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Estimation of Stimulus-Response Curves by Bayesian Least Squares

Published online by Cambridge University Press:  01 January 2025

H. D. Brunk
H. D. Brunk*
Affiliation:
Oregon State University
*
Requests for reprints should be addressed to H. D. Brunk, Department of Statistics, Oregon State University, Corvallis, Oregon, 97331.
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Abstract

Bayesian least squares techniques are adapted to estimation of stimulus-response curves, rather broadly conceived. Illustrative examples deal with estimation of person characteristic curves and item characteristic curves in the context of mental testing, and estimation of a stimulus-response curve using data from a psychophysical experiment.

Keywords

stimulus-responseBayesleast squaresorthogonal expansionsregression
Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 2 , June 1981 , pp. 115 - 128
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

The present paper is a version of an invited address of the same title, presented to the meetings of The Psychometric Society in Monterey, California on June 8, 1979, expanded by adding Example 1.

The writer gratefully acknowledges the benefit of conversations with Don Pierce, and with John Shih, whose related work on density estimation pointed up an error in the original version of Section 2. He acknowledges, gratefully, support by the National Science Foundation through Grants MCS 76-02166A01 and MCS 78-01932. And he wishes to express his gratitude for the cordial hospitality and gracious cooperation offered by Professor Donald M. MacKay and the staff of the Department of Communication, University of Keele, during spring and summer, 1976; in particular, by Professor Dennis P. Andrews and Keichi Uchikawa, who kindly furnished data, a small portion of which is used in the illustrative example, Example 2.

References

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Brunk, H. D. Bayesian least squares estimates of univariate regression functions. Communications in Statistics Theory and Methods, 1980, A-9, 1101–1136.CrossRefGoogle Scholar
Hartigan, J. A. Linear Bayes methods. Journal of the Royal Statistical Society, Series B, 1969, 31, 446–454.CrossRefGoogle Scholar
Lord, Frederic M., & Novick, Melvin R. Statistical theories of mental test scores, 1968. Reading, MA: Addison-Wesley.Google Scholar