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Bayesian estimation of multivariate-normal models when dimensions are absent

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  • Robert Zeithammer

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  • Peter Lenk

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Abstract

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

Suggested Citation

  • Robert Zeithammer & Peter Lenk, 2006. "Bayesian estimation of multivariate-normal models when dimensions are absent," Quantitative Marketing and Economics (QME), Springer, vol. 4(3), pages 241-265, September.
  • Handle: RePEc:kap:qmktec:v:4:y:2006:i:3:p:241-265
    DOI: 10.1007/s11129-005-9006-5
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    References listed on IDEAS

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    Cited by:

    1. Nikolaus Hautsch & Fuyu Yang, 2014. "Bayesian Stochastic Search for the Best Predictors: Nowcasting GDP Growth," University of East Anglia Applied and Financial Economics Working Paper Series 056, School of Economics, University of East Anglia, Norwich, UK..
    2. Yu-Cheng Ku & Tsun-Feng Chiang & Sheng-Mao Chang, 2017. "Is what you choose what you want?—outlier detection in choice-based conjoint analysis," Marketing Letters, Springer, vol. 28(1), pages 29-42, March.
    3. Subramanian Balachander & Bikram Ghosh, 2013. "Bayesian estimation of a simultaneous probit model using error augmentation: An application to multi-buying and churning behavior," Quantitative Marketing and Economics (QME), Springer, vol. 11(4), pages 437-458, December.
    4. Anindita Chakravarty & Rajdeep Grewal, 2011. "The Stock Market in the Driver's Seat! Implications for R&D and Marketing," Management Science, INFORMS, vol. 57(9), pages 1594-1609, March.
    5. Alexandre Belloni & Mitchell J. Lovett & William Boulding & Richard Staelin, 2012. "Optimal Admission and Scholarship Decisions: Choosing Customized Marketing Offers to Attract a Desirable Mix of Customers," Marketing Science, INFORMS, vol. 31(4), pages 621-636, July.
    6. Lynd Bacon & Peter Lenk, 2012. "Augmenting discrete-choice data to identify common preference scales for inter-subject analyses," Quantitative Marketing and Economics (QME), Springer, vol. 10(4), pages 453-474, December.

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