statsmodels.discrete.discrete_model.Probit.score

Probit.score(params)

Probit model score (gradient) vector

Parameters:params (array-like) – The parameters of the model Returns:score – The score vector of the model, i.e. the first derivative of the loglikelihood function, evaluated at params Return type:ndarray, 1-D

Notes

$$\frac{\partial\ln L}{\partial\beta}=\sum_{i=1}^{n}\left[\frac{q_{i}\phi\left(q_{i}x_{i}^{\prime}\beta\right)}{\Phi\left(q_{i}x_{i}^{\prime}\beta\right)}\right]x_{i}$$

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