A hierarchical Bayesian approach for examining heterogeneity in choice decisions. (English) Zbl 1402.91109
Summary: There is a vast behavioral decision theory literature that suggests different individuals may utilize and/or weigh different attributes of an object to form the basis of their opinions, attitudes, choices, and/or evaluations of such stimuli. This heterogeneity of information utilization and importance can be due to several different factors such as differing goals, level of expertise, contextual factors, knowledge accessibility, time pressure, involvement, mood states, task complexity, communication or influence of relevant others, etc. This phenomenon is particularly pertinent to the evaluation of stimuli involving large numbers of underlying attributes or features. We propose a new hierarchical Bayesian multivariate probit mixture model with variable selection accommodating such forms of choice heterogeneity. Based on a Monte Carlo simulation study, we demonstrate that the proposed model can successfully recover true parameters in a robust manner. Next, we provide a consumer psychology application involving consideration to buy choices for intended consumers of large sports utility vehicles. The application illustrates that the proposed model outperforms several comparison benchmark choice models with respect to face validity and choice predictive validation performance.
MSC:
| 91B06 | Decision theory |
| 62P15 | Applications of statistics to psychology |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 91E99 | Mathematical psychology |
Keywords:
finite mixtures; variable selection; Bayesian multivariate probit models; consumer psychology; choice heterogeneityReferences:
| [1] | Adelman, M. A., The economics of petroleum supply: Papers by MA Adelman, 1962-1993, (1962), MIT press |
| [2] | Alba, J. W.; Hutchinson, J. W., Dimensions of consumer expertise, Journal of Consumer Research, 13, 4, 411-454, (1987) |
| [3] | Andrews, J. L.; McNicholas, P. D., Variable selection for clustering and classification, Journal of Classification, 31, 2, 136-153, (2014) · Zbl 1360.62310 |
| [4] | Arminger, G.; Clogg, C. C.; Cheng, T., 1. regression analysis of multivariate binary response variables using rasch-type models and finite-mixture methods, Sociological Methodology, 30, 1, 1-26, (2000) |
| [5] | Benati, S.; García, S., A mixed integer linear model for clustering with variable selection, Computers & Operations Research, 43, 280-285, (2014) · Zbl 1349.62258 |
| [6] | Bhat, C. R. (2017). Incorporating observed and unobserved heterogeneity in urban work travel mode choice modeling. Working Paper, University of Texas, Austin TX.; Bhat, C. R. (2017). Incorporating observed and unobserved heterogeneity in urban work travel mode choice modeling. Working Paper, University of Texas, Austin TX. |
| [7] | Bontemps, D.; Toussile, W., Clustering and variable selection for categorical multivariate data, Electronic Journal of Statistics, 7, 2344-2371, (2013) · Zbl 1349.62259 |
| [8] | Bouveyron, C.; Brunet-Saumard, C., Discriminative variable selection for clustering with the sparse Fisher-EM algorithm, Computational Statistics, 29, 3-4, 489-513, (2014) · Zbl 1306.65033 |
| [9] | Celeux, G.; Forbes, F.; Robert, C. P.; Titterington, D. M., Deviance information criteria for missing data models, Bayesian Analysis, 1, 4, 651-673, (2006) · Zbl 1331.62329 |
| [10] | Chib, S.; Greenberg, E., Analysis of multivariate probit models, Biometrika, 85, 2, 347-361, (1998) · Zbl 0938.62020 |
| [11] | Cowley, E.; Mitchell, A. A., The moderating effect of product knowledge on the learning and organization of product information, Journal of Consumer Research, 30, 3, 443-454, (2003) |
| [12] | Cozzini, A.; Jasra, A.; Montana, G.; Persing, A., A Bayesian mixture of lasso regressions with t-errors, Computational Statistics & Data Analysis, 77, 84-97, (2014) · Zbl 1506.62050 |
| [13] | Dean, N.; Raftery, A. E., Latent class analysis variable selection, Annals of the Institute of Statistical Mathematics, 62, 1, 11-35, (2010) · Zbl 1422.62085 |
| [14] | Dellaert, B. G.; Stremersch, S., Marketing mass-customized products: striking a balance between utility and complexity, Journal of Marketing Research, 42, 2, 219-227, (2005) |
| [15] | DeSarbo, W. S., GENNCLUS: new models for general nonhierarchical clustering analysis, Psychometrika, 47, 4, 449-475, (1982) · Zbl 0566.62057 |
| [16] | DeSarbo, W. S.; Carroll, J. D., Three-way metric unfolding via alternating weighted least squares, Psychometrika, 50, 3, 275-300, (1985) · Zbl 0597.62113 |
| [17] | DeSarbo, W. S.; Cron, W. L., A maximum likelihood methodology for clusterwise linear regression, Journal of Classification, 5, 2, 249-282, (1988) · Zbl 0692.62052 |
| [18] | DeSarbo, W. S.; Fong, D. K.; Liechty, J.; Coupland, J. C., Evolutionary preference/utility functions: A dynamic perspective, Psychometrika, 70, 1, 179-202, (2005) · Zbl 1306.62402 |
| [19] | DeSarbo, W. S.; Park, J.; Rao, V. R., Deriving joint space positioning maps from consumer preference ratings, Marketing Letters, 22, 1, 1-14, (2011) |
| [20] | DeSoete, G.; DeSarbo, W. S., A latent class probit model for analyzing Pick any/n data, Journal of Classification, 8, 45-63, (1991) · Zbl 0725.62058 |
| [21] | Dubé, J. P., Multiple discreteness and product differentiation: demand for carbonated soft drinks, Marketing Science, 23, 1, 66-81, (2004) |
| [22] | Fan, J.; Li, R., Variable selection via nonconcave penalized likelihood and its oracle properties, Journal of the American Statistical Association, 96, 456, 1348-1360, (2001) · Zbl 1073.62547 |
| [23] | Feldman, J. M.; Lynch, J. G., Self-generated validity and other effects of measurement on belief, attitude, intention, and behavior, Journal of Applied Psychology, 73, 3, 421, (1988) |
| [24] | Freese, J.; Long, J. S., Regression models for categorical dependent variables using stata, (2006), Stata Press College Station · Zbl 1277.62008 |
| [25] | Gelman, A.; Carlin, J. B.; Stern, H. S.; Dunson, D. B.; Vehtari, A.; Rubin, D. B., Bayesian data analysis, (2014), Chapman and Hall/CRC · Zbl 1279.62004 |
| [26] | Gelman, A.; Rubin, D. B., Inference from iterative simulation using multiple sequences, Statistical Science, 7, 4, 457-511, (1992) · Zbl 1386.65060 |
| [27] | George, E. I.; McCulloch, R. E., Variable selection via Gibbs sampling, Journal of the American Statistical Association, 88, 423, 881-889, (1993) |
| [28] | George, E.; McCulloch, R., Approaches for Bayesian variable selection, Statistica Sinica, 7, 2, 339-373, (1997) · Zbl 0884.62031 |
| [29] | Geweke, J., Evaluating the accuracy of sampling-based approaches to calculating posterior moments, (Bernado, J. M.; Berger, J. O.; Dawid, A. P.; Smith, A. F.M, Bayesian statistics, Vol. 4, (1992), Clarendon Press Oxford, UK) |
| [30] | Ghosh, J.; Herring, A. H.; Siega-Riz, A. M., Bayesian variable selection for latent class models, Bioemtrics, 67, 3, 917-925, (2011) · Zbl 1226.62022 |
| [31] | Gilbride, T. J.; Allenby, G. M.; Brazell, J. D., Models for heterogeneous variable selection, Journal of Marketing Research, 43, 3, 420-430, (2006) |
| [32] | Green, P. E.; Srinivasan, V., Conjoint analysis in consumer research: issues and outlook, Journal of Consumer Research, 5, 2, 103-123, (1978) |
| [33] | Hauser, J. R., Consideration-set heuristics, Journal of Business Research, 67, 1688-1699, (2014) |
| [34] | Houston, D. A.; Sherman, S. J., Cancellation and focus: the role of shared and unique features in the choice process, Journal of Experimental Social Psychology, 31, 4, 357-378, (1995) |
| [35] | Hutchinson, J. W.; Alba, J. W., Ignoring irrelevant information: situational determinants of consumer learning, Journal of Consumer Research, 18, 3, 325-345, (1991) |
| [36] | Isen, A. M., Positive affect and decision making, (Lewis, M.; Haviland, J., Handbook of emotions, (1993), Guilford New York), 261-273 |
| [37] | Isen, A. M.; Daubman, K. A.; Nowicki, G. P., Positive affect facilitates creative problem solving, Journal of Personality and Social Psychology, 52, 6, 1122-1131, (1987) |
| [38] | Ishwaran, H.; Rao, J. S., Consistency of spike and slab regression, Statistics & Probability Letters, 81, 12, 1920-1928, (2011) · Zbl 1225.62096 |
| [39] | Jedidi, K.; DeSarbo, W. S., A stochastic multidimensional scaling procedure for the spatial representation of three-mode, three-way Pick any/J data, Psychometrika, 56, 3, 471-494, (1991) |
| [40] | Jeffreys, Harold, Theory of probability, (1961), Clarendon Press Oxford · Zbl 0096.38304 |
| [41] | Johnson, R. M. (1987). Markov chain monte carlo maximum likelihood. In Sawtooth software conference on perceptual mapping, conjoint analysis, and computer interviewing; Johnson, R. M. (1987). Markov chain monte carlo maximum likelihood. In Sawtooth software conference on perceptual mapping, conjoint analysis, and computer interviewing |
| [42] | Johnson, K. E.; Mervis, C. B., Effects of varying levels of expertise on the basic level of categorization, Journal of Experimental Psychology: General, 126, 3, 248, (1997) |
| [43] | Kamakura, W. A.; Kim, B. D.; Lee, J., Modeling preference and structural heterogeneity in consumer choice, Marketing Science, 15, 2, 152-172, (1996) |
| [44] | Khalili, A.; Chen, J., Variable selection in finite mixture of regression models, Journal of the American Statistical Association, 102, 479, 1025-1038, (2007) · Zbl 1469.62306 |
| [45] | Kim, J.; Allenby, G. M.; Rossi, P. E., Modeling consumer demand for variety, Marketing Science, 21, 3, 229-250, (2002) |
| [46] | Kim, S.; Fong, D. K.; DeSarbo, W. S., Model-based segmentation featuring simultaneous segment-level variable selection, Journal of Marketing Research, 49, 5, 725-736, (2012) |
| [47] | Kim, S.; Tadesse, M. G.; Vannucci, M., Variable selection in clustering via Dirichlet process mixture models, Biometrika, 877-893, (2006) · Zbl 1436.62266 |
| [48] | Kunda, Z., The case for motivated reasoning, Psychological Bulletin, 108, 3, 480, (1990) |
| [49] | Leong, W.; Hensher, D. A., Embedding decision heuristics in discrete choice model: A review, Transport Reviews, 32, 3, 313-331, (2012) |
| [50] | Li, Y.; Ansari, A., A Bayesian semiparametric approach for endogeneity and heterogeneity in choice models, Management Science, 60, 5, 1161-1179, (2014) |
| [51] | Li, S.; Sun, B.; Wilcox, R. T., Cross-selling sequentially ordered products: an application to consumer banking services, Journal of Marketing Research, 42, 2, 233-239, (2005) |
| [52] | Liechty, J.; Liechty, M.; Müller, P., Bayesian correlation estimation, Biometrika, 91, 1, 1-14, (2004) · Zbl 1132.62314 |
| [53] | Liu, X.; Daniels, M. J., A new algorithm for simulating a correlation matrix based on parameter expansion and reparameterization, Journal of Computational and Graphical Statistics, 15, 4, 897-914, (2006) |
| [54] | Liu, J. S.; Wu, Y. N., Parameter expansion for data augmentation, Journal of the American Statistical Association, 94, 448, 1264-1274, (1999) · Zbl 1069.62514 |
| [55] | Marin, J. M.; Robert, C., Bayesian core: A practical approach to computational Bayesian statistics, (2007), Springer Science & Business Media New York · Zbl 1137.62013 |
| [56] | Miller, K. E.; Ginter, J. L., An investigation of situational variation in brand choice behavior and attitude, Journal of Marketing Research, 16, 1, 111-123, (1979) |
| [57] | Mitchell, T. J.; Beauchamp, J. J., Bayesian variable selection in linear regression, Journal of the American Statistical Association, 83, 404, 1023-1032, (1988) · Zbl 0673.62051 |
| [58] | Okada, K.; Lee, M. D., A Bayesian approach to modeling group and individual differences in multidimensional scaling, Journal of Mathematical Psychology, 70, 1, 35-44, (2016) · Zbl 1359.62506 |
| [59] | Park, J.; DeSarbo, W. S.; Liechty, J., A hierarchical Bayesian multidimensional scaling methodology for accommodating both structural and preference heterogeneity, Psychometrika, 73, 4, 451-472, (2008) · Zbl 1301.62123 |
| [60] | Park, J., Rajagopel, P., Dillon, W., & Chaiy, S. (2017). A multidimensional unfolding model for assessing dimensionality selection in product positioning applications. Working Paper. Cox School of Business, Southern Methodist University, Dallas TX.; Park, J., Rajagopel, P., Dillon, W., & Chaiy, S. (2017). A multidimensional unfolding model for assessing dimensionality selection in product positioning applications. Working Paper. Cox School of Business, Southern Methodist University, Dallas TX. |
| [61] | Payne, J. W.; Bettman, J. R.; Johnson, E. J., The adaptive decision maker, (1993), Cambridge University Press Cambridge |
| [62] | Payne, J. W.; Bettman, J. R.; Luce, M. F., When time is money: decision behavior under opportunity-cost time pressure, Organizational Behavior and Human Decision Processes, 66, 2, 131-152, (1996) |
| [63] | Petty, R.; Cacioppo, J., Communication and persuasion: Central and peripheral routes to attitude change, (2012), Springer Science & Business Media New York |
| [64] | Petty, R. E.; Cacioppo, J. T.; Goldman, R., Personal involvement as a determinant of argument-based persuasion, Journal of Personality and Social Psychology, 41, 5, 847, (1981) |
| [65] | Raftery, A. E.; Dean, N., Variable selection for model-based clustering, Journal of the American Statistical Association, 101, 473, 168-178, (2006) · Zbl 1118.62339 |
| [66] | Ritter, G., Robust cluster analysis and variable selection, (2014), CRC Press New York |
| [67] | Rossi, P. E. (2017). Bayesian Inference for Marketing/Micro-econometrics. bayesm; Rossi, P. E. (2017). Bayesian Inference for Marketing/Micro-econometrics. bayesm |
| [68] | Rossi, P. E.; Allenby, G. M.; McCulloch, R. E., Bayesian statistics and marketing, 1-368, (2005), Wiley New York · Zbl 1094.62037 |
| [69] | Rousseeuw, P. J.; Molenberghs, G., The shape of correlation matrices, The American Statistician, 48, 4, 276-279, (1994) |
| [70] | Sperrin, M.; Jaki, T.; Wit, E., Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models, Statistics and Computing, 20, 3, 357-366, (2010) |
| [71] | Spiegelhalter, D. J.; Best, N. G.; Carlin, B. P.; Van Der Linde, A., Bayesian measures of model complexity and fit, Journal of the Royal Statistical Society. Series B. Statistical Methodology, 64, 4, 583-639, (2002) · Zbl 1067.62010 |
| [72] | Steele, R. J.; Raftery, A. E., Performance of Bayesian model selection criteria for Gaussian mixture models, (Chen, M.-H., Frontiers of statistical decision making and bayesian analysis, (2010), Springer New York), 113-130 |
| [73] | Sujan, M., Consumer knowledge: effects on evaluation strategies mediating consumer judgments, Journal of Consumer Research, 12, 1, 31-46, (1985) |
| [74] | Tadesse, M. G.; Sha, N.; Vannucci, M., Bayesian variable selection in clustering high-dimensional data, Journal of the American Statistical Association, 100, 470, 602-617, (2005) · Zbl 1117.62433 |
| [75] | Tibshirani, R., Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society. Series B. Statistical Methodology, 58, 1, 267-288, (1996) · Zbl 0850.62538 |
| [76] | Van Dyk, D. A.; Park, T., Partially collapsed Gibbs samplers: theory and methods, Journal of the American Statistical Association, 103, 482, 790-796, (2008) · Zbl 1471.62198 |
| [77] | Vicente, K. J.; Wang, J. H., An ecological theory of expertise effects in memory recall, Psychological Review, 105, 1, 33, (1998) |
| [78] | Wedel, M.; Kamakura, W., Market segmentation: Conceptual and methodological foundations, (2000), Springer-Verlag New York |
| [79] | Wedel, M.; Kamakura, W.; Arora, N.; Bemmaor, A.; Chiang, J.; Elrod, T., Discrete and continuous representations of unobserved heterogeneity in choice modeling, Marketing Letters, 10, 3, 219-232, (1999) |
| [80] | White, A.; Wyse, J.; Murphy, T. B., Bayesian variable selection for latent class analysis using a collapsed Gibbs sampler, Statistics and Computing, 26, 1-2, 511-527, (2016) · Zbl 1342.62112 |
| [81] | Wright, P.; Weitz, B., Time horizon effects on product evaluation strategies, Journal of Marketing Research, 14, 4, 429-443, (1977) |
| [82] | Yang, C., Modeling multiple sources of heterogeneity in mode choice models, Journal of Eastern Asia Society for Transportation Studies, 6, 2031-2045, (2005) |
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