A new random utility model with flexible correlation pattern and closed-form covariance expression: The CoRUM

- A new RUM with a cdf obtained as a finite mixture of cdfs.
- Choice probabilities and covariances obtainable as mixtures of choice probabilities and covariances of the mixing models.
- By mixing NL models new RUMs are obtained with closed form expressions of choice probabilities, covariances and elasticities.
- A new RUM easy to estimate which perform very well in terms of both in-sample and out-of-sample goodness of fit tests.
- Compact ad hoc specification for route choice able to easily target the expected route choice correlation pattern.

This paper proposes a new random utility model characterised by a cumulative distribution function (cdf) obtained as a finite mixture of different cdfs. This entails that choice probabilities, covariances and elasticities of this model are also a finite mixture of choice probabilities, covariances and elasticities of the mixing models. As a consequence, by mixing nested logit cdfs, a model is generated with closed-form expressions for choice probabilities, covariances and elasticities and with, potentially, a very flexible correlation pattern. Importantly, the closed-form covariance expression opens up interesting application possibilities in some special choice contexts, like route choice, where prior expectations in terms of the covariance matrix can be formulated.