Bayesian estimation of multivariate-normal models when dimensions are absent
Multivariate economic and business data frequently suffer from a missing data phenomenon that has not been sufficiently explored in the literature: both the independent and dependent variables for one or more dimensions are absent for some of the observational units. For example, in choice based conjoint studies, not all brands are available for consideration on every choice task. In this case, the analyst lacks information on both the response and predictor variables because the underlying stimuli, the excluded brands, are absent. This situation differs from the usual missing data problem where some of the independent variables or dependent variables are missing at random or by a known mechanism, and the “holes” in the data-set can be imputed from the joint distribution of the data. When dimensions are absent, data imputation may not be a well-poised question, especially in designed experiments. One consequence of absent dimensions is that the standard Bayesian analysis of the multi-dimensional covariances structure becomes difficult because of the absent dimensions. This paper proposes a simple error augmentation scheme that simplifies the analysis and facilitates the estimation of the full covariance structure. An application to a choice-based conjoint experiment illustrates the methodology and demonstrates that naive approaches to circumvent absent dimensions lead to substantially distorted and misleading inferences. Copyright Springer Science + Business Media, LLC 2006
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- J. A. Hausman & D. A. Wise, 1976.
"A Conditional Profit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences,"
173, Massachusetts Institute of Technology (MIT), Department of Economics.
- Hausman, Jerry A & Wise, David A, 1978. "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Econometrica, Econometric Society, vol. 46(2), pages 403-26, March.
- Elrod, Terry & Keane, Michael, 1995. "A Factor-Analytic Probit Model for Representing the Market Structure in Panel Data," MPRA Paper 52434, University Library of Munich, Germany.
- McCulloch, Robert E. & Polson, Nicholas G. & Rossi, Peter E., 2000. "A Bayesian analysis of the multinomial probit model with fully identified parameters," Journal of Econometrics, Elsevier, vol. 99(1), pages 173-193, November.
- Allenby, Greg M. & Rossi, Peter E., 1998. "Marketing models of consumer heterogeneity," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 57-78, November.
- McCulloch, Robert & Rossi, Peter E., 1994. "An exact likelihood analysis of the multinomial probit model," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 207-240.
- Michael D. Smith & Erik Brynjolfsson, 2001.
"Consumer Decision-making at an Internet Shopbot: Brand Still Matters,"
in: E-commerce, pages 541-558
National Bureau of Economic Research, Inc.
- Smith, Michael D & Brynjolfsson, Erik, 2001. "Consumer Decision-Making at an Internet Shopbot: Brand Still Matters," Journal of Industrial Economics, Wiley Blackwell, vol. 49(4), pages 541-58, December.
- Peter Lenk & Wayne DeSarbo, 2000. "Bayesian inference for finite mixtures of generalized linear models with random effects," Psychometrika, Springer;The Psychometric Society, vol. 65(1), pages 93-119, March.
- Peter J. Lenk & Wayne S. DeSarbo & Paul E. Green & Martin R. Young, 1996. "Hierarchical Bayes Conjoint Analysis: Recovery of Partworth Heterogeneity from Reduced Experimental Designs," Marketing Science, INFORMS, vol. 15(2), pages 173-191.
- Imai, Kosuke & van Dyk, David A., 2005. "A Bayesian analysis of the multinomial probit model using marginal data augmentation," Journal of Econometrics, Elsevier, vol. 124(2), pages 311-334, February.
- Rinus Haaijer & Michel Wedel & Marco Vriens & Tom Wansbeek, 1998. "Utility Covariances and Context Effects in Conjoint MNP Models," Marketing Science, INFORMS, vol. 17(3), pages 236-252.
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