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A Mixture Model for Distributions of Correlation Coefficients

Published online by Cambridge University Press:  01 January 2025

Hoben Thomas
Hoben Thomas*
Affiliation:
The Pennsylvania State University
*
Requests for reprints should be sent to Hoben Thomas, The Pennsylvania State University, 513 Moore Building, University Park, PA 16802.
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Abstract

An old problem in personnel psychology is to characterize distributions of test validity correlation coefficients. The proposed model views histograms of correlation coefficients as observations from a mixture distribution which, for a fixed sample size n, is a conditional mixture distribution h(r|n) = Σjλjh(r; ρj, n), where R is the correlation coefficient, ρj are population correlation coefficients and λj are the mixing weights. The associated marginal distribution of R is regarded as the parent distribution underlying histograms of empirical correlation coefficients. Maximum likelihood estimates of the parameters ρj and λj can be obtained with an EM algorithm solution and tests for the number of components t are achieved after the (one-component) density of R is replaced with a tractable modeling density h(r; ρj, n). Two illustrative examples are provided.

Keywords

validity generalizationfinite mixturescorrelation coefficientsmixture decompositionEM algorithm
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 3 , September 1989 , pp. 523 - 530
Copyright
Copyright © 1989 The Psychometric Society

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