A framework for analyzing rank-ordered data with application to automobile demand

Abstract

In this paper we develop a general random utility framework for analyzing data on individuals' rank orderings. Specifically, we show that in the case with 3 alternatives one can express the probability of a particular rank ordering as a simple function of first choice probabilities. This framework is applied to specify and estimate models of household demand for conventional gasoline cars and alternative fuel vehicles in Shanghai based on rank ordered data obtained from a stated preference survey. Subsequently, the framework is extended to allow for random effects in the utility specification to allow for intrapersonal correlation in tastes across stated preference questions. The preferred model is then used to calculate demand probabilities and elasticities and the distribution of willingness-to-pay for alternative fuel vehicles.

A Latent Class Nested Logit Model for Rank-Ordered Data with Application to Cork Oak Reforestation

“…Our latent class nested rank-ordered logit (LC-NROL) model exploits the modeling framework of Dagsvik and Liu (2009) for rank-ordered data, and operationalizes the mixed nested logit approach that Train (2009, pp.167-168) has conceptualized. The resulting model is like a mixed multinomial logit model (McFadden and Train, 2000) in that it incorporates person-specific random parameters to capture panel correlation over 8 choice scenarios and interpersonal heterogeneity in systematic tastes.…”

“…In what follows, we initially focus on the nested rank-ordered logit (NROL) of Dagsvik and Liu (2009) that forms the kernel of our mixed model. Let n = 1, 2, · · · , N index a person; t = 1, 2, · · · , T n a choice scenario; and j ∈ J = {1, 2, 3} an alternative.…”

“…The existing approach to analyzing rank-ordered data usually exploits extensions and variants of the exploded logit (Chapman and Staelin, 1982), both within (Chang, Lusk and Norwood, 2009;Scarpa et al, 2011;Resano, Sanjuan and Albisu, 2012;Othman and Rahajeng, 2013;Varela et al, 2014) and outside (Fok, Paap and Van Dijk, 2012;Yoo and Doiron, 2013) the environmental valuation literature. Our strategy adds to the empirical practitioner's toolkit an approach building on the nested rank-ordered logit of Dagsvik and Liu (2009) that allows for more plausible substitution patterns. Unlike the exploded logit, the nested rank-ordered logit does not exhibit the independence-of-irrelevant-alternatives property (even without incorporating a mixture specification).…”

“…extreme value ε nt,j implying IIA, the probability of a rank ordering is difficult to derive analytically. Dagsvik and Liu (2009) propose the following way around this challenge to obtain the rank-ordered data counterpart to…”

“…Layton and Lee (2006a;2006b) exploit it to develop likelihood ratio tests for the poolability of different formats of stated preference responses, including rankings and ratings. To our best knowledge, however, the study of Dagsvik and Liu (2009) is the first one to derive and estimate the nested rank-ordered logit model which relaxes IIA of the exploded logit while maintaining a closed-form likelihood.…”