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:
- hess
ndarray, (k_vars,k_vars) The Hessian, second derivative of loglikelihood function, evaluated at params
- hess
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 \(q=2y-1\)