algorithms.statistics.models.family.family¶
Module: algorithms.statistics.models.family.family
¶
Inheritance diagram for 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
-
link
¶
-
links
= [<nipy.algorithms.statistics.models.family.links.Logit object>, <nipy.algorithms.statistics.models.family.links.CDFLink object>, <nipy.algorithms.statistics.models.family.links.CDFLink object>, <nipy.algorithms.statistics.models.family.links.Log object>, <nipy.algorithms.statistics.models.family.links.CLogLog object>]¶
-
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
-
link
¶
-
links
= []¶
-
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
-
link
¶
-
links
= [<nipy.algorithms.statistics.models.family.links.Log object>, <nipy.algorithms.statistics.models.family.links.Power object>, <nipy.algorithms.statistics.models.family.links.Power object>]¶
-
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
-
link
¶
-
links
= [<nipy.algorithms.statistics.models.family.links.Log object>, <nipy.algorithms.statistics.models.family.links.Power object>, <nipy.algorithms.statistics.models.family.links.Power object>]¶
-
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
-
link
¶
-
links
= [<nipy.algorithms.statistics.models.family.links.Power object>, <nipy.algorithms.statistics.models.family.links.Power object>, <nipy.algorithms.statistics.models.family.links.Power object>, <nipy.algorithms.statistics.models.family.links.Log object>]¶
-
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
-
link
¶
-
links
= [<nipy.algorithms.statistics.models.family.links.Log object>, <nipy.algorithms.statistics.models.family.links.Power object>, <nipy.algorithms.statistics.models.family.links.Power object>]¶
-
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