Stated Preference and the 'Ecological Fallacy'
BATES J J, John Bates Services and TERZIS G, The MVA Consultaney, UK
Stated Preference (SP) data are normally analysed using techniques of Discrete Choice analysis. However, they differ from classical "Revealed Preference" (liP) data in that a single respondent contributes more than one observation. This problem of "repeat
Stated Preference (SP) data are normally analysed using techniques of Discrete Choice analysis. However, they differ from classical "Revealed Preference" (liP) data in that a single respondent contributes more than one observation. This problem of "repeated measurements" has been generally recognised, but ignored in practice.
It has usually been assumed that the consequences of ignoring the problem are not serious, at least as far as the coefficient estimates are concerned, though clearly the standard errors are likely to be under-estimated, leading to an exaggerated impression of the significance of the variables in the model. Some coarse correction procedures have been suggested, such as multiplying the standard errors by QI',I, where N is the number of observations contributed by an individual. This implicitly assumes that the error terms for a given individual are perfectly correlated, which can be expected to be highly conservative. A further ad hoc variant is to multiply the standard errors by 3"~/N, which should be less conservative.
More recently, Cirillo, Daly & Lindveld (1996) [CDL] have made use of "jackknifing" and "bootstrapping" techniques to obtain a better idea of how the coefficient estimates vary with different sizes of random sub-samples. They recommend this as a straightforward technique for correcting the variance-covariance matrix as obtained from standard estimation packages. Implicitly, the coefficient estimates themselves are taken to be unbiased, a result which appeared to be confirmed in their work.
As has often been acknowledged (e.g. Bates (1988)), the repeated measurements problem is part of a wider question of the specification of the error term. Although the CDL correction is probably sufficient in certain cases, a more careful treatment of the error structure shows that in other circumstances, quite commonly encountered, the coefficients themselves as obtained by standard estimation apprbaches may be seriously biased, to the extent of being more or less worthless. The purpose of this paper is to throw some light on when such cases may occur.
Association for European Transport