statsmodels.discrete.discrete_model.MNLogit.hessian_factor

MNLogit.hessian_factor(params)

Multinomial logit Hessian weights for each observation.

For MNLogit the Hessian has a block structure that cannot be reduced to a single scalar weight per observation. Instead, each observation contributes a (J-1, J-1) weight matrix, so the full Hessian for design matrix X is:

H[j,l] = sum_i w[i,j,l] * X[i] @ X[i].T

The weight for observation i is:

w[i,j,l] = -pr[i,j] * (1(j==l) - pr[i,l])

Parameters:

paramsarray_like

The parameters of the model, flattened in column-major order with shape (K * (J-1),).

Returns:

hessian_factorndarray, shape (nobs, J-1, J-1)

The per-observation weight matrix for the Hessian.