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# Handbook of Choice Modelling

## Edited by Stephane Hess and Andrew Daly

Choice modelling is an increasingly important technique for forecasting and valuation, with applications in fields such as transportation, health and environmental economics. For this reason it has attracted attention from leading academics and practitioners and methods have advanced substantially in recent years. This Handbook, composed of contributions from senior figures in the field, summarises the essential analytical techniques and discusses the key current research issues. It will be of interest to academics, students and practitioners in a wide range of areas.
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# Chapter 11: Nonparametric approaches to describing heterogeneity

## Extract

This chapter considers the estimation of binomial and multinomial discrete choice models that contain a random preference parameter with an unknown distribution, focusing on simple approaches where this unknown distribution is directly estimated. The unknown distribution is possibly multivariate. We talk about approaches that are nonparametric in the sense that the description of some unknown distribution is nonparametric. This unknown distribution may be embedded in an otherwise parametric model and the combination would then be called semiparametric. In a discrete choice model, the random preference parameter may enter in some function describing the indirect utilities associated with alternatives. Let us say the model prescribes the probability of choosing alternative y _ {1, . . . , J} to be P(y = j|x, _), where y is the choice, j indexes alternatives, x is a vector of observed variables and b is a random parameter vector with cumulative distribution function (CDF) F. Depending on the circumstances, _ may be univariate or multivariate. We use bold letters to indicate vectors (that may still be univariate) while variables in plain font must be univariate. We shall maintain a random effect assumption, namely that the distribution of b is independent of x. The random effect assumption is very convenient, but it is not always credible and it is by no means an innocuous assumption.

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