statsmodels.discrete.discrete_model.MNLogit.score_obs¶

MNLogit.score_obs(params)[source]¶

Jacobian matrix for multinomial logit model log-likelihood

Parameters:¶

paramsndarray

The parameters of the multinomial logit model.

Returns:¶

jacarray_like

The derivative of the loglikelihood for each observation evaluated at params .

Notes

$$\frac{\partial \ln L_i}{\partial {\beta }_j}=(d_{ij}-\frac{\exp \left({\beta }_j^{\prime }{x}_i\right)}{\sum _{k=0}^J\exp \left({\beta }_k^{\prime }{x}_i\right)})x_i$$

for $j=1,...,J$, for observations $i=1,...,n$

In the multinomial model the score vector is K x (J-1) but is returned as a flattened array. The Jacobian has the observations in rows and the flattened array of derivatives in columns.