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statsmodels.discrete.discrete_model.Probit.hessian

Probit.hessian(params)[source]

Probit model Hessian matrix of the log-likelihood

Parameters:

params : array-like

The parameters of the model

Returns:

hess : ndarray, (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

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