statsmodels.discrete.discrete_model.Probit.hessian

Probit.hessian(params)

Probit model Hessian matrix of the log-likelihood

Parameters:params (array-like) – The parameters of the model Returns:hess – The Hessian, second derivative of loglikelihood function, evaluated at params Return type:ndarray, (k_vars, k_vars)

Notes

$$\frac{\partial^{2}\ln L}{\partial\beta\partial\beta^{\prime}}=-\lambda_{i}\left(\lambda_{i}+x_{i}^{\prime}\beta\right)x_{i}x_{i}^{\prime}$$

where

$$\lambda_{i}=\frac{q_{i}\phi\left(q_{i}x_{i}^{\prime}\beta\right)}{\Phi\left(q_{i}x_{i}^{\prime}\beta\right)}$$

and $q=2y-1$