Nonparametric approaches to describing heterogeneity

TY - CHAP

T1 - Nonparametric approaches to describing heterogeneity

AU - Fosgerau, Mogens

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84958148918&partnerID=8YFLogxK

U2 - 10.4337/9781781003152.00018

DO - 10.4337/9781781003152.00018

M3 - Book chapter

AN - SCOPUS:84958148918

SN - 9781781003145

SP - 257

EP - 267

BT - Handbook of Choice Modelling

PB - Edward Elgar Publishing

ER -