statsmodels.discrete.discrete_model.Probit.score_factor¶

Probit.score_factor(params)[source]¶

Probit model Jacobian for each observation

Parameters:¶

params : array-like¶

The parameters of the model

Returns:¶

score_factor – The derivative of the loglikelihood function for each observation with respect to linear predictor evaluated at params

Return type:¶

array_like (nobs,)

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.