# Source code for statsmodels.stats.knockoff_regeffects

```
import numpy as np
class RegressionEffects:
"""
Base class for regression effects used in RegressionFDR.
Any implementation of the class must provide a method called
'stats' that takes a RegressionFDR object and returns effect sizes
for the model coefficients. Greater values for these statistics
imply greater evidence that the effect is real.
Knockoff effect sizes are based on fitting the regression model to
an extended design matrix [X X'], where X' is a design matrix with
the same shape as the actual design matrix X. The construction of
X' guarantees that there are no true associations between the
columns of X' and the dependent variable of the regression. If X
has p columns, then the effect size of covariate j is based on the
strength of the estimated association for coefficient j compared
to the strength of the estimated association for coefficient p+j.
"""
def stats(self, parent):
raise NotImplementedError
[docs]class CorrelationEffects(RegressionEffects):
"""
Marginal correlation effect sizes for FDR control.
Parameters
----------
parent : RegressionFDR
The RegressionFDR instance to which this effect size is
applied.
Notes
-----
This class implements the marginal correlation approach to
constructing test statistics for a knockoff analysis, as
described under (1) in section 2.2 of the Barber and Candes
paper.
"""
[docs] def stats(self, parent):
s1 = np.dot(parent.exog1.T, parent.endog)
s2 = np.dot(parent.exog2.T, parent.endog)
return np.abs(s1) - np.abs(s2)
[docs]class ForwardEffects(RegressionEffects):
"""
Forward selection effect sizes for FDR control.
Parameters
----------
parent : RegressionFDR
The RegressionFDR instance to which this effect size is
applied.
pursuit : bool
If True, 'basis pursuit' is used, which amounts to performing
a full regression at each selection step to adjust the working
residual vector. If False (the default), the residual is
adjusted by regressing out each selected variable marginally.
Setting pursuit=True will be considerably slower, but may give
better results when exog is not orthogonal.
Notes
-----
This class implements the forward selection approach to
constructing test statistics for a knockoff analysis, as
described under (5) in section 2.2 of the Barber and Candes
paper.
"""
def __init__(self, pursuit):
self.pursuit = pursuit
[docs] def stats(self, parent):
nvar = parent.exog.shape[1]
rv = parent.endog.copy()
vl = [(i, parent.exog[:, i]) for i in range(nvar)]
z = np.empty(nvar)
past = []
for i in range(nvar):
dp = np.r_[[np.abs(np.dot(rv, x[1])) for x in vl]]
j = np.argmax(dp)
z[vl[j][0]] = nvar - i - 1
x = vl[j][1]
del vl[j]
if self.pursuit:
for v in past:
x -= np.dot(x, v)*v
past.append(x)
rv -= np.dot(rv, x) * x
z1 = z[0:nvar//2]
z2 = z[nvar//2:]
st = np.where(z1 > z2, z1, z2) * np.sign(z1 - z2)
return st
[docs]class OLSEffects(RegressionEffects):
"""
OLS regression for knockoff analysis.
Parameters
----------
parent : RegressionFDR
The RegressionFDR instance to which this effect size is
applied.
Notes
-----
This class implements the ordinary least squares regression
approach to constructing test statistics for a knockoff analysis,
as described under (2) in section 2.2 of the Barber and Candes
paper.
"""
[docs] def stats(self, parent):
from statsmodels.regression.linear_model import OLS
model = OLS(parent.endog, parent.exog)
result = model.fit()
q = len(result.params) // 2
stats = np.abs(result.params[0:q]) - np.abs(result.params[q:])
return stats
[docs]class RegModelEffects(RegressionEffects):
"""
Use any regression model for Regression FDR analysis.
Parameters
----------
parent : RegressionFDR
The RegressionFDR instance to which this effect size is
applied.
model_cls : class
Any model with appropriate fit or fit_regularized
functions
regularized : bool
If True, use fit_regularized to fit the model
model_kws : dict
Keywords passed to model initializer
fit_kws : dict
Dictionary of keyword arguments for fit or fit_regularized
"""
def __init__(self, model_cls, regularized=False, model_kws=None,
fit_kws=None):
self.model_cls = model_cls
self.regularized = regularized
self.model_kws = model_kws if model_kws is not None else {}
self.fit_kws = fit_kws if fit_kws is not None else {}
[docs] def stats(self, parent):
model = self.model_cls(parent.endog, parent.exog, **self.model_kws)
if self.regularized:
params = model.fit_regularized(**self.fit_kws).params
else:
params = model.fit(**self.fit_kws).params
q = len(params) // 2
stats = np.abs(params[0:q]) - np.abs(params[q:])
return stats
```