1.2.15.1.16. statsmodels.api.Probit.score_obs

Probit.score_obs(params)

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.