/Statsmodels

# statsmodels.discrete.discrete_model.MNLogit.score_obs

MNLogit.score_obs(params) [source]

Jacobian matrix for multinomial logit model log-likelihood

Parameters: params (array) – The parameters of the multinomial logit model. jac – The derivative of the loglikelihood for each observation evaluated at params . array-like

#### Notes

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

for $$j=1,...,J$$, 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 flatteded array of derivatives in columns.