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# Factor Analysis

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Factor Analysis book

# Factor Analysis

DOI link for Factor Analysis

Factor Analysis book

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## ABSTRACT

Factor analysis is a method of modeling the covariation among a set of observed variables as a function of one or more latent constructs. Here, we use the term construct to refer to an unobservable but theoretically defensible entity, such as intelligence, self-efficacy, or creativity. Such constructs are typically considered to be latent in the sense that they are not directly observable (see Bollen, 2002, for a more detailed discussion of latent constructs). The purpose of factor analysis is to assist researchers in identifying and/or understanding the nature of the latent constructs underlying the variables of interest. Technically, these descriptions exclude component analysis, which is a method for reducing the dimensionality of a set of observed variables through the creation of an optimum number of weighted composites. A major difference between factor and component analysis is that in the latter all of the variance is analyzed, whereas in factor analysis, only the shared (common) variance is analyzed. For this reason, factor analysis is sometimes referred to as common factor analysis. In many ways, however, component analysis is very similar to common factor analysis, and many of the desiderata for exploratory factor analysis presented here apply equally to component analysis. Given that the goal of component analysis is to explain as much observed variance as possible via the weighted composites and not, as in common factor analysis, to model the relations among variables as functions of underlying latent variables, those desiderata relating to the importance of theory for factor analysis do not necessarily apply to component analysis (see Widaman, 2007, for a detailed explanation of the conceptual and mathematical distinction between exploratory factor analysis and principal components analysis). This is because, although components may represent constructs, component analysis can still have utility as a data reduction method even if the components themselves are not interpreted. In such cases, the components do not provide an explanation for the variables’ shared variance, but are instead used to represent that shared variance in the most parsimonious manner possible.