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Additive and Multiplicative Models for Gamma Distributed Random Variables, and their Application as Psychometric Models for Response Times

Published online by Cambridge University Press:  01 January 2025

Eric Maris
Eric Maris*
Affiliation:
University of Leuven
*
Requests for reprints should be sent to Eric Marls, Psychologisch Laboratorium, Universiteit Nijmegen, PO Box 9104, 6500 HE Nijmegen, THE NETHERLANDS.
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Abstract

A class of models for gamma distributed random variables is presented. These models are shown to be more flexible than the classical linear models with respect to the structure that can be imposed on the expected value. In particular, both additive, multiplicative, and combined additive-multiplicative models can be formulated. As a special case, a class of psychometric models for reaction times is presented, together with their psychological interpretation. By means of a comparison with existing models, this class of models is shown to offer some possibilities that are not available in existing methods. Parameter estimation by means of maximum likelihood (ML) is shown to have some attractive properties, since the models belong to the exponential family. Then, the results of a simulation study of the bias in the ML estimates are presented. Finally, the application of these models is illustrated by an analysis of the data from a mental rotation experiment. This analysis is preceded by an evaluation of the appropriateness of the gamma distribution for these data.

Keywords

gamma distributionresponse timespsychometric modelsmental rotation
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 3 , September 1993 , pp. 445 - 469
Copyright
Copyright © 1993 The Psychometric Society

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Footnotes

The author wishes to thank Paul De Boeck, Ivo Molenaar, Susan Embretson, Gerard van Breuketen, and Gert Storms for their helpful comments, Gerard van Breukelen for the use of his data, and Rob Stroobants for plotting the graphs.

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