statsmodels.discrete.discrete_model.MNLogit.loglikeobs

MNLogit.loglikeobs(params)[source]

Log-likelihood of the multinomial logit model for each observation.

Parameters:

params : array-like

The parameters of the multinomial logit model.
Returns:

loglike : ndarray (nobs,)

The log likelihood for each observation of the model evaluated at params. See Notes

Notes

\ln L_{i}=\sum_{j=0}^{J}d_{ij}\ln\left(\frac{\exp\left(\beta_{j}^{\prime}x_{i}\right)}{\sum_{k=0}^{J}\exp\left(\beta_{k}^{\prime}x_{i}\right)}\right)

for observations i=1,...,n

where d_{ij}=1 if individual i chose alternative j and 0 if not.