statsmodels.discrete.discrete_model.MNLogit.loglikeobs

MNLogit.loglikeobs(params)

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

Parameters:params (array-like) – The parameters of the multinomial logit model. Returns:loglike – The log likelihood for each observation of the model evaluated at params. See Notes Return type:array-like

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.