Source code for statsmodels.genmod.families.varfuncs

"""
Variance functions for use with the link functions in statsmodels.family.links
"""
import numpy as np
FLOAT_EPS = np.finfo(float).eps


[docs] class VarianceFunction: """ Relates the variance of a random variable to its mean. Defaults to 1. Methods ------- call Returns an array of ones that is the same shape as `mu` Notes ----- After a variance function is initialized, its call method can be used. Alias for VarianceFunction: constant = VarianceFunction() See Also -------- statsmodels.genmod.families.family """ def __call__(self, mu): """ Default variance function Parameters ---------- mu : array_like mean parameters Returns ------- v : ndarray ones(mu.shape) """ mu = np.asarray(mu) return np.ones(mu.shape, np.float64)
[docs] def deriv(self, mu): """ Derivative of the variance function v'(mu) """ return np.zeros_like(mu)
constant = VarianceFunction() constant.__doc__ = """ The call method of constant returns a constant variance, i.e., a vector of ones. constant is an alias of VarianceFunction() """
[docs] class Power: """ Power variance function Parameters ---------- power : float exponent used in power variance function Methods ------- call Returns the power variance Notes ----- Formulas V(mu) = numpy.fabs(mu)**power Aliases for Power: mu = Power() mu_squared = Power(power=2) mu_cubed = Power(power=3) """ def __init__(self, power=1.): self.power = power def __call__(self, mu): """ Power variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray numpy.fabs(mu)**self.power """ return np.power(np.fabs(mu), self.power)
[docs] def deriv(self, mu): """ Derivative of the variance function v'(mu) May be undefined at zero. """ der = self.power * np.fabs(mu) ** (self.power - 1) ii = np.flatnonzero(mu < 0) der[ii] *= -1 return der
mu = Power() mu.__doc__ = """ Returns np.fabs(mu) Notes ----- This is an alias of Power() """ mu_squared = Power(power=2) mu_squared.__doc__ = """ Returns np.fabs(mu)**2 Notes ----- This is an alias of statsmodels.family.links.Power(power=2) """ mu_cubed = Power(power=3) mu_cubed.__doc__ = """ Returns np.fabs(mu)**3 Notes ----- This is an alias of statsmodels.family.links.Power(power=3) """
[docs] class Binomial: """ Binomial variance function Parameters ---------- n : int, optional The number of trials for a binomial variable. The default is 1 for p in (0,1) Methods ------- call Returns the binomial variance Notes ----- Formulas : V(mu) = p * (1 - p) * n where p = mu / n Alias for Binomial: binary = Binomial() A private method _clean trims the data by machine epsilon so that p is in (0,1) """ def __init__(self, n=1): self.n = n def _clean(self, p): return np.clip(p, FLOAT_EPS, 1 - FLOAT_EPS) def __call__(self, mu): """ Binomial variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray variance = mu/n * (1 - mu/n) * self.n """ p = self._clean(mu / self.n) return p * (1 - p) * self.n # TODO: inherit from super
[docs] def deriv(self, mu): """ Derivative of the variance function v'(mu) """ return 1 - 2*mu
binary = Binomial() binary.__doc__ = """ The binomial variance function for n = 1 Notes ----- This is an alias of Binomial(n=1) """
[docs] class NegativeBinomial: ''' Negative binomial variance function Parameters ---------- alpha : float The ancillary parameter for the negative binomial variance function. `alpha` is assumed to be nonstochastic. The default is 1. Methods ------- call Returns the negative binomial variance Notes ----- Formulas : V(mu) = mu + alpha*mu**2 Alias for NegativeBinomial: nbinom = NegativeBinomial() A private method _clean trims the data by machine epsilon so that p is in (0,inf) ''' def __init__(self, alpha=1.): self.alpha = alpha def _clean(self, p): return np.clip(p, FLOAT_EPS, np.inf) def __call__(self, mu): """ Negative binomial variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray variance = mu + alpha*mu**2 """ p = self._clean(mu) return p + self.alpha*p**2
[docs] def deriv(self, mu): """ Derivative of the negative binomial variance function. """ p = self._clean(mu) return 1 + 2 * self.alpha * p
nbinom = NegativeBinomial() nbinom.__doc__ = """ Negative Binomial variance function. Notes ----- This is an alias of NegativeBinomial(alpha=1.) """

Last update: Feb 14, 2024