Probit.hessian()

Probit.hessian(params) [source]

Probit model Hessian matrix of the log-likelihood

Parameters:

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`

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

$\frac{\partial^{2}\ln L}{\partial\beta\partial\beta^{\prime}}=-\lambda_{i}\left(\lambda_{i}+x_{i}^{\prime}\beta\right)x_{i}x_{i}^{\prime}$

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 $q=2y-1$

Links:

doc_statsmodels

2025-01-10 15:47:30

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