statsmodels.discrete.discrete_model.MNLogit.hessian
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MNLogit.hessian(params)[source] -
Multinomial logit Hessian matrix of the log-likelihood
Parameters: params : array-like
The parameters of the model
Returns: hess : ndarray, (J*K, J*K)
The Hessian, second derivative of loglikelihood function with respect to the flattened parameters, evaluated at
paramsNotes
![\frac{\partial^{2}\ln L}{\partial\beta_{j}\partial\beta_{l}}=-\sum_{i=1}^{n}\frac{\exp\left(\beta_{j}^{\prime}x_{i}\right)}{\sum_{k=0}^{J}\exp\left(\beta_{k}^{\prime}x_{i}\right)}\left[\boldsymbol{1}\left(j=l\right)-\frac{\exp\left(\beta_{l}^{\prime}x_{i}\right)}{\sum_{k=0}^{J}\exp\left(\beta_{k}^{\prime}x_{i}\right)}\right]x_{i}x_{l}^{\prime}](http://statsmodels.sourceforge.net/stable/_images/math/be8e2c0fd37af492bea68d083d98fc7d7cf7d094.png)
where
equals 1 if j=land 0 otherwise.The actual Hessian matrix has J**2 * K x K elements. Our Hessian is reshaped to be square (J*K, J*K) so that the solvers can use it.
This implementation does not take advantage of the symmetry of the Hessian and could probably be refactored for speed.
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