statsmodels.discrete.discrete_model.MNLogit.score

MNLogit.score(params)

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

$$\frac{\partial\ln L}{\partial\beta_{j}}=\sum_{i}\left(d_{ij}-\frac{\exp\left(\beta_{j}^{\prime}x_{i}\right)}{\sum_{k=0}^{J}\exp\left(\beta_{k}^{\prime}x_{i}\right)}\right)x_{i}$$

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.