statsmodels.discrete.discrete_model.MNLogit.loglike

MNLogit.loglike(params)

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.