The estimation of mixed logit models is one of the most popular empirical approaches to the accommodation of preference heterogeneity in choice data. In the mixed logit model the purpose of estimation is to identify the parameters of the distribution from which tastes are drawn. The researcher is required, ex ante, to specify the functional form of this distribution.

The choice of functional form for preference distributions within the mixed logit model is one of the two foci of this paper. More specifically, we contend that insufficient attention is typically paid to this choice of functional form in analyses based on the mixed logit model. This is problematic given that the functional form chosen can have a major impact on resulting WTP estimates and associated inferences. Of particular interest is the use of bounded preference distributions.

The reticence to address alternative functional forms for preference distributions may in part be because competing mixed logit models are non-nested and hence not easily amenable to testing. In this paper we highlight one advantage of using Bayesian methods to estimate the mixed logit model since, as we set out, it is possible to derive a single measure of performance across non-nested models: the Marginal Likelihood (ML).

These two issues: the impacts of alternative assumptions regarding distributional forms, and the use of the ML as an overall measure of model performance, are brought together in the empirical application.

Data are analysed from a CE concerning food attributes in which one of the attributes is the use of GM technology in the food’s production. The expectation is that preferences for such food may well be misrepresented by the (typically assumed) normal distribution, since people are likely to dislike, or be indifferent to, the attribute. They are unlikely to positively prefer GM food. This suggests the use of a bounded distribution, however the most common bounded distributions used (triangular, lognormal) are unable to capture indifference – they have a zero probability mass at indifference.

In the paper we report analysis of the CE data using a range of bounded and unbounded distributions of preferences. We also use rarely used bounded distributions (censored normal and S_B distributions) to address the possibility of probability mass points near indifference.

We use the Bayesian Marginal Likelihood, extended here to reflect the multiple option character of the CE data, to analyse model performance. We find that models using the censored normal and S_B functional forms outperform models using typically assumed functional forms.

We find that the rankings of model performance using the ML are markedly different from those based on the simulated log likelihood which has been used as a “rule of thumb” for model comparison in early Bayesian implementations of the mixed logit model (Train and Sonnier 2005; Train and Weeks 2005). Finally we highlight the differences in inference regarding market shares between the preferred ‘bounded’ model and typical ‘unbounded’ models.