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Regression component decompositions (RCD) are defined as a special class of component decompositions where the pattern contains the regression weights for predicting the observed variables from the latent variables. Compared to factor analysis, RCD has a broader range of applicability, greater ease and simplicity of computation, and a more logical and straightforward theory. The usual distinction between factor analysis as a falsifiable model, and component analysis as a tautology, is shown to be misleading, since a special case of regression component decomposition can be defined which is not only falsifiable, but empirically indistinguishable from the factor model.