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Generalized measurement error: Intrinsic and incidental measurement error

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  • Edward Kroc

Abstract

In this paper, we generalize the notion of measurement error on deterministic sample datasets to accommodate sample data that are random-variable-valued. This leads to the formulation of two distinct kinds of measurement error: intrinsic measurement error, and incidental measurement error. Incidental measurement error will be recognized as the traditional kind that arises from a set of deterministic sample measurements, and upon which the traditional measurement error modelling literature is based, while intrinsic measurement error reflects some subjective quality of either the measurement tool or the measurand itself. We define calibrating conditions that generalize common and classical types of measurement error models to this broader measurement domain, and explain how the notion of generalized Berkson error in particular mathematicizes what it means to be an expert assessor or rater for a measurement process. We then explore how classical point estimation, inference, and likelihood theory can be generalized to accommodate sample data composed of generic random-variable-valued measurements.

Suggested Citation

  • Edward Kroc, 2023. "Generalized measurement error: Intrinsic and incidental measurement error," PLOS ONE, Public Library of Science, vol. 18(6), pages 1-41, June.
    • Handle: RePEc:plo:pone00:0286680
    DOI: 10.1371/journal.pone.0286680
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    References listed on IDEAS

    as
    1. Manit Mishra, 2016. "Confirmatory Factor Analysis (CFA) as an Analytical Technique to Assess Measurement Error in Survey Research," Paradigm, , vol. 20(2), pages 97-112, December.
    2. Garthwaite, Paul H. & Kadane, Joseph B. & O'Hagan, Anthony, 2005. "Statistical Methods for Eliciting Probability Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 680-701, June.
    3. repec:cdl:uctcwp:qt2t08s22q is not listed on IDEAS
    4. Edward Kroc, 2020. "Measurement protocols, random-variable-valued measurements, and response process error: Estimation and inference when sample data are not deterministic," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-25, October.
    5. Jerry Hausman, 2001. "Mismeasured Variables in Econometric Analysis: Problems from the Right and Problems from the Left," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 57-67, Fall.
    6. repec:cdl:uctcwp:qt3gb0k9b5 is not listed on IDEAS
    7. Brownstone, David & Valletta, Robert G, 1996. "Modeling Earnings Measurement Error: A Multiple Imputation Approach," The Review of Economics and Statistics, MIT Press, vol. 78(4), pages 705-717, November.
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