Hostname: page-component-6bf8c574d5-b4m5d Total loading time: 0 Render date: 2025-02-19T21:05:26.092Z Has data issue: false hasContentIssue false
  • English
  • Français

A Monte Carlo Investigation of Conjoint Analysis Index-of-Fit: Goodness of Fit, Significance and Power

Published online by Cambridge University Press:  01 January 2025

U. N. Umesh  and
Sanjay Mishra
U. N. Umesh*
Affiliation:
Washington State University
Sanjay Mishra
Affiliation:
Washington State University
*
Requests for reprints should be sent to U. N. Umesh, College of Business and Economics, Washington State University, Pullman, WA 99164.
Get access Rights & Permissions [Opens in a new window]

Abstract

Researchers in the field of conjoint analysis know the index-of-fit values worsen as the judgmental error of evaluation increases. This simulation study provides guidelines on the goodness of fit based on distribution of index-of-fit for different conjoint analysis designs. The study design included the following factors: number of profiles, number of attributes, algorithm used and judgmental model used. Critical values are provided for deciding the statistical significance of conjoint analysis results. Using these cumulative distributions, the power of the test used to reject the null hypothesis of random ranking is calculated. The test is found to be quite powerful except for the case of very small residual degrees of freedom.

Keywords

conjoint analysisindex-of-fitmonotone regressionMonte Carlo simulationpower
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 1 , March 1990 , pp. 33 - 44
Copyright
Copyright © 1990 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.)

Footnotes

The authors thank the editor, the three reviewers and Ellen Foxman for helpful comments on the paper. Sanjay Mishra was a doctoral student at Washington State University at the time this research was completed. He is currently in the Department of Marketing at the University of Kansas.

References

Addelman, S. (1962). Orthogonal main-effect plans for asymmetrical factorial experiments. Technometrics, 4(1), 21–58.CrossRefGoogle Scholar
Carmone, F. J., Green, P. E., Jain, A. K. (1978). Robustness of conjoint analysis: some Monte Carlo results. Journal of Marketing Research, 15, 300–303.Google Scholar
Cattin, P., Bliemel, F. (1978). Metric vs. nonmetric procedures for multiattribute modeling: Some simulation results. Decision Sciences, 9, 472–80.CrossRefGoogle Scholar
Cattin, P., Wittink, D. R. (1982). Commercial uses of conjoint analysis: A survey. Journal of Marketing, 46, 44–53.CrossRefGoogle Scholar
de Leeuw, J., Stoop, I. (1984). Upper bounds for Kruskal's Stress. Psychometrika, 49, 392–402.CrossRefGoogle Scholar
Emery, D. R., Barron, F. H. (1979). Axiomatic and numerical conjoint measurement: An evaluation of diagnostic efficacy. Psychometrika, 44, 195–210.CrossRefGoogle Scholar
Green, P. E., Goldberg, S. M., Montemayor, M. (1981). A hybrid utility estimation model for conjoint analysis. Journal of Marketing, 45, 33–4.CrossRefGoogle Scholar
Green, P. E., Srinivasan, V. (1978). Conjoint analysis in consumer research: Issues and outlook. Journal of Consumer Research, 5, 103–23.CrossRefGoogle Scholar
Green, P. E., Wind, Y. (1975). A new way to measure consumers' judgments. Harvard Business Review, 53, 107–117.Google Scholar
International, Mathematical, Statistical, Libraries (1982). IMSL Library Reference Manual 9th ed.,, Houston, TX: Author.Google Scholar
Jain, A. K., Acito, F., Malhotra, N. K., Mahajan, V. (1979). A comparison of the internal validity of alternative parameter estimation methods in decompositional multiattribute preference models. Journal of Marketing Research, 16, 313–322.CrossRefGoogle Scholar
Johnson, R. M. (1975). A simple method for pairwise monotone regression. Psychometrika, 40, 163–8.CrossRefGoogle Scholar
Klahr, D. (1969). A Monte Carlo investigation of the statistical significance of Kruskal's nonmetric scaling procedure. Psychometrika, 34, 319–30.CrossRefGoogle Scholar
Knuth, D. E. (1981). The art of computer programming: Semi-numerical algorithms 2nd ed.,, Reading, MA: Addison-Wesley.Google Scholar
Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1–27.CrossRefGoogle Scholar
Kruskal, J. B. (1965). Analysis of factorial experiments by estimating monotone transformations of the data. Journal of the Royal Statistical Society, Series B, 2, 251–63.CrossRefGoogle Scholar
Mullet, G. M., Karson, M. J. (1986). Percentiles of LINMAP conjoint indices of fit for various orthogonal arrays: A simulation study. Journal of Marketing Research, 23, 286–90.CrossRefGoogle Scholar
Nygren, T. E. (1986). A two-stage algorithm for assessing violations of additivity via axiomatic and numerical conjoint analysis. Psychometrika, 51, 483–491.CrossRefGoogle Scholar
SAS Institute (1985). SAS User's Guide: Statistics, Version 5, Cary, NC: Author.Google Scholar
Shapiro, S. S., Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52, 591–611.CrossRefGoogle Scholar
Srinivasan, V., Shocker, A. D. (1973). Linear programming techniques for multidimensional analysis of preferences. Psychometrika, 38, 337–369.CrossRefGoogle Scholar
Takane, Y. (1982). Maximum likelihood additivity analysis. Psychometrika, 47, 225–241.CrossRefGoogle Scholar
Umesh, U. N. (1987). Transferability of preference models across segments and geographic areas. Journal of Marketing, 51, 59–70.CrossRefGoogle Scholar
Wittink, D. R., Cattin, P. (1981). Alternative estimation methods for conjoint analysis: A Monte Carlo study. Journal of Marketing Research, 18, 101–6.Google Scholar