Development and Application of the Mixed Ordered Response Logit Model
Gerard Whelan, Nigel Tapley, Institute of Transport Studies, University of Leeds, UK
We develop a mixed ordered response logit model with randomly distributed structural coefficients to estimate the value of time from strength-of-preference (ratings) data. The technique overcomes problems with interpersonal comparison of preferences.
In transport related market research, the use of strength-of-preference indicators (e.g. ranking and rating) to elicit consumer preferences has declined in favour of more basic choice tasks. The frequently cited reason for this trend is that choosing a preferred alternative from a given choice set is more natural to consumers than ranking or rating choice options. That said, in some circumstances the respondent might welcome the opportunity to indicate their strength of preference to communicate a strongly preferred option or where they are indifferent between options (Burge et al, 2000, Swallow, 2001). Allowing respondents to rank or rate alternatives could therefore enhance the respondent experience and potentially provide a richer dataset for model estimation. There are however technical issues regarding interpersonal comparison of preferences when working with strength-of-preference data - does the statement ?Strongly Prefer Option A? mean the same thing to different individuals?
In this paper, we extend and apply the ordered response logit model to data from the 1987 UK Value of Time Study (MVA, 1987). This data involves a preference rating exercise for two travel options described in terms of time and cost. To examine the influence of model structure on the value of time we estimate a series or models ranging from a simple binary logit through to a brand new specification referred to a mixed ordered response logit. Details of each model specification are set out below.
(i) Model 1 - The Base Model - This is a binary logit with utility specified according to the specification of the preferred 1987 model.
(ii) Model 2 - An ordered response logit model with.utility specified as the base model. In this model, four additional structural parameters are specified to demark preference boundaries between the 5 preference ratings.
(iii) Model 3 - As Model 2 with the structural coefficients specified as a function of the respondent?s socioeconomic characteristics. This allows for deterministic variation in preference boundaries between individuals.
(iv) Model 4 - As Model 3 with normally distributed coefficients attached to the time attribute to account for random taste variation.
(v) Model 5 ? As Model 4 with normally distributed structural coefficients. The addition of these error components take account of differences in preference ratings between individuals and therefore overcome the technical constraint surrounding interpersonal comparison of preferences.
As expected, the levels of model fit improve as the models become more complex but it is interesting to note particularly significant improvements when random variation of the structural coefficients of the ordered response logit are specified.
Association for European Transport