statsmodels.discrete.discrete_model.Poisson.hessian¶

Poisson.hessian(params)[source]¶

Poisson model Hessian matrix of the loglikelihood

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

$\frac{\partial^{2}\ln L}{\partial\beta\partial\beta^{\prime}}=-\sum_{i=1}^{n}\lambda_{i}x_{i}x_{i}^{\prime}$

where the loglinear model is assumed

$\ln\lambda_{i}=x_{i}\beta$