statsmodels.discrete.discrete_model.Probit.hessian¶

Probit.hessian(params)[source]¶

Probit model Hessian matrix of the log-likelihood

Parameters:¶

paramsarray_like

The parameters of the model

Returns:¶

hessndarray, (k_vars, k_vars)

The Hessian, second derivative of loglikelihood function, evaluated at params

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 \(q=2y-1\)