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Fitting Psychometric Models with Methods Based on Automatic Differentiation

Published online by Cambridge University Press:  01 January 2025

Robert Cudeck
Robert Cudeck*
Affiliation:
Ohio State University
*
Correspondence should be addressed to R. Cudeck, Psychology Department, Ohio State University, 240K Lazenby Hall, Columbus, OH 43210, USA. E-mail: cudeck.1@osu.edu
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Abstract

Quantitative psychology is concerned with the development and application of mathematical models in the behavioral sciences. Over time, models have become more complex, a consequence of the increasing complexity of research designs and experimental data, which is also a consequence of the utility of mathematical models in the science. As models have become more elaborate, the problems of estimating them have become increasingly challenging. This paper gives an introduction to a computing tool called automatic differentiation that is useful in calculating derivatives needed to estimate a model. As its name implies, automatic differentiation works in a routine way to produce derivatives accurately and quickly. Because so many features of model development require derivatives, the method has considerable potential in psychometric work. This paper reviews several examples to demonstrate how the methodology can be applied.

Keywords

Estimationmodel fittingdifferentiation
Type
2005 Presidential Address
Information
Psychometrika , Volume 70 , Issue 4 , December 2005 , pp. 599 - 617
Copyright
Copyright © 2005 The Psychometric Society

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Footnotes

From the Presidential Address delivered at the 70th Annual Meeting of the Psychometric Society, Tilburg University, The Netherlands, July 5–8, 2005.

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