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Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable

Published online by Cambridge University Press:  01 January 2025

Stephen H. C. du Toit  and
Robert Cudeck
Stephen H. C. du Toit
Affiliation:
Scientific Software International, Inc.
Robert Cudeck*
Affiliation:
Ohio State University
*
Requests for reprints should be sent to Robert Cudeck, Psychology Department, Ohio State University, 240K Lazenby Hall, Columbus, OH 43210, USA. E-mail: cudeck.1@osu.edu
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Abstract

A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution then requires an integral equation that is of dimension equal to the number of nonlinear terms. For nonlinear functions that have linear coefficients, the improvement in computational speed and accuracy using the new algorithm can be dramatic. An illustration of the method with repeated measures data from a learning experiment is presented.

Keywords

random coefficient modelnonlinear regressionsubject-specific modelrepeated measures datanumerical integration
Type
Theory and Methods
Information
Psychometrika , Volume 74 , Issue 1 , March 2009 , pp. 65 - 82
Copyright
Copyright © 2009 The Psychometric Society

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