statsmodels.discrete.discrete_model.MNLogit.loglike¶

MNLogit.loglike(params)[source]¶

Log-likelihood of the multinomial logit model.

Parameters:¶

paramsarray_like

The parameters of the multinomial logit model.

Returns:¶

loglikefloat

The log-likelihood function of the model evaluated at params. See notes.

Notes

\[\ln L=\sum_{i=1}^{n}\sum_{j=0}^{J}d_{ij}\ln \left(\frac{\exp\left(\beta_{j}^{\prime}x_{i}\right)} {\sum_{k=0}^{J} \exp\left(\beta_{k}^{\prime}x_{i}\right)}\right)\]

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