statsmodels.discrete.discrete_model.Probit.score_obs

Probit.score_obs(params)[source]

Probit model Jacobian for each observation

Parameters:

params : array-like

The parameters of the model
Returns:

jac : ndarray, (nobs, k_vars)

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

Notes

\frac{\partial\ln L_{i}}{\partial\beta}=\left[\frac{q_{i}\phi\left(q_{i}x_{i}^{\prime}\beta\right)}{\Phi\left(q_{i}x_{i}^{\prime}\beta\right)}\right]x_{i}

for observations i=1,...,n

Where q=2y-1. This simplification comes from the fact that the normal distribution is symmetric.