Obtaining Further Insights into Taste Heterogeneity by Conditioning on Observed Choices
S Hess, Imperial College London, UK; J Rose, University of Sydney, AU
This paper discusses the use of distributions conditioned on observed choices in random coefficients models
The increasing use of random coefficients models such as Mixed Logit has meant that an increasing number of studies now accommodate differences in tastes, and hence behaviour, across respondents in a random fashion. While the use of random coefficients models often leads to very significant improvements in model performance, the tangible benefits in terms of understanding/explaining taste heterogeneity are less obvious. Indeed, knowing that the distribution of tastes in a sample population can more or less accurately be represented by some target distribution such as a Normal provides us with preciously little information about the tastes of individual respondents. Furthermore, as is well documented in existing work, there are potentially significant discrepancies between standard statistical distributions and the actual distribution of a specific taste coefficient. On the other hand, it is often not possible to attempt to explain significant levels of taste heterogeneity by basic segmentations and other deterministic methods.
In this paper, we highlight the advantages of an alternative approach, making use of conditioning on observed choice behaviour. The process begins by estimating a random coefficients model in the standard fashion, yielding the unconditional distributions for the various taste coefficients. For each individual, a conditional distribution for each coefficient can then be obtained through conditioning on the observed sequence of choices for that respondent. While this approach has been discussed a number of times in the existing literature, there have been very few actual applications using conditional distributions, and a lot remains to be done.
In this paper, we illustrate the advantages of conditional distributions with the help of various Stated Preference (SP) datasets. Specifically, we show how working with conditional distributions can lead to a significant reduction in issues with incorrectly signed coefficient values, which are often just a result of inappropriate shape assumptions for the unconditional distributions. Furthermore, we illustrate how one can obtain further information on the distribution of tastes with the help of a posterior analysis, linking the conditional taste coefficients of an individual to socio-demographic information. Finally, we show how it is often possible to retrieve significantly more information on the correlation structure in place between individual taste coefficients when working with conditional rather than unconditional taste coefficients.
A further topic addressed in the paper is that of the use of conditional distributions in estimation as opposed to posterior analysis. Here, we develop an iterative approach that conditions on individual-specific draws for one taste coefficient in the reestimation of the remaining coefficients. The results of our analysis show that this leads to significant improvements in model performance, through a gradual correction of the values/distributions for the various coefficients. Finally, we also investigate the impact of the unconditional distributional assumptions on the conditional distributions, showing an advantage for flexible distributions, which is however not as significant as when working solely with unconditional distributions.
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