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.