statsmodels.discrete.discrete_model.Probit.score_factor¶

Probit.score_factor(params)[source]¶

Probit model Jacobian for each observation

Parameters:¶

paramsarray_like

The parameters of the model

Returns:¶

score_factorarray_like (nobs,)

The derivative of the loglikelihood function for each observation with respect to linear predictor 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.