algorithms.statistics.models.family.links¶

Module: `algorithms.statistics.models.family.links`¶

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

digraph inheritancead4ca599ab { rankdir=LR; size="8.0, 12.0"; "family.links.CDFLink" [URL="#nipy.algorithms.statistics.models.family.links.CDFLink",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",fontsize=10,height=0.25,shape=box,style="setlinewidth(0.5)",target="_top",tooltip="The use the CDF of a scipy.stats distribution as a link function:"]; "family.links.Logit" -> "family.links.CDFLink" [arrowsize=0.5,style="setlinewidth(0.5)"]; "family.links.CLogLog" [URL="#nipy.algorithms.statistics.models.family.links.CLogLog",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",fontsize=10,height=0.25,shape=box,style="setlinewidth(0.5)",target="_top",tooltip="The complementary log-log transform as a link function:"]; "family.links.Logit" -> "family.links.CLogLog" [arrowsize=0.5,style="setlinewidth(0.5)"]; "family.links.Link" [URL="#nipy.algorithms.statistics.models.family.links.Link",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",fontsize=10,height=0.25,shape=box,style="setlinewidth(0.5)",target="_top",tooltip="A generic link function for one-parameter exponential"]; "family.links.Log" [URL="#nipy.algorithms.statistics.models.family.links.Log",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",fontsize=10,height=0.25,shape=box,style="setlinewidth(0.5)",target="_top",tooltip="The log transform as a link function:"]; "family.links.Link" -> "family.links.Log" [arrowsize=0.5,style="setlinewidth(0.5)"]; "family.links.Logit" [URL="#nipy.algorithms.statistics.models.family.links.Logit",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",fontsize=10,height=0.25,shape=box,style="setlinewidth(0.5)",target="_top",tooltip="The logit transform as a link function:"]; "family.links.Link" -> "family.links.Logit" [arrowsize=0.5,style="setlinewidth(0.5)"]; "family.links.Power" [URL="#nipy.algorithms.statistics.models.family.links.Power",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",fontsize=10,height=0.25,shape=box,style="setlinewidth(0.5)",target="_top",tooltip="The power transform as a link function:"]; "family.links.Link" -> "family.links.Power" [arrowsize=0.5,style="setlinewidth(0.5)"]; }

Classes¶

`CDFLink`¶

class nipy.algorithms.statistics.models.family.links.CDFLink(dbn=<scipy.stats._continuous_distns.norm_gen object>)[source]¶

Bases: nipy.algorithms.statistics.models.family.links.Logit

The use the CDF of a scipy.stats distribution as a link function:

g(x) = dbn.ppf(x)

__init__(dbn=<scipy.stats._continuous_distns.norm_gen object>)[source]¶: Initialize self. See help(type(self)) for accurate signature.

inverse(z)[source]¶

Derivative of CDF link

g(z) = self.dbn.cdf(z)

INPUTS:: z – linear predictors in GLM
OUTPUTS: p: p – inverse of CDF link of z

deriv(p)[source]¶

Derivative of CDF link

g(p) = 1/self.dbn.pdf(self.dbn.ppf(p))

INPUTS:: x – mean parameters
OUTPUTS: z: z – derivative of CDF transform of x

clean(p)¶

Clip logistic values to range (tol, 1-tol)

INPUTS:: p – probabilities
OUTPUTS: pclip: pclip – clipped probabilities

initialize(Y)¶

tol = 1e-10¶

`CLogLog`¶

class nipy.algorithms.statistics.models.family.links.CLogLog[source]¶

Bases: nipy.algorithms.statistics.models.family.links.Logit

The complementary log-log transform as a link function:

g(x) = log(-log(x))

__init__($self, /, *args, **kwargs)¶: Initialize self. See help(type(self)) for accurate signature.

inverse(z)[source]¶

Inverse of C-Log-Log transform

g(z) = exp(-exp(z))

INPUTS:: z – linear predictor scale
OUTPUTS: p: p – mean parameters

deriv(p)[source]¶

Derivatve of C-Log-Log transform

g(p) = - 1 / (log(p) * p)

INPUTS:: p – mean parameters
OUTPUTS: z: z – - 1 / (log(p) * p)

clean(p)¶

Clip logistic values to range (tol, 1-tol)

INPUTS:: p – probabilities
OUTPUTS: pclip: pclip – clipped probabilities

initialize(Y)¶

tol = 1e-10¶

`Link`¶

class nipy.algorithms.statistics.models.family.links.Link[source]¶

Bases: object

A generic link function for one-parameter exponential family, with call, inverse and deriv methods.

__init__($self, /, *args, **kwargs)¶: Initialize self. See help(type(self)) for accurate signature.

initialize(Y)[source]¶

inverse(z)[source]¶

deriv(p)[source]¶

`Log`¶

class nipy.algorithms.statistics.models.family.links.Log[source]¶

Bases: nipy.algorithms.statistics.models.family.links.Link

The log transform as a link function:

g(x) = log(x)

__init__($self, /, *args, **kwargs)¶: Initialize self. See help(type(self)) for accurate signature.

tol = 1e-10¶

clean(x)[source]¶

inverse(z)[source]¶

Inverse of log transform

g(x) = exp(x)

INPUTS:: z – linear predictors in GLM
OUTPUTS: x: x – exp(z)

deriv(x)[source]¶

Derivative of log transform

g(x) = 1/x

INPUTS:: x – mean parameters
OUTPUTS: z: z – derivative of log transform of x

initialize(Y)¶

`Logit`¶

class nipy.algorithms.statistics.models.family.links.Logit[source]¶

Bases: nipy.algorithms.statistics.models.family.links.Link

The logit transform as a link function:

g’(x) = 1 / (x * (1 - x)) g^(-1)(x) = exp(x)/(1 + exp(x))

__init__($self, /, *args, **kwargs)¶: Initialize self. See help(type(self)) for accurate signature.

tol = 1e-10¶

clean(p)[source]¶

Clip logistic values to range (tol, 1-tol)

INPUTS:: p – probabilities
OUTPUTS: pclip: pclip – clipped probabilities

inverse(z)[source]¶

Inverse logit transform

h(z) = exp(z)/(1+exp(z))

INPUTS:: z – logit transform of p
OUTPUTS: p: p – probabilities

deriv(p)[source]¶

Derivative of logit transform

g(p) = 1 / (p * (1 - p))

INPUTS:: p – probabilities
OUTPUTS: y: y – derivative of logit transform of p

initialize(Y)¶

`Power`¶

class nipy.algorithms.statistics.models.family.links.Power(power=1.0)[source]¶

Bases: nipy.algorithms.statistics.models.family.links.Link

The power transform as a link function:

g(x) = x**power

__init__(power=1.0)[source]¶: Initialize self. See help(type(self)) for accurate signature.

inverse(z)[source]¶

Inverse of power transform

g(x) = x**(1/self.power)

INPUTS:: z – linear predictors in GLM
OUTPUTS: x: x – mean parameters

deriv(x)[source]¶

Derivative of power transform

g(x) = self.power * x**(self.power - 1)

INPUTS:: x – mean parameters
OUTPUTS: z: z – derivative of power transform of x

initialize(Y)¶