Better Rating Scale Scores with Information–Based Psychometrics
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Department of Psychology, McGill University, 2748 Howe St., Ottawa, ON H3A 0G4, Canada
2
Neuroscience Program, Ottawa Hospital Research Institute, Ottawa, ON K1H 8L6, Canada
3
Department of Statistics, USBE, Umeå University, 901 87 Umeå, Sweden
*
Author to whom correspondence should be addressed.
Psych 2020, 2(4), 347-369; https://doi.org/10.3390/psych2040026
Received: 14 October 2020
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Revised: 25 November 2020
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Accepted: 26 November 2020
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Published: 15 December 2020
(This article belongs to the Special Issue Learning from Psychometric Data)
Diagnostic scales are essential to the health and social sciences, and to the individuals that provide the data. Although statistical models for scale data have been researched for decades, it remains nearly universal that scale scores are sums of weights assigned a priori to question choice options (sum scores), respectively. We propose several modifications of psychometric testing theory that together demonstrate remarkable improvements in the quality of rating scale scores. Our model represents performance as a space with a metric structure by transforming probability into surprisal or information. The estimation algorithm permits the analysis of data from tens and hundreds of thousands of test takers in a few minutes on consumer level computing equipment. Standard errors of performance estimates are shown to be as small as a quarter of those of sum scores. Open access software resources are presented.
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Keywords:
scale curve; percentile index; sum score; expected score; surprisal; spline smoothing; arc length; information theory
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
MDPI and ACS Style
Ramsay, J.; Li, J.; Wiberg, M. Better Rating Scale Scores with Information–Based Psychometrics. Psych 2020, 2, 347-369. https://doi.org/10.3390/psych2040026
AMA Style
Ramsay J, Li J, Wiberg M. Better Rating Scale Scores with Information–Based Psychometrics. Psych. 2020; 2(4):347-369. https://doi.org/10.3390/psych2040026
Chicago/Turabian StyleRamsay, James, Juan Li, and Marie Wiberg. 2020. "Better Rating Scale Scores with Information–Based Psychometrics" Psych 2, no. 4: 347-369. https://doi.org/10.3390/psych2040026
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