statsmodels.discrete.discrete_model.Probit.score_obs

Probit.score_obs(params)

Probit model Jacobian for each observation

Parameters:

paramsarray_like

The parameters of the model

Returns:

jacarray_like

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

Notes

$$\frac{\partial \ln L_i}{\partial \beta }=\left[\frac{q_i\varphi \left(q_i{x}_i^{\prime }\beta \right)}{\mathrm{\Phi }\left(q_i{x}_i^{\prime }\beta \right)}\right]x_i$$

for observations $i=1,...,n$

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