statsmodels.discrete.discrete_model.MNLogit.score_obs

MNLogit.score_obs(params)

Jacobian matrix for multinomial logit model log-likelihood

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