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 – The Hessian, second derivative of loglikelihood function, evaluated at params

Return type:¶

ndarray, (k_vars, k_vars)

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

\[\ln\lambda_{i}=x_{i}\beta\]