Unidimensional factor models imply weaker partial correlations than zero-order correlations

Fuente: arXiv
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Autori principali: van Bork, Riet, Grasman, Raoul P. P. P., Waldorp, Lourens J.
Natura: Preprint
Pubblicazione: 2016
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author van Bork, Riet
Grasman, Raoul P. P. P.
Waldorp, Lourens J.
author_facet van Bork, Riet
Grasman, Raoul P. P. P.
Waldorp, Lourens J.
contents In a unidimensional factor model it is assumed that the set of indicators that loads on this factor are conditionally independent given the latent factor. Two indicators are, however, never conditionally independent given (a set of) other indicators that load on this factor, as this would require one of the indicators that is conditioned on to correlate one with the latent factor. Although partial correlations between two indicators given the other indicators can thus never equal zero (Holland and Rosenbaum, 1986), we show in this paper that the partial correlations do need to be always weaker than the zero-order correlations. More precisely, we prove that the partial correlation between two observed variables that load on one factor given all other observed variables that load on this factor, is always closer to zero than the zero-order correlation between these two variables.
format Preprint
id arxiv_https___arxiv_org_abs_1610_03375
institution arXiv
publishDate 2016
record_format arxiv
spellingShingle Unidimensional factor models imply weaker partial correlations than zero-order correlations
van Bork, Riet
Grasman, Raoul P. P. P.
Waldorp, Lourens J.
Statistics Theory
In a unidimensional factor model it is assumed that the set of indicators that loads on this factor are conditionally independent given the latent factor. Two indicators are, however, never conditionally independent given (a set of) other indicators that load on this factor, as this would require one of the indicators that is conditioned on to correlate one with the latent factor. Although partial correlations between two indicators given the other indicators can thus never equal zero (Holland and Rosenbaum, 1986), we show in this paper that the partial correlations do need to be always weaker than the zero-order correlations. More precisely, we prove that the partial correlation between two observed variables that load on one factor given all other observed variables that load on this factor, is always closer to zero than the zero-order correlation between these two variables.
title Unidimensional factor models imply weaker partial correlations than zero-order correlations
topic Statistics Theory
url https://arxiv.org/abs/1610.03375