THE ANALYSIS OF DISCRETE CHOICE EXPERIMENTS WITH CORRELATED ERROR STRUCTURE

• Published in: Communications in statistics. Theory and methods Vol. 30; no. 4; pp. 615 - 626
• Main Authors: Montopoli, George, Anderson, Donald A.
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 31.03.2001; Taylor & Francis
• Subjects: Consumer choice experiments; Exact sciences and technology; Log-odds analysis; Logistic regression; Mathematics; Multinomial logit model; Nonparametric inference; Parametric inference; Probability and statistics; Sciences and techniques of general use; Statistics; Parameter estimation; Mathematical matrix; Error analysis; Choice; Error estimation; Confidence limit; Non parametric estimation; Tolerance limit; Computing; Utilities; Consumer; Least squares method; Example; Independent set; Multinomial distribution; Logit model; Likelihood function; Estimation error; Covariance analysis; Independence; Statistical estimation; Covariance matrix; Variance analysis; Confidence interval; Statistical regression; Simulation; Utility theory; Correlation analysis; Asymptotic normality; Independence test; Alternative method; Maximum likelihood
• DOI: 10.1081/STA-100002140
• ISSN: 0361-0926

In a stated preference discrete choice experiment each subject is typically presented with several choice sets, and each choice set contains a number of alternatives. The alternatives are defined in terms of their name (brand) and their attributes at specified levels. The task for the subject is to choose from each choice set the alternative with highest utility for them. The multinomial is an appropriate distribution for the responses to each choice set since each subject chooses one alternative, and the multinomial logit is a common model. If the responses to the several choice sets are independent, the likelihood function is simply the product of multinomials. The most common and generally preferred method of estimating the parameters of the model is maximum likelihood (that is, selecting as estimates those values that maximize the likelihood function). If the assumption of within-subject independence to successive choice tasks is violated (it is almost surely violated), the likelihood function is incorrect and maximum likelihood estimation is inappropriate. The most serious errors involve the estimation of the variance-covariance matrix of the model parameter estimates, and the corresponding variances of market shares and changes in market shares. In this paper we present an alternative method of estimation of the model parameter coefficients that incorporates a first-order within-subject covariance structure. The method involves the familiar log-odds transformation and application of the multivariate delta method. Estimation of the model coefficients after the transformation is a straightforward generalized least squares regression, and the corresponding improved estimate of the variance-covariance matrix is in closed form. Estimates of market share (and change in market share) follow from a second application of the multivariate delta method. The method and comparison with maximum likelihood estimation are illustrated with several simulated and actual data examples. Advantages of the proposed method are: 1) it incorporates the within-subject covariance structure; 2) it is completely data driven; 3) it requires no additional model assumptions; 4) assuming asymptotic normality, it provides a simple procedure for computing confidence regions on market shares and changes in market shares; and 5) it produces results that are asymptotically equivalent to those produced by maximum likelihood when the data are independent.