Advances in Ordered Choice Modeling

                                    International Choice Modelling Conference, 2009

                                    Institute of Transport Studies, University of Leeds

                The modern form of the ordered choice model was proposed in 1975 by McElvey and Zavoina (1975).  There has been a huge number of applications in fields across the social and natural sciences in the 30 years since the model’s introduction.  Significant advances in the methodology have appeared more recently, along with a spike in the rate of applications in the past few years.  In Greene and Hensher (2008), we survey the methodology and evolution of the model.

                Recent extensions of the basic model have proposed elaborate specifications to accommodate individual heterogeneity.  In Greene and Hensher (2008) and Hensher and Greene (2008), we develop a mixed model of ordered choices with random thresholds and heterogeneous disturbance variances.  The model provides for systematic and random variation in location parameters, disturbance variation and threshold parameters.  In Hollingsworth, Harris, Greene and Maitra (2008), the ordered choice model is further estended to allow for endogenous, discrete variation in the underlying structure.  In this paper, I will summarize the innovations in these two studies.

Hensher and Greene (2008)

                A growing number of empirical studies involve the assessment of influences on a choice amongst ordered discrete alternatives. Ordered logit and probit models are well known, including extensions to accommodate random parameters and heteroscedasticity in unobserved variance. This paper extends the ordered choice random parameter model to permit random parameterization of thresholds and decomposition to establish observed sources of systematic variation in the threshold parameter distribution.  We illustrate the empirical gains of this model in the context of an individual’s choice amongst unlabelled attribute packages of alternative tolled and non-tolled routes for the commuting trip, and the role that each attribute plays, in the sense of being ignored or not. The ordering represents the number of attributes attended to from the full fixed set. The evidence suggests that there is significant heterogeneity associated with the thresholds that can be connected to systematic sources associated with the respondent (i.e., gender) and the choice experiment (i.e., aggregation treatment of components of travel time).

Greene, Harris, Hollingsworth and Maitra (2008)

                Obesity is a major risk factor for several diseases including diabetes, heart disease and stroke. Increasing rates of obesity internationally are set to cost health systems increasing resources. In the US a conservative estimate puts resources already spent on obesity at $120 billion annually. Given scarce health care resources it is important that categorisation of the overweight and obese is accurate, such that health promotion and public health targeting can be as effective as possible. To test the accuracy of current categorisation within the overweight and obese we extend the discrete data latent class literature by explicitly defining a latent variable for class membership as a function of both observables and unobservables, thereby allowing the equations defining class membership and observed outcomes to be correlated. The procedure is then applied to modeling observed obesity outcomes, based upon an underlying ordered probit equation. We find the standard boundaries for converting body mass index into categories may be inappropriate for individuals at the margin, which is then allowed for in estimation.