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:
hessndarray, (nobs,)

The Hessian factor, second derivative of loglikelihood function with respect to linear predictor 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 $$q=2y-1$$