algorithms.statistics.models.family.family

Module: algorithms.statistics.models.family.family

Inheritance diagram for nipy.algorithms.statistics.models.family.family:

Inheritance diagram of nipy.algorithms.statistics.models.family.family

Classes

Binomial

class nipy.algorithms.statistics.models.family.family.Binomial(link=<nipy.algorithms.statistics.models.family.links.Logit object>, n=1)

Bases: nipy.algorithms.statistics.models.family.family.Family

Binomial exponential family.

INPUTS:
link – a Link instance n – number of trials for Binomial

Methods

deviance(Y, mu[, scale]) Deviance of (Y,mu) pair.
devresid(Y, mu) Binomial deviance residual
fitted(eta) Fitted values based on linear predictors eta.
predict(mu) Linear predictors based on given mu values.
variance
weights(mu) Weights for IRLS step.
__init__(link=<nipy.algorithms.statistics.models.family.links.Logit object>, n=1)
deviance(Y, mu, scale=1.0)

Deviance of (Y,mu) pair. Deviance is usually defined as the difference

DEV = (SUM_i -2 log Likelihood(Y_i,mu_i) + 2 log Likelihood(mu_i,mu_i)) / scale

INPUTS:
Y – response variable mu – mean parameter scale – optional scale in denominator of deviance
OUTPUTS: dev
dev – DEV, as described aboce
devresid(Y, mu)

Binomial deviance residual

INPUTS:
Y – response variable mu – mean parameter
OUTPUTS: resid
resid – deviance residuals
fitted(eta)

Fitted values based on linear predictors eta.

INPUTS:
eta – values of linear predictors, say,
X beta in a generalized linear model.
OUTPUTS: mu
mu – link.inverse(eta), mean parameter based on eta
predict(mu)

Linear predictors based on given mu values.

INPUTS:
mu – mean parameter of one-parameter exponential family
OUTPUTS: eta
eta – link(mu), linear predictors, based on
mean parameters mu
tol = 1e-05
valid = [-inf, inf]
variance = <nipy.algorithms.statistics.models.family.varfuncs.Binomial object>
weights(mu)

Weights for IRLS step.

w = 1 / (link’(mu)**2 * variance(mu))

INPUTS:
mu – mean parameter in exponential family
OUTPUTS:
w – weights used in WLS step of GLM/GAM fit

Family

class nipy.algorithms.statistics.models.family.family.Family(link, variance)

Bases: object

A class to model one-parameter exponential families.

INPUTS:

link – a Link instance variance – a variance function (models means as a function

of mean)

Methods

deviance(Y, mu[, scale]) Deviance of (Y,mu) pair.
devresid(Y, mu) The deviance residuals, defined as the residuals in the deviance.
fitted(eta) Fitted values based on linear predictors eta.
predict(mu) Linear predictors based on given mu values.
weights(mu) Weights for IRLS step.
__init__(link, variance)
deviance(Y, mu, scale=1.0)

Deviance of (Y,mu) pair. Deviance is usually defined as the difference

DEV = (SUM_i -2 log Likelihood(Y_i,mu_i) + 2 log Likelihood(mu_i,mu_i)) / scale

INPUTS:
Y – response variable mu – mean parameter scale – optional scale in denominator of deviance
OUTPUTS: dev
dev – DEV, as described aboce
devresid(Y, mu)

The deviance residuals, defined as the residuals in the deviance.

Without knowing the link, they default to Pearson residuals

resid_P = (Y - mu) * sqrt(weight(mu))

INPUTS:
Y – response variable mu – mean parameter
OUTPUTS: resid
resid – deviance residuals
fitted(eta)

Fitted values based on linear predictors eta.

INPUTS:
eta – values of linear predictors, say,
X beta in a generalized linear model.
OUTPUTS: mu
mu – link.inverse(eta), mean parameter based on eta
predict(mu)

Linear predictors based on given mu values.

INPUTS:
mu – mean parameter of one-parameter exponential family
OUTPUTS: eta
eta – link(mu), linear predictors, based on
mean parameters mu
tol = 1e-05
valid = [-inf, inf]
weights(mu)

Weights for IRLS step.

w = 1 / (link’(mu)**2 * variance(mu))

INPUTS:
mu – mean parameter in exponential family
OUTPUTS:
w – weights used in WLS step of GLM/GAM fit

Gamma

class nipy.algorithms.statistics.models.family.family.Gamma(link=<nipy.algorithms.statistics.models.family.links.Power object>)

Bases: nipy.algorithms.statistics.models.family.family.Family

Gamma exponential family.

INPUTS:
link – a Link instance
BUGS:
no deviance residuals?

Methods

deviance(Y, mu[, scale]) Deviance of (Y,mu) pair.
devresid(Y, mu) The deviance residuals, defined as the residuals in the deviance.
fitted(eta) Fitted values based on linear predictors eta.
predict(mu) Linear predictors based on given mu values.
variance
weights(mu) Weights for IRLS step.
__init__(link=<nipy.algorithms.statistics.models.family.links.Power object>)
deviance(Y, mu, scale=1.0)

Deviance of (Y,mu) pair. Deviance is usually defined as the difference

DEV = (SUM_i -2 log Likelihood(Y_i,mu_i) + 2 log Likelihood(mu_i,mu_i)) / scale

INPUTS:
Y – response variable mu – mean parameter scale – optional scale in denominator of deviance
OUTPUTS: dev
dev – DEV, as described aboce
devresid(Y, mu)

The deviance residuals, defined as the residuals in the deviance.

Without knowing the link, they default to Pearson residuals

resid_P = (Y - mu) * sqrt(weight(mu))

INPUTS:
Y – response variable mu – mean parameter
OUTPUTS: resid
resid – deviance residuals
fitted(eta)

Fitted values based on linear predictors eta.

INPUTS:
eta – values of linear predictors, say,
X beta in a generalized linear model.
OUTPUTS: mu
mu – link.inverse(eta), mean parameter based on eta
predict(mu)

Linear predictors based on given mu values.

INPUTS:
mu – mean parameter of one-parameter exponential family
OUTPUTS: eta
eta – link(mu), linear predictors, based on
mean parameters mu
tol = 1e-05
valid = [-inf, inf]
variance = <nipy.algorithms.statistics.models.family.varfuncs.Power object>
weights(mu)

Weights for IRLS step.

w = 1 / (link’(mu)**2 * variance(mu))

INPUTS:
mu – mean parameter in exponential family
OUTPUTS:
w – weights used in WLS step of GLM/GAM fit

Gaussian

class nipy.algorithms.statistics.models.family.family.Gaussian(link=<nipy.algorithms.statistics.models.family.links.Power object>)

Bases: nipy.algorithms.statistics.models.family.family.Family

Gaussian exponential family.

INPUTS:
link – a Link instance

Methods

deviance(Y, mu[, scale]) Deviance of (Y,mu) pair.
devresid(Y, mu[, scale]) Gaussian deviance residual
fitted(eta) Fitted values based on linear predictors eta.
predict(mu) Linear predictors based on given mu values.
variance
weights(mu) Weights for IRLS step.
__init__(link=<nipy.algorithms.statistics.models.family.links.Power object>)
deviance(Y, mu, scale=1.0)

Deviance of (Y,mu) pair. Deviance is usually defined as the difference

DEV = (SUM_i -2 log Likelihood(Y_i,mu_i) + 2 log Likelihood(mu_i,mu_i)) / scale

INPUTS:
Y – response variable mu – mean parameter scale – optional scale in denominator of deviance
OUTPUTS: dev
dev – DEV, as described aboce
devresid(Y, mu, scale=1.0)

Gaussian deviance residual

INPUTS:
Y – response variable mu – mean parameter scale – optional scale in denominator (after taking sqrt)
OUTPUTS: resid
resid – deviance residuals
fitted(eta)

Fitted values based on linear predictors eta.

INPUTS:
eta – values of linear predictors, say,
X beta in a generalized linear model.
OUTPUTS: mu
mu – link.inverse(eta), mean parameter based on eta
predict(mu)

Linear predictors based on given mu values.

INPUTS:
mu – mean parameter of one-parameter exponential family
OUTPUTS: eta
eta – link(mu), linear predictors, based on
mean parameters mu
tol = 1e-05
valid = [-inf, inf]
variance = <nipy.algorithms.statistics.models.family.varfuncs.VarianceFunction object>
weights(mu)

Weights for IRLS step.

w = 1 / (link’(mu)**2 * variance(mu))

INPUTS:
mu – mean parameter in exponential family
OUTPUTS:
w – weights used in WLS step of GLM/GAM fit

InverseGaussian

class nipy.algorithms.statistics.models.family.family.InverseGaussian(link=<nipy.algorithms.statistics.models.family.links.Power object>)

Bases: nipy.algorithms.statistics.models.family.family.Family

InverseGaussian exponential family.

INPUTS:
link – a Link instance n – number of trials for Binomial

Methods

deviance(Y, mu[, scale]) Deviance of (Y,mu) pair.
devresid(Y, mu) The deviance residuals, defined as the residuals in the deviance.
fitted(eta) Fitted values based on linear predictors eta.
predict(mu) Linear predictors based on given mu values.
variance
weights(mu) Weights for IRLS step.
__init__(link=<nipy.algorithms.statistics.models.family.links.Power object>)
deviance(Y, mu, scale=1.0)

Deviance of (Y,mu) pair. Deviance is usually defined as the difference

DEV = (SUM_i -2 log Likelihood(Y_i,mu_i) + 2 log Likelihood(mu_i,mu_i)) / scale

INPUTS:
Y – response variable mu – mean parameter scale – optional scale in denominator of deviance
OUTPUTS: dev
dev – DEV, as described aboce
devresid(Y, mu)

The deviance residuals, defined as the residuals in the deviance.

Without knowing the link, they default to Pearson residuals

resid_P = (Y - mu) * sqrt(weight(mu))

INPUTS:
Y – response variable mu – mean parameter
OUTPUTS: resid
resid – deviance residuals
fitted(eta)

Fitted values based on linear predictors eta.

INPUTS:
eta – values of linear predictors, say,
X beta in a generalized linear model.
OUTPUTS: mu
mu – link.inverse(eta), mean parameter based on eta
predict(mu)

Linear predictors based on given mu values.

INPUTS:
mu – mean parameter of one-parameter exponential family
OUTPUTS: eta
eta – link(mu), linear predictors, based on
mean parameters mu
tol = 1e-05
valid = [-inf, inf]
variance = <nipy.algorithms.statistics.models.family.varfuncs.Power object>
weights(mu)

Weights for IRLS step.

w = 1 / (link’(mu)**2 * variance(mu))

INPUTS:
mu – mean parameter in exponential family
OUTPUTS:
w – weights used in WLS step of GLM/GAM fit

Poisson

class nipy.algorithms.statistics.models.family.family.Poisson(link=<nipy.algorithms.statistics.models.family.links.Log object>)

Bases: nipy.algorithms.statistics.models.family.family.Family

Poisson exponential family.

INPUTS:
link – a Link instance

Methods

deviance(Y, mu[, scale]) Deviance of (Y,mu) pair.
devresid(Y, mu) Poisson deviance residual
fitted(eta) Fitted values based on linear predictors eta.
predict(mu) Linear predictors based on given mu values.
variance
weights(mu) Weights for IRLS step.
__init__(link=<nipy.algorithms.statistics.models.family.links.Log object>)
deviance(Y, mu, scale=1.0)

Deviance of (Y,mu) pair. Deviance is usually defined as the difference

DEV = (SUM_i -2 log Likelihood(Y_i,mu_i) + 2 log Likelihood(mu_i,mu_i)) / scale

INPUTS:
Y – response variable mu – mean parameter scale – optional scale in denominator of deviance
OUTPUTS: dev
dev – DEV, as described aboce
devresid(Y, mu)

Poisson deviance residual

INPUTS:
Y – response variable mu – mean parameter
OUTPUTS: resid
resid – deviance residuals
fitted(eta)

Fitted values based on linear predictors eta.

INPUTS:
eta – values of linear predictors, say,
X beta in a generalized linear model.
OUTPUTS: mu
mu – link.inverse(eta), mean parameter based on eta
predict(mu)

Linear predictors based on given mu values.

INPUTS:
mu – mean parameter of one-parameter exponential family
OUTPUTS: eta
eta – link(mu), linear predictors, based on
mean parameters mu
tol = 1e-05
valid = [0, inf]
variance = <nipy.algorithms.statistics.models.family.varfuncs.Power object>
weights(mu)

Weights for IRLS step.

w = 1 / (link’(mu)**2 * variance(mu))

INPUTS:
mu – mean parameter in exponential family
OUTPUTS:
w – weights used in WLS step of GLM/GAM fit