statsmodels.discrete.discrete_model.MNLogit.jac¶

MNLogit.jac(*args, **kwds)¶

jac is deprecated, use score_obs instead! Use score_obs method. jac will be removed in 0.7

Jacobian matrix for multinomial logit model log-likelihood

Parameters:

params : array

The parameters of the multinomial logit model.

Returns:

jac : ndarray, (nobs, k_vars*(J-1))

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

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.