Utility Covariances and Context Effects in Conjoint MNP Models
Experimental conjoint choice analysis is among the most frequently used methods for measuring and analyzing consumer preferences. The data from such experiments have been typically analyzed with the Multinomial Logit (MNL) model. However, there are several problems associated with the standard MNL model because it is based on the assumption that the error terms of the underlying random utilities are independent across alternatives, choice sets, and subjects. The Multinomial Probit model (MNP) is well known to alleviate this assumption of independence of the error terms. Accounting for covariances in utilities in modeling choice experiments with the MNP is important because variation of the coefficients in the choice model may occur due to context effects. Previous research has shown that subjects' utilities for alternatives depend on the choice context, that is, the particular set of alternatives evaluated. Simonson and Tversky's tradeoff contrast principle describes the effect of the choice context on attribute importance and patterns of choice. They distinguish , which are caused by the alternatives in the offered set only, and , which are due to the influence of alternatives previously considered in choice experiments. These effects are hypothesized to cause correlations in the utilities of alternatives within and across choice sets, respectively. The purpose of this study is to develop an MNP model for conjoint choice experiments. This model is important for a more detailed study of choice patterns in those experiments. In developing the MNP model for conjoint choice experiments, several hurdles need to be taken related to the identification of the model and to the prediction of holdout profiles. To overcome those problems, we propose a random coefficients (RC) model that assumes a multivariate normal distribution of the regression coefficients with a rank one factor structure on the covariance matrix of these regression coefficients. The parameters in this covariance matrix can be used to identify which attributes and levels of attributes are potentional sources of dependencies between the alternatives and choice sets in a conjoint choice experiment. We present several versions of this model. Moreover, for each of these models we allow utilities to be either correlated or independent across choice sets. The Independent Probit (IP) model is used as a benchmark. Given the dimensionality of the integrations involved in computing the choice probabilities, the models are estimated with simulated likelihood, where simulations are used to approximate the integrals involved in the choice probabilities. We apply and compare the models in two conjoint choice experiments. In both applications, the random coefficients MNP model that allows choices in different choice sets to be correlated (RC) displays superior fit and predictive validity compared with all other models. We hypothesize that the difference in fit occurs because the RC model accommodates correlations among choice sets that are caused by background contrast effects, whereas the model that treats choice sets as independent (iRC) accounts for local contrast effects only. The iRC model shows superior model fit compared with the IP model, but its predictions are worse than those of the IP model. We find differences in the importance of local and background contrast effects for choice sets containing different numbers of alternatives: The background contrast effect may be stronger for smaller choice sets, whereas the local contrast effect may be stronger for bigger choice sets. We illustrate the differences in simulated market shares that are obtained from the RC, iRC, and IP models in three hypothetical situations: product modification, product line extension, and the introduction of a me-too brand. In all of those situations, substantially different market shares are predicted by the three models, which illustrates the extent to which erroneous predictions may be obtained from the misspecified iRC and IP models.
Volume (Year): 17 (1998)
Issue (Month): 3 ()
|Contact details of provider:|| Postal: 7240 Parkway Drive, Suite 300, Hanover, MD 21076 USA|
Web page: http://www.informs.org/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Axel Borsch-Supan & Vassilis Hajivassiliou & Laurence J. Kotlikoff, 1992.
"Health, Children, and Elderly Living Arrangements: A Multiperiod-Multinomial Probit Model with Unobserved Heterogeneity and Autocorrelated Errors,"
NBER Chapters,in: Topics in the Economics of Aging, pages 79-108
National Bureau of Economic Research, Inc.
- Axel Borsch-Supan & Vassilis Hajivassiliou & Laurence J. Kotlikoff & John N. Morris, 1990. "Health, Children, and Elderly Living Arrangements: A Multiperiod-Multinomial Probit Model with Unobserved Heterogeneity and Autocorrelated Errors," NBER Working Papers 3343, National Bureau of Economic Research, Inc.
- Simonson, Itamar, 1989. " Choice Based on Reasons: The Case of Attraction and Compromise Effects," Journal of Consumer Research, Oxford University Press, vol. 16(2), pages 158-174, September.
- Lee, Lung-Fei, 1992. "On Efficiency of Methods of Simulated Moments and Maximum Simulated Likelihood Estimation of Discrete Response Models," Econometric Theory, Cambridge University Press, vol. 8(04), pages 518-552, December.
- Lee, L-F., 1990. "On Efficiency of Methods of Simulated Moments and Maximum Simulated Likelihood Estimation of Discrete Response Models," Papers 260, Minnesota - Center for Economic Research.
- 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 403-426, March.
- J. A. Hausman & D. A. Wise, 1976. "A Conditional Profit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Working papers 173, Massachusetts Institute of Technology (MIT), Department of Economics.
- Geweke, John & Keane, Michael P & Runkle, David, 1994. "Alternative Computational Approaches to Inference in the Multinomial Probit Model," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 609-632, November.
- John F. Geweke & Michael P. Keane & David E. Runkle, 1994. "Alternative computational approaches to inference in the multinomial probit model," Staff Report 170, Federal Reserve Bank of Minneapolis.
- McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
- Daniel McFadden, 1987. "A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration," Working papers 464, Massachusetts Institute of Technology (MIT), Department of Economics.
- Borsch-Supan, Axel & Hajivassiliou, Vassilis A., 1993. "Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models," Journal of Econometrics, Elsevier, vol. 58(3), pages 347-368, August.
- Vassilis A. Hajivassiliou & Axel Borsch-Supan, 1990. "Smooth Unbiased Multivariate Probability Simulators for Maximum Likelihood Estimation of Limited Dependent Variable Models," Cowles Foundation Discussion Papers 960, Cowles Foundation for Research in Economics, Yale University.
- Keane, Michael, 1997. "Current Issues in Discrete Choice Modeling," MPRA Paper 52515, University Library of Munich, Germany.
- Purushottam Papatla, 1996. "A Multiplicative Fixed-Effects Model of Consumer Choice," Marketing Science, INFORMS, vol. 15(3), pages 243-261.
- Huber, Joel & Puto, Christopher, 1983. " Market Boundaries and Product Choice: Illustrating Attraction and Substitution Effects," Journal of Consumer Research, Oxford University Press, vol. 10(1), pages 31-44, June.
- Amemiya, Takeshi, 1981. "Qualitative Response Models: A Survey," Journal of Economic Literature, American Economic Association, vol. 19(4), pages 1483-1536, December.
- Daniel L. McFadden, 1976. "Quantal Choice Analaysis: A Survey," NBER Chapters,in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 363-390 National Bureau of Economic Research, Inc.
- Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
- Vassilis A. Hajivassiliou & Daniel L. McFadden & Paul Ruud, 1993. "Simulation of Multivariate Normal Rectangle Probabilities and their Derivatives: Theoretical and Computational Results," Working Papers _024, Yale University.
- Bunch, David S., 1991. "Estimability in the Multinomial Probit Model," University of California Transportation Center, Working Papers qt1gf1t128, University of California Transportation Center.
- Peter E. Rossi & Robert E. McCulloch & Greg M. Allenby, 1996. "The Value of Purchase History Data in Target Marketing," Marketing Science, INFORMS, vol. 15(4), pages 321-340.
- Füsun Gönül & Kannan Srinivasan, 1993. "Modeling Multiple Sources of Heterogeneity in Multinomial Logit Models: Methodological and Managerial Issues," Marketing Science, INFORMS, vol. 12(3), pages 213-229.
- Green, Paul E & Srinivasan, V, 1978. " Conjoint Analysis in Consumer Research: Issues and Outlook," Journal of Consumer Research, Oxford University Press, vol. 5(2), pages 103-123, Se.
- Keane, Michael P, 1992. "A Note on Identification in the Multinomial Probit Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 193-200, April.
- 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.
- Huber, Joel & Payne, John W & Puto, Christopher, 1982. " Adding Asymmetrically Dominated Alternatives: Violations of Regularity and the Similarity Hypothesis," Journal of Consumer Research, Oxford University Press, vol. 9(1), pages 90-98, June.
- 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.
- Heckman, James J & Sedlacek, Guilherme, 1985. "Heterogeneity, Aggregation, and Market Wage Functions: An Empirical Model of Self-selection in the Labor Market," Journal of Political Economy, University of Chicago Press, vol. 93(6), pages 1077-1125, December.
- Bunch, David S., 1991. "Estimability in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 25(1), pages 1-12, February. Full references (including those not matched with items on IDEAS)