Connections between graphical Gaussian models and factor analysis

Salgueiro, M. Fátima, Smith, Peter and McDonald, John (2010) Connections between graphical Gaussian models and factor analysis. Multivariate Behavioral Research, 45 (1), Spring Issue, 135-152. (doi:10.1080/00273170903504851).

Record type: Article

Abstract

Connections between graphical Gaussian models and classical single-factor models are obtained by parameterizing the single-factor model as a graphical Gaussian model. Models are represented by independence graphs, and associations between each manifest variable and the latent factor are measured by factor partial correlations. Power calculations for the single-factor graphical Gaussian model are facilitated by expressing the manifest partial correlations as functions of the factor partial correlations. The power of selecting a graphical Gaussian model with an association structure between manifest variables compatible with a single-factor model is investigated. The results are illustrated using 2 examples: the 1st is a hypothetical factor model with parallel measures. The 2nd uses data from the British Household Panel Survey on job satisfaction.

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