statsmodels.genmod.families.links.inverse_power.inverse_deriv inverse_power.inverse_deriv(z) Derivative of the inverse of the power transform Parameters: z : array-like z is usually the linear predictor for a GLM or GEE model. Returns: The value of the derivative of the inverse of the power transform : function :

statsmodels.genmod.families.links.inverse_power.inverse inverse_power.inverse(z) Inverse of the power transform link function Parameters: `z` : array-like Value of the transformed mean parameters at p Returns: `p` : array Mean parameters Notes g^(-1)(z`) = z`**(1/`power)

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

statsmodels.genmod.families.links.inverse_power.deriv inverse_power.deriv(p) Derivative of the power transform Parameters: p : array-like Mean parameters Returns: g?(p) : array Derivative of power transform of p Notes g?(p) = power * p`**(`power - 1)

statsmodels.genmod.families.family.InverseGaussian.starting_mu InverseGaussian.starting_mu(y) Starting value for mu in the IRLS algorithm. Parameters: y : array The untransformed response variable. Returns: mu_0 : array The first guess on the transformed response variable. Notes Only the Binomial family takes a different initial value.

statsmodels.genmod.families.family.InverseGaussian.resid_dev InverseGaussian.resid_dev(endog, mu, scale=1.0) [source] Returns the deviance residuals for the inverse Gaussian family. 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 dev_resid = sign(endog-mu)*sqrt((endog-mu)**2/(en

statsmodels.genmod.families.family.InverseGaussian.resid_anscombe InverseGaussian.resid_anscombe(endog, mu) [source] The Anscombe residuals for the inverse Gaussian distribution Parameters: endog : array Endogenous response variable mu : array Fitted mean response variable Returns: resid_anscombe : array The Anscombe residuals for the inverse Gaussian distribution as defined below Notes resid_anscombe = log(endog/mu)/sqrt(mu)

statsmodels.genmod.families.family.InverseGaussian.predict InverseGaussian.predict(mu) Linear predictors based on given mu values. Parameters: mu : array The mean response variables Returns: lin_pred : array Linear predictors based on the mean response variables. The value of the link function at the given mu.

statsmodels.genmod.families.family.InverseGaussian.loglike InverseGaussian.loglike(endog, mu, scale=1.0) [source] Loglikelihood function for inverse Gaussian distribution. Parameters: endog : array-like Endogenous response variable mu : array-like Fitted mean response variable scale : float, optional The default is 1. Returns: llf : float The value of the loglikelihood function evaluated at (endog,mu,scale) as defined below. Notes llf = -(1/2.)*sum((endog-mu)**2/(endog*mu**2*sca