HIERARCHICAL BAYES CONJOINT-ANALYSIS - RECOVERY OF PARTWORTH HETEROGENEITY FROM REDUCED EXPERIMENTAL-DESIGNS

The drive to satisfy customers in narrowly defined market segments has led firms to offer wider arrays of products and services. Delivering products and services with the appropriate mix of features for these h ighly fragmented market segments requires understanding the value that customers place on these features. Conjoint analysis endeavors to unr avel the value, or partworths, that customers place on the product or service's attributes from experimental subjects' evaluation of profile s based on hypothetical products or services. When the goal is to esti mate the heterogeneity in the customers' partworths, traditional estim ation methods, such as least squares, require each subject to respond to more profiles than product attributes, resulting in lengthy questio nnaires for complex, multiattributed products or services. Long questi onnaires pose practical and theoretical problems. Response rates tend to decrease with increasing questionnaire length, and more importantly , academic evidence indicates that long questionnaires may induce resp onse biases. The problems associated with long questionnaires call for experimental designs and estimation methods that recover the heteroge neity in the partworths with shorter questionnaires. Unlike more popul ar estimation methods, Hierarchical Bayes (HE) random effects models d o not require that individual-level design matrices be of full rank, w hich leads to the possibility of using fewer profiles per subject than currently used. Can this theoretical possibility be practically imple mented? This paper tests this conjecture with empirical studies and ma thematical analysis. The random effects model in the paper describes t he heterogeneity in subject-level partworths or regression coefficient s with a linear model that can include subject-level covariates. In ad dition, the error variances are specific to the subjects, thus allowin g for the differential use of the measurement scale by different subje cts. In the empirical study, subjects' responses to a full profile des ign are randomly deleted to test the performance of HE methods with de clining sample sizes. These simple experiments indicate that HE method s can recover heterogeneity and estimate individual-level partworths, even when individual-level least squares estimators do not exist due t o insufficient degrees of freedom. Motivated by these empirical studie s, the paper analytically investigates the trade-off between the numbe r of profiles per subject and the number of subjects on the statistica l accuracy of the estimators that describe the partworth heterogeneity . The paper considers two experimental designs: each subject receives the same set of profiles, and subjects receive different blocks of a f ractional factorial design. In the first case, the optimal design, sub ject to a budget constraint, uses more subjects and fewer profiles per subject when the ratio of unexplained, part worth heterogeneity to un explained response variance is large. In the second case, one can main tain a given level of estimation accuracy as the number of profiles pe r subject decreases by increasing the number of subjects assigned to e ach block. These results provide marketing researchers the option of u sing shorter questionnaires for complex products or services. The anal ysis assumes that response quality is independent of questionnaire len gth and does not address the impact of design factors on response qual ity. If response quality and questionnaire length were, in fact, unrel ated, then marketing researchers would still find the paper's results useful in improving the efficiency of their conjoint designs. However, if response quality were to decline with questionnaire length, as the preponderance of academic research indicates, then the option to use shorter questionnaires would become even more valuable.