Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-07T18:10:51.089Z Has data issue: false hasContentIssue false
  • English
  • Français

A New Zero-Inflated Negative Binomial Methodology for Latent Category Identification

Published online by Cambridge University Press:  01 January 2025

Simon J. Blanchard  and
Wayne S. DeSarbo
Simon J. Blanchard*
Affiliation:
McDonough School of Business, Georgetown University
Wayne S. DeSarbo
Affiliation:
Department of Marketing, Pennsylvania State University
*
Requests for reprints should be sent to Simon J. Blanchard, McDonough School of Business, Georgetown University, 37th and O St. N.W., Washington, DC 20057, USA. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We introduce a new statistical procedure for the identification of unobserved categories that vary between individuals and in which objects may span multiple categories. This procedure can be used to analyze data from a proposed sorting task in which individuals may simultaneously assign objects to multiple piles. The results of a synthetic example and a consumer psychology study involving categories of restaurant brands illustrate how the application of the proposed methodology to the new sorting task can account for a variety of categorization phenomena including multiple category memberships and for heterogeneity through individual differences in the saliency of latent category structures.

Keywords

categorizationunobserved categoriesheterogeneitysorting taskconsumer psychology
Type
Original Paper
Information
Psychometrika , Volume 78 , Issue 2 , April 2013 , pp. 322 - 340
Copyright
Copyright © 2013 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716723CrossRefGoogle Scholar
Arabie, P., Carroll, J.D., DeSarbo, W.S., Wind, J. (1981). Overlapping clustering: a new method for product positioning. Journal of Marketing Research, 18(3), 310317CrossRefGoogle Scholar
Basford, K.E., McLachlan, G.J. (1985). The mixture method of clustering applied to three-way data. Journal of Classification, 2(1), 109125CrossRefGoogle Scholar
Bijmolt, T.H.A., Wedel, M. (1995). The effects of alternative methods of collecting similarity data for multidimensional scaling. International Journal of Research in Marketing, 12(4), 363371CrossRefGoogle Scholar
Blanchard, S.J., Aloise, D., DeSarbo, W.S. (2012). The heterogenous p-median for categorization based clustering. Psychometrika, 77(4), 741762CrossRefGoogle Scholar
Blanchard, S.J., DeSarbo, W.S., Atalay, A.S., Harmancioglu, N. (2011). Identifying consumer heterogeneity in unobserved categories. Marketing Letters, 23(1), 177194CrossRefGoogle Scholar
Bozdogan, H. (1987). Model selection and Akaike’s information criterion (AIC): the general theory and its analytical extensions. Psychometrika, 52(3), 345370CrossRefGoogle Scholar
Cameron, A.C., Windmeijer, F.A.G. (1997). An R-squared measure of goodness of fit for some common nonlinear regression models. Journal of Econometrics, 77(2), 329342CrossRefGoogle Scholar
Carlson, K.A., Meloy, M.G., Russo, J.E. (2006). Leader-driven primacy: using attribute order to affect consumer choice. Journal of Consumer Research, 32(March), 513518CrossRefGoogle Scholar
Carroll, J.D., Arabie, P. (1983). INDCLUS: an individual differences generalization of the ADCLUS model and the MAPCLUS algorithm. Psychometrika, 48(2), 157169CrossRefGoogle Scholar
Carroll, J.D., Clark, L.A., DeSarbo, W.S. (1984). The representation of three-way proximity data by single and multiple tree structure models. Journal of Classification, 1(1), 2574CrossRefGoogle Scholar
Coxon, A.P.M. (1999). Sorting data: collection and analysis, Thousand Oaks: SageCrossRefGoogle Scholar
Daws, J.T. (1996). The analysis of free-sorting data: beyond pairwise co-occurrence. Journal of Classification, 13(1), 5780CrossRefGoogle Scholar
Degerman, R. (1982). Ordered binary trees constructed through an application of Kendall’s tau. Psychometrika, 47(4), 523527CrossRefGoogle Scholar
DeSarbo, W.S., Cho, J. (1989). A stochastic multidimensional vector threshold model for the spatial representation of ‘pick any/n’data. Psychometrika, 54(1), 105129CrossRefGoogle Scholar
DeSarbo, W.S., Wu, J. (2001). The joint spatial representation of multiple variable batteries collected in marketing research. Journal of Marketing Research, 38(2), 244253CrossRefGoogle Scholar
DeSarbo, W.S., Jedidi, K., Johnson, M.D. (1991). A new clustering methodology for the analysis of sorted or categorized stimuli. Marketing Letters, 2(3), 267279CrossRefGoogle Scholar
Ehrenberg, A.S.C. (1988). Repeat-buying: facts, theory and applications, New York: Oxford University PressGoogle Scholar
Evans, S.H., Arnoult, M. (1967). Schematic concept formation: demonstration in a free sorting task. Psychonomic Science, 9(4), 221222CrossRefGoogle Scholar
Gill, P.E., Murray, W., Wright, M.H. (1981). Practical optimization, New York: Academic PressGoogle Scholar
Goldstone, R.L. (1994). The role of similarity in categorization: providing groundwork. Cognition, 52(2), 125157CrossRefGoogle ScholarPubMed
Goodhardt, G.J., Ehrenberg, A.S.C., Chatfield, C. (1984). The Dirichlet: a comprehensive model of buying behaviour with discussion. Journal of the Royal Statistical Society. Series A, 147(5), 621655CrossRefGoogle Scholar
Green, W.H. (1994). Accounting for excess zeros and sample selection in Poisson and negative binomial regression models (Working Paper EC-94-10). New York University. Google Scholar
Gregan-Paxton, J., Hoeffler, S., Zhao, M. (2005). When categorization is ambiguous: factors that facilitate the use of a multiple category inference strategy. Journal of Consumer Psychology, 15(2), 127140CrossRefGoogle Scholar
Grogger, J.T., Carson, R.T. (1991). Models for truncated counts. Journal of Applied Econometrics, 6(3), 225238CrossRefGoogle Scholar
Hampton, J.A. (1998). Similarity-based categorization and fuzziness of natural categories. Cognition, 65(2–3), 137165CrossRefGoogle ScholarPubMed
Hunt, L.A., Basford, K.E. (2001). Fitting a mixture model to three-mode three-way data with missing information. Journal of Classification, 18(2), 209226CrossRefGoogle Scholar
Isen, A.M. (1984). Toward understanding the role of affect in cognition. In Wyer, R.S. Jr., Srull, T.K. (Eds.), Handbook of social cognition, Hillsdale: Lawrence Erlbaum 179236Google Scholar
Johnson, S.C. (1967). Hierarchical clustering schemes. Psychometrika, 32(3), 241254CrossRefGoogle ScholarPubMed
Klastorin, T.T. (1980). Merging groups to maximize object partition comparison. Psychometrika, 45(4), 425433CrossRefGoogle Scholar
Laran, J., Janiszewski, C., Cunha, M. Jr.. (2008). Context-dependent effects on goal primes. Journal of Consumer Research, 35(December), 653667CrossRefGoogle Scholar
Lee, M.D. (2001). On the complexity of additive clustering models. Journal of Mathematical Psychology, 45(February), 131148CrossRefGoogle ScholarPubMed
Li, S., Liechty, J.C., & Montgomery, A.L. (2002). Modeling category viewership of web users with multivariate count models (Working Paper). Indiana University. Google Scholar
Loken, B., Ward, J. (1990). Alternative approaches to understanding the determinants of typicality. Journal of Consumer Research, 17(2), 111126CrossRefGoogle Scholar
Loken, B., Barsalou, L.W., Joiner, C. (2008). Categorization theory and research in consumer psychology: category representation and category-based inference. In Haugtvedt, P.M., Herr, P.M., Kardes, F.R. (Eds.), Handbook of consumer psychology, Mahwah: ErlbaumGoogle Scholar
MacKay, D.B., Easley, R.F., Zinnes, J.L. (1995). A single ideal point model for market structure analysis. Journal of Marketing Research, 32(4), 433443CrossRefGoogle Scholar
Macrae, C.N., Bodenhausen, G.V., Milne, A.B. (1995). The dissection of selection in person perception: inhibitory processes in social stereotyping. Journal of Personality and Social Psychology, 69(3), 397407CrossRefGoogle ScholarPubMed
Malt, B.C., Ross, B.H., Murphy, G.L. (1995). Predicting features for members of natural categories when categorization is uncertain. Journal of Experimental Psychology. Learning, Memory, and Cognition, 21(3), 646661CrossRefGoogle ScholarPubMed
McLachlan, P., Nelder, J.A. (1983). Generalized linear models, London: Chapman & HallGoogle Scholar
Medin, D.L., Goldstone, R.L., Gentner, D. (1993). Respects for similarity. Psychological Review, 100(2), 254278CrossRefGoogle Scholar
Mervis, C.B., Rosch, E. (1981). Categorization of natural objects. Annual Review of Psychology, 32(January), 89115CrossRefGoogle Scholar
Moreau, C.P., Markman, A.B., Lehmann, D.R. (2001). “What is it?” Categorization flexibility and consumers’ responses to really new products. Journal of Consumer Research, 27(4), 489498CrossRefGoogle Scholar
Murphy, G.L., Ross, B.H. (1994). Predictions from uncertain categorizations. Cognitive Psychology, 24(2), 148193CrossRefGoogle Scholar
Nocedal, J., Wright, S. (1999). Numerical optimization, New York: SpringerCrossRefGoogle Scholar
Pothos, E.M., Chater, N. (2005). Unsupervised categorization and category learning. The Quartely Journal of Experimental Psychology Section A, 58(4), 733752CrossRefGoogle ScholarPubMed
Rajagopal, P., Burnkrant, R.E. (2008). Consumer evaluations of hybrid products. Journal of Consumer Research, 36(August), 232241CrossRefGoogle Scholar
Ramaswamy, V., Anderson, E.W., DeSarbo, W.S. (1994). A disaggregate negative binomial regression procedure for count data analysis. Management Science, 40(3), 405417CrossRefGoogle Scholar
Ramsay, J.O. (1977). Maximum likelihood estimation in multidimensional scaling. Psychometrika, 42(2), 241266CrossRefGoogle Scholar
Ramsay, J.O. (1982). The joint analysis of direct ratings, pairwise preferences, and dissimilarities. Psychometrika, 45(2), 149165CrossRefGoogle Scholar
Rao, V.R., Katz, R. (1971). Alternative multidimensional scaling methods for large stimulus sets. Journal of Marketing Research, 8(4), 488494CrossRefGoogle Scholar
Rosch, E.H. (1973). Natural categories. Cognitive Psychology, 4(3), 328350CrossRefGoogle Scholar
Rosch, E. (1978). Principles of categorization. In Rosch, E., Lloyd, B.B. (Eds.), Cognition and categorization, Hillsdale: ErlbaumGoogle Scholar
Rosenberg, S., Kim, M.P. (1975). Method of sorting as a data-gathering procedure in multivariate research. Multivariate Behavioral Research, 10(4), 489502CrossRefGoogle ScholarPubMed
Ross, B.H., Murphy, G.L. (1999). Food for thought: cross-classification and category organization in a complex real-world domain. Cognitive Psychology, 38(4), 495554CrossRefGoogle Scholar
Schwarz, G.E. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461464CrossRefGoogle Scholar
Shepard, R.N., Arabie, P. (1979). Additive clustering: representation of similarities as combinations of discrete overlapping properties. Psychological Review, 86(2), 87123CrossRefGoogle Scholar
Takane, Y. (1980). Analysis of categorizing behavior using a quantification method. Behaviormetrika, 7(8), 7586CrossRefGoogle Scholar
Tversky, A. (1977). Features of similarity. Psychological Review, 84(4), 327352CrossRefGoogle Scholar
Vermunt, J.K. (2007). A hierarchical mixture model for clustering three-way data sets. Computational Statistics & Data Analysis, 51(11), 53685376CrossRefGoogle Scholar
Vlek, C., Stallen, P.J. (1981). Judging risks and benefits in the small and in the large. Organizational Behavior and Human Performance, 28(2), 235271CrossRefGoogle Scholar
Wedel, M., DeSarbo, W.S. (1993). A latent class binomial logit methodology for the analysis of paired comparison choice data. Decision Sciences, 24(6), 11571170CrossRefGoogle Scholar
Wedel, M., Kamakura, W.A. (2000). Market segmentation: conceptual and methodological foundations, Boston: Kluwer AcademicCrossRefGoogle Scholar
Winsberg, S., Carroll, J.D. (1989). A quasi-nonmetric method for multidimensional scaling via an extended Euclidean model. Psychometrika, 54(2), 217229CrossRefGoogle Scholar
Winsberg, S., De Soete, G. (1993). A latent class approach to fitting the weighted Euclidean model, CLASCAL. Psychometrika, 58(2), 315330CrossRefGoogle Scholar
Yang, C.-C., Yang, C.-C. (2007). Separating latent classes by information criteria. Journal of Classification, 24(2), 183203CrossRefGoogle Scholar