statsmodels.discrete.discrete_model.MNLogit.score¶

MNLogit.score(params)[source]¶

Score matrix for multinomial logit model log-likelihood

Parameters:¶

paramsndarray

The parameters of the multinomial logit model.

Returns:¶

scorendarray, (K * (J-1),)

The 2-d score vector, i.e. the first derivative of the loglikelihood function, of the multinomial logit model evaluated at params.

Notes

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

for $j=1,...,J$

In the multinomial model the score matrix is K x J-1 but is returned as a flattened array to work with the solvers.