Normalization and correlation of cross-nested logit models

We address two fundamental issues associated with the use of cross-nested logit models. On the one hand, we justify the adequate normalization of the model proposed by Wen and Koppelman [Wen, C.-H., Koppelman, F.S., 2001. The generalized nested logit model. Transportation Research Part B 35(7), 627-641]. On the other hand, we provide an analysis of the correlation structure of the CNL, based on random utility theory. We evaluate the validity of the approximation proposed by Papola [Papola, A., 2004. Some developments on the cross-nested logit model. Transportation Research B 38(9), 833-851], both using theoretical arguments and numerical examples based on the exact formula of the correlation.