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Selective Influence Through Conditional Independence

Published online by Cambridge University Press:  01 January 2025

Ehtibar N. Dzhafarov
Ehtibar N. Dzhafarov*
Affiliation:
Purdue University
*
Requests for reprints should be sent to Ehtibar N. Dzhafarov, Department of Psychological Sciences, Purdue University, 703 Third Street, West Lafayette, IN 47907-2004. E-Mail: ehtibar@purdue.edu
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Abstract

Let each of several (generally interdependent) random vectors, taken separately, be influenced by a particular set of external factors. Under what kind of the joint dependence of these vectors on the union of these factor sets can one say that each vector is selectively influenced by “its own” factor set? The answer proposed and elaborated in this paper is: One can say this if and only if one can find a factor-independent random vector given whose value the vectors in question are conditionally independent, with their conditional distributions selectively influenced by the corresponding factor sets. Equivalently, the random vectors should be representable as deterministic functions of “their” factor sets and of some mutually independent and factor-independent random variables, some of which may be shared by several of the functions.

Keywords

selective influenceconditional independencemarginal selectivityprocessing architecturesThurstonian modeling
Type
Articles
Information
Psychometrika , Volume 68 , Issue 1 , March 2003 , pp. 7 - 25
Copyright
Copyright © 2003 The Psychometric Society

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Footnotes

This research has been supported by the NSF Grant SES-0001925. I am grateful to Hans Colonius and Richard Schweickert for helpful critical comments.

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