Probabilistic Subset-Conjunctive Models for Heterogeneous Consumers

A variety of approaches have been used to infer decision rules used by consumers. These approaches include protocol methods, self-reports, and non-linear compensatory and noncompensatory models of judgement. But there is little work on inferring the rules from choice or preference data, a situation that stands in contrast with the great progress in data-analytic techniques for linear models. There are well-known reasons for this, the most important being the ability of a linear model to predict preferences even when people use non-compensatory heuristics, and the ready availability of software programs that enable sophisticated analysis using linear compensatory models. A more desirable situation is to augment the existing analytical approaches by models that do not compromise on predictive ability and permit inferences about the underlying decision process. Ideally, the implementation of these approaches should be simple and allow use of standard software programs. The authors introduce one such model, which infers generalized forms of conjunctive/disjunctive rules from binary (acceptable/unacceptable) classifications of multiattribute alternatives. The first generalization is the introduction of a subset-conjunctive rule that requires an acceptable alternative to be satisfactory on some (possibly unknown) minimum number of attributes. A disjunctive rule is a special case when this number equals one; and a conjunctive rule is a special case when this number equals the number of attributes. The second generalization is that each attribute level is acceptable or unacceptable not with certainty but with a probability that can differ from one attribute level to another; the standard acceptable/unacceptable classification is obtained as a special case in which all probabilities associated with attribute levels go to extreme (0/1) values. The two generalizations are embedded in a latent-class model that allows segment level inferences about the structure of subset-conjunctive rules using binary (acceptable/unacceptable) classifications of multi-attribute alternatives. The results of simulations and an application suggest that the model does well in inferring the rules when the data arise from a subset-conjunctive process, and that it does as well as a linear model in terms of predictive accuracy. (Non-compensatory decision heuristics; conjunctive/disjunctive heuristics; subset-conjunctive heuristics; consideration sets; choice models; finite-mixture models; latent-class models; maximum likelihood estimation.)