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The Metric Quality of Ordered Categorical Data

Author

Listed:
  • V. Srinivasan

    (Stanford University)

  • Amiya K. Basu

    (University of Illinois)

Abstract

We quantify the information loss incurred by categorizing an unobserved continuous variable () into an ordered categorical scale (). The continuous variable is conceptualized as true score (Ï„) (which varies across individuals) plus random error ((epsilon)), with both components assumed to be normally distributed. The index of metric quality is operationalized as 2 (, Ï„)/ 2 (, Ï„), where 2 , the squared correlation coefficient, is a descriptive measure of the power of or to predict Ï„. The index is useful in defining limits on explanatory power (population 2 ) in multiple regression models in which an ordered categorical variable is regressed against a set of predictors. The index can also be used to correct correlations for the effects of ordered categorical measurement. The index of metric quality is extended to the case when several ordered categorical scales are averaged as in the multi-item measurement of a construct. We prove theoretically that as long as the error variance is “large,” the index of metric quality for the average of ordered categorical scales goes to 1 as the number of scales becomes “large.” The index for averaged data is useful in answering questions such as whether the measurement of a construct by averaging three 5-point scales is better or worse than the measurement obtained by averaging five 3-point scales. The results indicate that the loss of information by marketing researchers' ad hoc use of as opposed to the more refined is small (

Suggested Citation

  • V. Srinivasan & Amiya K. Basu, 1989. "The Metric Quality of Ordered Categorical Data," Marketing Science, INFORMS, vol. 8(3), pages 205-230.
    • Handle: RePEc:inm:ormksc:v:8:y:1989:i:3:p:205-230
    DOI: 10.1287/mksc.8.3.205
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    Cited by:

    1. Weijters, Bert & Cabooter, Elke & Schillewaert, Niels, 2010. "The effect of rating scale format on response styles: The number of response categories and response category labels," International Journal of Research in Marketing, Elsevier, vol. 27(3), pages 236-247.
    2. Leonardo Becchetti & Riccardo Massari & Paolo Naticchioni, 2014. "The drivers of happiness inequality: suggestions for promoting social cohesion," Oxford Economic Papers, Oxford University Press, vol. 66(2), pages 419-442.
    3. Atasi Basu & Randal Elder & Mohamed Onsi, 2012. "Reported earnings, auditor's opinion, and compensation: theory and evidence," Accounting and Business Research, Taylor & Francis Journals, vol. 42(1), pages 29-48, March.
    4. Diamantopoulos, Adamantios & Winklhofer, Heidi, 2003. "Export sales forecasting by UK firms: Technique utilization and impact on forecast accuracy," Journal of Business Research, Elsevier, vol. 56(1), pages 45-54, January.
    5. Bijmolt, T.H.A. & Wedel, M., 1996. "A Monte Carlo Evaluation of Maximum Likelihood Multidimensional Scaling Methods," Other publications TiSEM f72cc9d8-f370-43aa-a224-4, Tilburg University, School of Economics and Management.
    6. Teichert, Thorsten Andreas, 1997. "A model of ranked conjoint-data and implications for evaluation," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 461, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    7. Michael Alles & Amin Amershi & Srikant Datar & Ratna Sarkar, 2000. "Information and Incentive Effects of Inventory in JIT Production," Management Science, INFORMS, vol. 46(12), pages 1528-1544, December.
    8. Darmon, Rene Y. & Rouzies, Dominique, 1999. "Internal Validity of Conjoint Analysis Under Alternative Measurement Procedures," Journal of Business Research, Elsevier, vol. 46(1), pages 67-81, September.
    9. Chauhan, Vivek & Gupta, Akshay & Parida, Manoranjan, 2021. "Demystifying service quality of Multimodal Transportation Hub (MMTH) through measuring users’ satisfaction of public transport," Transport Policy, Elsevier, vol. 102(C), pages 47-60.
    10. Kim, Junghwan & Song, Jaeki & Jones, Donald R., 2011. "The cognitive selection framework for knowledge acquisition strategies in virtual communities," International Journal of Information Management, Elsevier, vol. 31(2), pages 111-120.
    11. Bijmolt, T.H.A. & Wedel, M., 1996. "A Monte Carlo Evaluation of Maximum Likelihood Multidimensional Scaling Methods," Research Memorandum 725, Tilburg University, School of Economics and Management.
    12. P. K. Kannan & Barbara Kline Pope & Sanjay Jain, 2009. "—Pricing Digital Content Product Lines: A Model and Application for the National Academies Press," Marketing Science, INFORMS, vol. 28(4), pages 620-636, 07-08.
    13. J Christopher Westland, 2015. "The information content of financial survey response data," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 1(1), pages 1-20, December.
    14. He, Jiaxiu & Wang, Xin (Shane) & Curry, David J., 2017. "Mediation analysis: A new test when all or some variables are categorical," International Journal of Research in Marketing, Elsevier, vol. 34(4), pages 780-798.
    15. Baranchuk, Nina & Prasad, Ashutosh, 2023. "Design of product quality scales for conveying information by infomediaries," International Journal of Research in Marketing, Elsevier, vol. 40(1), pages 210-225.
    16. Wesley Friske & Atanas Nik Nikolov & Todd Morgan, 2024. "Making the grade: An analysis of sustainability reporting standards and Global Reporting Initiative adherence ratings," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 31(3), pages 2098-2108, May.

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