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Measurement errors in multivariate measurement scales


  • Tarkkonen, L.
  • Vehkalahti, K.


Our aim is to construct a general measurement framework for analyzing the effects of measurement errors in multivariate measurement scales. We define a measurement model, which forms the core of the framework. The measurement scales in turn are often produced by methods of multivariate statistical analysis. As a central element of the framework, we introduce a new, general method of estimating the reliability of measurement scales. It is more appropriate than the classical procedures, especially in the context of multivariate analyses. The framework provides methods for various topics related to the quality of measurement, such as assessing the structural validity of the measurement model, estimating the standard errors of measurement, and correcting the predictive validity of a measurement scale for attenuation. A proper estimate of reliability is a requisite in each task. We illustrate the idea of the measurement framework with an example based on real data.

Suggested Citation

  • Tarkkonen, L. & Vehkalahti, K., 2005. "Measurement errors in multivariate measurement scales," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 172-189, September.
  • Handle: RePEc:eee:jmvana:v:96:y:2005:i:1:p:172-189

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    References listed on IDEAS

    1. Melvin Novick & Charles Lewis, 1967. "Coefficient alpha and the reliability of composite measurements," Psychometrika, Springer;The Psychometric Society, vol. 32(1), pages 1-13, March.
    2. Jos Berge & Willem Hofstee, 1999. "Coefficients alpha and reliabilities of unrotated and rotated components," Psychometrika, Springer;The Psychometric Society, vol. 64(1), pages 83-90, March.
    3. Frederic Lord, 1955. "Sampling fluctuations resulting from the sampling of test items," Psychometrika, Springer;The Psychometric Society, vol. 20(1), pages 1-22, March.
    4. G. Kuder & M. Richardson, 1937. "The theory of the estimation of test reliability," Psychometrika, Springer;The Psychometric Society, vol. 2(3), pages 151-160, September.
    5. Lee Cronbach, 1951. "Coefficient alpha and the internal structure of tests," Psychometrika, Springer;The Psychometric Society, vol. 16(3), pages 297-334, September.
    6. Charles Mosier, 1943. "On the reliability of a weighted composite," Psychometrika, Springer;The Psychometric Society, vol. 8(3), pages 161-168, September.
    7. Nambury Raju, 1977. "A generalization of coefficient alpha," Psychometrika, Springer;The Psychometric Society, vol. 42(4), pages 549-565, December.
    8. Leonard Feldt, 1965. "The approximate sampling distribution of Kuder-Richardson reliability coefficient twenty," Psychometrika, Springer;The Psychometric Society, vol. 30(3), pages 357-370, September.
    9. Lee Cronbach, 1988. "Internal consistency of tests: Analyses old and new," Psychometrika, Springer;The Psychometric Society, vol. 53(1), pages 63-70, March.
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    Cited by:

    1. Peter M. Bentler, 2016. "Covariate-free and Covariate-dependent Reliability," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 907-920, December.
    2. Ariel Alonso & Annouschka Laenen & Geert Molenberghs & Helena Geys & Tony Vangeneugden, 2010. "A Unified Approach to Multi-item Reliability," Biometrics, The International Biometric Society, vol. 66(4), pages 1061-1068, December.
    3. Vehkalahti, Kimmo & Puntanen, Simo & Tarkkonen, Lauri, 2007. "Effects of measurement errors in predictor selection of linear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1183-1195, October.


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