rely on the data, e.g. `predict()` or `vcov()`.	`True`
lean	bool	False by default. If True, then all large objects are removed from the returned result: this will save memory but will block the possibility to use many methods. It is recommended to use the argument vcov to obtain the appropriate standard-errors at estimation time, since obtaining different SEs won’t be possible afterwards.	`False`
context	int or Mapping[str, Any]	A dictionary containing additional context variables to be used by formulaic during the creation of the model matrix. This can include custom factorization functions, transformations, or any other variables that need to be available in the formula environment.	`None`
split	str \| None	A character string, i.e. ‘split = var’. If provided, the sample is split according to the variable and one estimation is performed for each value of that variable. If you also want to include the estimation for the full sample, use the argument fsplit instead.	`None`
fsplit	str \| None	This argument is the same as split but also includes the full sample as the first estimation.	`None`
accelerate	bool	Whether to use acceleration tricks developed in the ppmlhdfe paper (warm start and adaptive fixed effects tolerance) for models with fixed effects. Produces numerically identical results faster, so we recommend to always set it to True.	`True`

Returns

Name	Type	Description
	object	An instance of the Feglm class (or one of its subclasses: Felogit, Feprobit, Fegaussian) or an instance of class FixestMulti for multiple models specified via `fml`.

Examples

The example below fits a logit model with fixed effects. As in feols(), fixed effects are specified after the | symbol.

import pyfixest as pf
import numpy as np

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

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

###

Estimation:  Logit
Dep. var.: Y_bin, Fixed effects: f1
sample: None = all
Inference:  iid
Observations:  998

| Coefficient   |   Estimate |   Std. Error |   t value |   Pr(>|t|) |   2.5% |   97.5% |
|:--------------|-----------:|-------------:|----------:|-----------:|-------:|--------:|
| X1            |     -1.016 |        0.109 |    -9.297 |      0.000 | -1.231 |  -0.802 |
| X2            |     -0.166 |        0.028 |    -5.831 |      0.000 | -0.222 |  -0.110 |
---
Deviance: 961.445

To compare families with the same specification:

fit_probit = pf.feglm("Y_bin ~ X1 + X2 | f1", data, family="probit")
fit_gaussian = pf.feglm("Y_bin ~ X1 + X2 | f1", data, family="gaussian")
pf.etable([fit_logit, fit_probit, fit_gaussian])

	Y_bin
	(1)	(2)	(3)
coef
X1	-1.016 (0.109)	-0.588 (0.062)	-0.166 (0.04)
X2	-0.166 (0.028)	-0.097 (0.016)	-0.025 (0.011)
fe
f1	x	x	x
stats
Observations	998	998	998
R²	-	-	-
Format of coefficient cell: Coefficient (Std. Error)

PyFixest also integrates with the marginaleffects package. To compute average marginal effects for the logit model above:

from marginaleffects import avg_slopes
avg_slopes(fit_logit, variables="X1")

shape: (1, 3)

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

We can also compute marginal effects by group (group average marginal effects):

avg_slopes(fit_logit, 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

Shared arguments such as vcov, ssc, split, fsplit, context, and typed demeaners work the same way as in feols(). See the feols() reference for those details, and the Marginal Effects guide for a compact post-estimation workflow.