statsmodels.discrete.discrete_model.Probit.hessian_factor¶
- Probit.hessian_factor(params)[source]¶
Probit model Hessian factor of the log-likelihood
- Parameters:¶
- paramsarray_like
The parameters of the model
- Returns:¶
- hess
ndarray
, (nobs,) The Hessian factor, second derivative of loglikelihood function with respect to linear predictor 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 \(q=2y-1\)
Last update:
Dec 11, 2024