A mixture model for distributions of correlation coefficients |
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Authors: | Hoben Thomas |
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Institution: | (1) The Pennsylvania State University, 513 Moore Building, 16802 University Park, PA |
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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 sizen, is a conditional mixture distributionh(r|n) =
j
j
h(r;
j
,n), whereR is the correlation coefficient,
j
are population correlation coefficients and
j
are the mixing weights. The associated marginal distribution ofR is regarded as the parent distribution underlying histograms of empirical correlation coefficients. Maximum likelihood estimates of the parameters
j
and
j
can be obtained with an EM algorithm solution and tests for the number of componentst are achieved after the (one-component) density ofR is replaced with a tractable modeling densityh(r;
j
,n). Two illustrative examples are provided. |
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Keywords: | validity generalization finite mixtures correlation coefficients mixture decomposition EM algorithm |
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