Knowledge that Transforms

Over the last decade, numerous methods for the multidimensional scaling (MDS) of perceptions and preferences have been applied by researchers in marketing. However, one notable gap in MDS methodology has been the lack of suitable models for analyzing inherently asymmetric data relationships. Recently, Harshman (Harshman, R. A. 1978. Models for analysis of asymmetrical relationships among N objects or stimuli. Paper presented at the First Joint Meeting of the Psychometric Society and the Society for Mathematical Psychology. McMaster University, Hamilton, Ontario, August; Harshman, R. A. 1982a. DEDICOM: A family of models generalizing factor analysis and multidimensional scaling for decomposition of asymmetric relationships. Unpublished manuscript, University of Western Ontario.) has proposed a new family of models—called DEDICOM (DEcomposition into Directional COMponents)—for analyzing data matrices that are intrinsically asymmetric. In this article, the single-domain DEDICOM model is described and applied to two illustrative cases in marketing research. The examples demonstrate that DEDICOM solutions will sometimes make more substantive sense and provide significantly better fits to asymmetric data than solutions obtained by factor analysis or MDS. DEDICOM also provides a novel type of information—a description of asymmetric relations among dimensions or clusters. Such information will often have useful marketing implications.

This paper reports some further analyses and applications of Morrison's model of the predictive relationship between measures of intentions and subsequent purchasing behavior. A review of published studies bearing on the threats to predictive validity of intention scales represented in Morrison's model is presented. Findings from a test-retest study of intention ratings for concept stimuli are shown to be consistent with the levels of reliability expected under the model's assumptions of beta binomial distributed scores. Evidence of the predictive validity of intention measures is found in a re-analysis of several sets of relevant data but a different form of predictive relationship is shown to hold for generic durable goods as compared to branded packaged goods. Whereas a linear relationship is supported in the case of durable goods, the presence of a threshold phenomenon in the branded packaged goods data suggests the use of a piecewise linear model. There is reason to believe that the nature and sources of systematic error present in intentions ratings are different for these two types of purchases.

A maximum likelihood approach is proposed for estimating an innovation diffusion model of new product acceptance originally considered by Bass (Bass, F. M. 1969. A new product growth model for consumer durables. Management Sci. 15 (January) 215–227.). The suggested approach allows: (1) computation of approximate standard errors for the diffusion model parameters, and (2) determination of the required sample size for forecasting the adoption level to any desired degree of accuracy. Using histograms from eight different product innovations, the maximum likelihood estimates are shown to outperform estimates from a model calibrated using ordinary least squares, in terms of both goodness of fit measures and one-step ahead forecasts. However, these advantages are not obtained without cost. The coefficients of innovation and imitation are easily interpreted in terms of the expected adoption pattern, but individual adoption times must be assumed to represent independent draws from this distribution. In addition, instead of using standard linear regression, another (simple) program must be employed to estimate the model. Thus, tradeoffs between the maximum likelihood and least squares approaches are also discussed.