statsmodels.genmod.families.links.CDFLink.deriv2 CDFLink.deriv2(p) [source] Second derivative of the link function g??(p) implemented through numerical differentiation

statsmodels.genmod.families.links.CDFLink.deriv CDFLink.deriv(p) [source] Derivative of CDF link Parameters: p : array-like mean parameters Returns: g?(p) : array The derivative of CDF transform at p Notes g?(p) = 1./ dbn.pdf(dbn.ppf(p))

statsmodels.genmod.families.links.cauchy.inverse_deriv cauchy.inverse_deriv(z) Derivative of the inverse of the CDF transformation link function Parameters: z : array The inverse of the link function at p Returns: The value of the derivative of the inverse of the logit function :

statsmodels.genmod.families.links.cauchy.inverse cauchy.inverse(z) The inverse of the CDF link Parameters: z : array-like The value of the inverse of the link function at p Returns: p : array Mean probabilities. The value of the inverse of CDF link of z Notes g^(-1)(z) = dbn.cdf(z)

statsmodels.genmod.families.links.cauchy.deriv2 cauchy.deriv2(p) Second derivative of the link function g??(p) implemented through numerical differentiation

statsmodels.genmod.families.links.cauchy.deriv cauchy.deriv(p) Derivative of CDF link Parameters: p : array-like mean parameters Returns: g?(p) : array The derivative of CDF transform at p Notes g?(p) = 1./ dbn.pdf(dbn.ppf(p))

statsmodels.genmod.families.family.Binomial.weights Binomial.weights(mu) Weights for IRLS steps Parameters: mu : array-like The transformed mean response variable in the exponential family Returns: w : array The weights for the IRLS steps Notes w = 1 / (link?(mu)**2 * variance(mu))

statsmodels.genmod.families.family.Binomial.starting_mu Binomial.starting_mu(y) [source] The starting values for the IRLS algorithm for the Binomial family. A good choice for the binomial family is starting_mu = (y + .5)/2

statsmodels.genmod.families.family.Binomial.resid_dev Binomial.resid_dev(endog, mu, scale=1.0) [source] Binomial deviance residuals Parameters: endog : array-like Endogenous response variable mu : array-like Fitted mean response variable scale : float, optional An optional argument to divide the residuals by scale Returns: resid_dev : array Deviance residuals as defined below Notes If endog is binary: resid_dev = sign(endog-mu)*sqrt(-2*log(I_one*mu + I_zero*(1-mu))) where I_one i

statsmodels.genmod.families.family.Binomial.resid_anscombe Binomial.resid_anscombe(endog, mu) [source] The Anscombe residuals Parameters: endog : array-like Endogenous response variable mu : array-like Fitted mean response variable Returns: resid_anscombe : array The Anscombe residuals as defined below. Notes sqrt(n)*(cox_snell(endog)-cox_snell(mu))/(mu**(1/6.)*(1-mu)**(1/6.)) where cox_snell is defined as cox_snell(x) = betainc(2/3., 2/3., x)*betainc(2/3.,2/3.) where betainc is th