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Table Of Contents

  • algorithms.statistics.models.family.links
    • Module: algorithms.statistics.models.family.links
    • Classes
      • CDFLink
      • CLogLog
      • Link
      • Log
      • Logit
      • Power

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algorithms.statistics.models.family.links¶

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

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

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

Classes¶

CDFLink¶

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

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)

Methods

__call__(p) CDF link
clean(p) Clip logistic values to range (tol, 1-tol)
deriv(p) Derivative of CDF link
initialize(Y)
inverse(z) Derivative of CDF link
__init__(dbn=<scipy.stats._continuous_distns.norm_gen object>)¶
clean(p)¶

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

INPUTS:
p – probabilities
OUTPUTS: pclip
pclip – clipped probabilities
deriv(p)¶

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
initialize(Y)¶
inverse(z)¶

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
tol = 1e-10¶

CLogLog¶

class nipy.algorithms.statistics.models.family.links.CLogLog¶

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

The complementary log-log transform as a link function:

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

Methods

__call__(p) C-Log-Log transform
clean(p) Clip logistic values to range (tol, 1-tol)
deriv(p) Derivatve of C-Log-Log transform
initialize(Y)
inverse(z) Inverse of C-Log-Log transform
__init__()¶

x.__init__(…) initializes x; see help(type(x)) for signature

clean(p)¶

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

INPUTS:
p – probabilities
OUTPUTS: pclip
pclip – clipped probabilities
deriv(p)¶

Derivatve of C-Log-Log transform

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

INPUTS:
p – mean parameters
OUTPUTS: z
z – - 1 / (log(p) * p)
initialize(Y)¶
inverse(z)¶

Inverse of C-Log-Log transform

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

INPUTS:
z – linear predictor scale
OUTPUTS: p
p – mean parameters
tol = 1e-10¶

Link¶

class nipy.algorithms.statistics.models.family.links.Link¶

Bases: object

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

Methods

__call__(p)
deriv(p)
initialize(Y)
inverse(z)
__init__()¶

x.__init__(…) initializes x; see help(type(x)) for signature

deriv(p)¶
initialize(Y)¶
inverse(z)¶

Log¶

class nipy.algorithms.statistics.models.family.links.Log¶

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

The log transform as a link function:

g(x) = log(x)

Methods

__call__(x, **extra) Log transform
clean(x)
deriv(x) Derivative of log transform
initialize(Y)
inverse(z) Inverse of log transform
__init__()¶

x.__init__(…) initializes x; see help(type(x)) for signature

clean(x)¶
deriv(x)¶

Derivative of log transform

g(x) = 1/x

INPUTS:
x – mean parameters
OUTPUTS: z
z – derivative of log transform of x
initialize(Y)¶
inverse(z)¶

Inverse of log transform

g(x) = exp(x)

INPUTS:
z – linear predictors in GLM
OUTPUTS: x
x – exp(z)
tol = 1e-10¶

Logit¶

class nipy.algorithms.statistics.models.family.links.Logit¶

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))

Methods

__call__(p) Logit transform
clean(p) Clip logistic values to range (tol, 1-tol)
deriv(p) Derivative of logit transform
initialize(Y)
inverse(z) Inverse logit transform
__init__()¶

x.__init__(…) initializes x; see help(type(x)) for signature

clean(p)¶

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

INPUTS:
p – probabilities
OUTPUTS: pclip
pclip – clipped probabilities
deriv(p)¶

Derivative of logit transform

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

INPUTS:
p – probabilities
OUTPUTS: y
y – derivative of logit transform of p
initialize(Y)¶
inverse(z)¶

Inverse logit transform

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

INPUTS:
z – logit transform of p
OUTPUTS: p
p – probabilities
tol = 1e-10¶

Power¶

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

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

The power transform as a link function:

g(x) = x**power

Methods

__call__(x) Power transform
deriv(x) Derivative of power transform
initialize(Y)
inverse(z) Inverse of power transform
__init__(power=1.0)¶
deriv(x)¶

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)¶
inverse(z)¶

Inverse of power transform

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

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

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