def linear_component(formula, data, priors=None,
intercept_prior=None,
regressor_prior=None,
init=True, init_vals=None, family=None,
model=None):
"""Create linear model according to patsy specification.
Parameters
----------
formula : str
Patsy linear model descriptor.
data : array
Labeled array (e.g. pandas DataFrame, recarray).
priors : dict
Mapping prior name to prior distribution.
E.g. {'Intercept': Normal.dist(mu=0, sd=1)}
intercept_prior : pymc distribution
Prior to use for the intercept.
Default: Normal.dist(mu=0, tau=1.0E-12)
regressor_prior : pymc distribution
Prior to use for all regressor(s).
Default: Normal.dist(mu=0, tau=1.0E-12)
init : bool
Whether to set the starting values via statsmodels
Default: True
init_vals : dict
Set starting values externally: parameter -> value
Default: None
family : statsmodels.family
Link function to pass to statsmodels (init has to be True).
See `statsmodels.api.families`
Default: identity
Output
------
(y_est, coeffs) : Estimate for y, list of coefficients
Example
-------
# Logistic regression
y_est, coeffs = glm('male ~ height + weight',
htwt_data,
family=glm.families.Binomial(links=glm.link.Logit))
y_data = Bernoulli('y', y_est, observed=data.male)
"""
if intercept_prior is None:
intercept_prior = Normal.dist(mu=0, tau=1.0E-12)
if regressor_prior is None:
regressor_prior = Normal.dist(mu=0, tau=1.0E-12)
if priors is None:
priors = defaultdict(None)
# Build patsy design matrix and get regressor names.
_, dmatrix = patsy.dmatrices(formula, data)
reg_names = dmatrix.design_info.column_names
if init_vals is None and init:
init_vals = glm_sm(formula, data, family=family).fit().params
else:
init_vals = defaultdict(lambda: None)
# Create individual coefficients
model = modelcontext(model)
coeffs = []
if reg_names[0] == 'Intercept':
prior = priors.get('Intercept', intercept_prior)
coeff = model.Var(reg_names.pop(0), prior)
coeff.tag.test_value = init_vals['Intercept']
coeffs.append(coeff)
for reg_name in reg_names:
prior = priors.get(reg_name, regressor_prior)
coeff = model.Var(reg_name, prior)
coeff.tag.test_value = init_vals[reg_name]
coeffs.append(coeff)
y_est = theano.dot(np.asarray(dmatrix), theano.tensor.stack(*coeffs)).reshape((1, -1))
return y_est, coeffs
def linear_component(formula, data, priors=None,
intercept_prior=None,
regressor_prior=None,
init=True, init_vals=None, family=None,
model=None):
"""Create linear model according to patsy specification.
Parameters
----------
formula : str
Patsy linear model descriptor.
data : array
Labeled array (e.g. pandas DataFrame, recarray).
priors : dict
Mapping prior name to prior distribution.
E.g. {'Intercept': Normal.dist(mu=0, sd=1)}
intercept_prior : pymc3 distribution
Prior to use for the intercept.
Default: Normal.dist(mu=0, tau=1.0E-12)
regressor_prior : pymc3 distribution
Prior to use for all regressor(s).
Default: Normal.dist(mu=0, tau=1.0E-12)
init : bool
Whether to set the starting values via statsmodels
Default: True
init_vals : dict
Set starting values externally: parameter -> value
Default: None
family : statsmodels.family
Link function to pass to statsmodels (init has to be True).
See `statsmodels.api.families`
Default: identity
Output
------
(y_est, coeffs) : Estimate for y, list of coefficients
Example
-------
# Logistic regression
y_est, coeffs = glm('male ~ height + weight',
htwt_data,
family=glm.families.Binomial(links=glm.link.Logit))
y_data = Bernoulli('y', y_est, observed=data.male)
"""
if intercept_prior is None:
intercept_prior = Normal.dist(mu=0, tau=1.0E-12)
if regressor_prior is None:
regressor_prior = Normal.dist(mu=0, tau=1.0E-12)
if priors is None:
priors = defaultdict(None)
# Build patsy design matrix and get regressor names.
_, dmatrix = patsy.dmatrices(formula, data)
reg_names = dmatrix.design_info.column_names
if init_vals is None and init:
init_vals = glm_sm(formula, data, family=family).fit().params
else:
init_vals = defaultdict(lambda: None)
# Create individual coefficients
model = modelcontext(model)
coeffs = []
if reg_names[0] == 'Intercept':
prior = priors.get('Intercept', intercept_prior)
coeff = model.Var(reg_names.pop(0), prior)
coeff.tag.test_value = init_vals['Intercept']
coeffs.append(coeff)
for reg_name in reg_names:
prior = priors.get(reg_name, regressor_prior)
coeff = model.Var(reg_name, prior)
coeff.tag.test_value = init_vals[reg_name]
coeffs.append(coeff)
y_est = theano.dot(np.asarray(dmatrix), theano.tensor.stack(*coeffs)).reshape((1, -1))
return y_est, coeffs
Fare 0.0008 0.000 2.206 0.028 8.73e-05 0.001
Pclass_1 0.2398 0.046 5.228 0.000 0.150 0.330
Pclass_2 0.1943 0.038 5.110 0.000 0.120 0.269
Embarked_C 0.5044 0.048 10.580 0.000 0.411 0.598
Embarked_S 0.4092 0.037 11.136 0.000 0.337 0.481
Sex_male -0.4022 0.030 -13.398 0.000 -0.461 -0.343
==============================================================================
Omnibus: 49.900 Durbin-Watson: 1.872
Prob(Omnibus): 0.000 Jarque-Bera (JB): 53.293
Skew: 0.570 Prob(JB): 2.68e-12
Kurtosis: 2.632 Cond. No. 255.
==============================================================================
"""
from statsmodels.formula.api import glm as glm_sm
glm_model = glm_sm('Y ~ X', train, family=sm.families.Binomial()).fit()
glm_model.summary()
"""
Generalized Linear Model Regression Results
==============================================================================
Dep. Variable: Y No. Observations: 891
Model: GLM Df Residuals: 883
Model Family: Binomial Df Model: 7
Link Function: logit Scale: 1.0000
Method: IRLS Log-Likelihood: -399.16
Date: Fri, 15 Jan 2021 Deviance: 798.33
Time: 18:49:28 Pearson chi2: 936.
No. Iterations: 5
Covariance Type: nonrobust
==============================================================================
coef std err z P>|z| [0.025 0.975]