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

$$\frac{{\partial }^2\ln L}{\partial \beta \partial {\beta }^{\prime }}=-{\lambda }_i({\lambda }_i+x_i^{\prime }\beta )x_i{x}_i^{\prime }$$

where

$${\lambda }_i=\frac{q_i\varphi \left(q_i{x}_i^{\prime }\beta \right)}{\mathrm{\Phi }\left(q_i{x}_i^{\prime }\beta \right)}$$

and $q=2y-1$