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import numpy as N
import scipy.stats
class Link:
def initialize(self, Y):
return N.asarray(Y).mean() * N.ones(Y.shape)
class Logit(Link):
"""
The logit transform as a link function:
g(x) = log(x / (1 - x))
"""
tol = 1.0e-10
def clean(self, p):
return N.clip(p, Logit.tol, 1. - Logit.tol)
def __call__(self, p):
p = self.clean(p)
return N.log(p / (1. - p))
def inverse(self, z):
t = N.exp(z)
return t / (1. + t)
def deriv(self, p):
p = self.clean(p)
return 1. / (p * (1 - p))
logit = Logit()
class Power(Link):
"""
The power transform as a link function:
g(x) = x**power
"""
def __init__(self, power=1.):
self.power = power
def __call__(self, x):
return N.power(x, self.power)
def inverse(self, x):
return N.power(x, 1. / self.power)
def deriv(self, x):
return self.power * N.power(x, self.power - 1)
inverse = Power(power=-1.)
inverse.__doc__ = """
The inverse transform as a link function:
g(x) = 1 / x
"""
sqrt = Power(power=0.5)
sqrt.__doc__ = """
The square-root transform as a link function:
g(x) = sqrt(x)
"""
inverse_squared = Power(power=-2.)
inverse_squared.__doc__ = """
The inverse squared transform as a link function:
g(x) = 1 / x**2
"""
identity = Power(power=1.)
identity.__doc__ = """
The identity transform as a link function:
g(x) = x
"""
class Log(Link):
"""
The log transform as a link function:
g(x) = log(x)
"""
tol = 1.0e-10
def clean(self, x):
return N.clip(x, Logit.tol, N.inf)
def __call__(self, x, **extra):
x = self.clean(x)
return N.log(x)
def inverse(self, z):
return N.exp(z)
def deriv(self, x):
x = self.clean(x)
return 1. / x
log = Log()
class CDFLink(Logit):
"""
The use the CDF of a scipy.stats distribution as a link function:
g(x) = dbn.ppf(x)
"""
def __init__(self, dbn=scipy.stats.norm):
self.dbn = dbn
def __call__(self, p):
p = self.clean(p)
return self.dbn.ppf(p)
def inverse(self, z):
return self.dbn.cdf(z)
def deriv(self, p):
p = self.clean(p)
return 1. / self.dbn.pdf(self(p))
probit = CDFLink()
probit.__doc__ = """
The probit (standard normal CDF) transform as a link function:
g(x) = scipy.stats.norm.ppf(x)
"""
cauchy = CDFLink(dbn=scipy.stats.cauchy)
cauchy.__doc__ = """
The Cauchy (standard Cauchy CDF) transform as a link function:
g(x) = scipy.stats.cauchy.ppf(x)
"""
class CLogLog(Logit):
"""
The complementary log-log transform as a link function:
g(x) = log(-log(x))
"""
def __call__(self, p):
p = self.clean(p)
return N.log(-N.log(p))
def inverse(self, z):
return N.exp(-N.exp(z))
def deriv(self, p):
p = self.clean(p)
return -1. / (N.log(p) * p)
cloglog = CLogLog()
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