Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1131948 | Transportation Research Part B: Methodological | 2013 | 11 Pages |
Abstract
This paper proposes a practically tractable mathematical procedure for the calculation of the covariances underlying whatever given Cross-Nested Logit (CNL) model, based on the variance of a one-dimensional random variable, whose cumulative distribution function and density probability function are given in closed form. This allows expressing the CNL covariances as a function of just a one-dimensional integral, which can be evaluated easily and effectively by means of standard numerical techniques, implementable also in basic computer spreadsheets. Firstly, a formal theoretical proof of the procedure is illustrated. Then, a comparison with the calculations performed by Marzano and Papola [Marzano, V., Papola, ., 2008. On the covariance structure of the Cross-Nested Logit model. Transportation Research B 42(2), 83-98] is proposed, and details about the practical implementation of the procedure are discussed. Finally, estimation of the CNL model in contexts with prior expectations on covariances/correlations is addressed practically, thanks to the simplification achieved in the calculation of the CNL covariances.
Keywords
Related Topics
Social Sciences and Humanities
Decision Sciences
Management Science and Operations Research
Authors
Vittorio Marzano, Andrea Papola, Fulvio Simonelli, Roberta Vitillo,