An Integrated Approach to the Analysis of Binary Choice Data

Abstract

An integrated package of statistics is described for measuring the relationship between binary dominance data, such as choices, and predictor variables that measure the objects or stimuli. The degree of fit between predictors and choices is defined, and procedures for determining the maximum possible fit and minimum acceptable fit are described. The statistics are applied, for illustrative purposes, to a practical data set.In the course of work on a problem in applied psychological measurement, a collection of techniques for analyzing binary choice data was assembled. Individually, the techniques are not new. Collectively, the techniques allow the asking of a set of questions that previously had not been applied to binary choice data in an integrated way. The questions themselves are commonly asked of other sorts of data To make the discussion concrete, suppose there is a set of items and an ordering of them by preferability (or by utility or goodness, for example) is being sought. Suppose also that various attributes of each item can be measured and that there is some point in accounting for the preferability of items in terms of these measured attributes.Some index of fit between preferability and a of an attribute can be computed, for example, a correlation. The following questions can be asked or are implicit in the use of most fit statistics: (1) How well does a given measure account for preferability compared to the maximum possible fit? (2) How well does the measure perform compared to the minimum possible fit? If rated preferability and some measure of the were being correlated, these questions would be trivial: The maximum possible correlation is 1.0 (or -1.0) and the minimum is 0.0. If accounting for choices between pairs of items by means of measured attributes were being attempted, the same questions would be more difficult. The topic of this paper is the problem of assessing how well a measure, or an independent variable, accounts for observed choices. In solving this problem several questions must be asked of the data, including the two questions above. Methods are presented for answering these questions, and the present approach to the problem is illustrated with a practical data set.First, why collect disaggregated choice data? More generally, why observe binary dominance data? Dominance is one of the most primitive relationships between two items, and choice is a basic observable indicator of the relative preferability of two items. Choice between two items is a simple task for untrained individuals; it avoid the use of response scales, and it does not require persons to match numbers to items. The experimenter assumes very little about persons, at NORTH DAKOTA STATE UNIV LIB on June 9, 2015 apm.sagepub.com Downloaded from