Factor Loadings

Overview

Factor analysis, primarily EFA, assumes that common factors do exist that are indirectly measured by observed variables, and that each observed variable is a weighted sum of common factors plus a unique component. Common factors are latent and they influence one or more observed variables. The unique component represents all those independent things, both systematic and random, that are specific to a particular observed [Page 481]variable. In other words, a common factor is loaded by at least one observed variable, whereas each unique component corresponds to one and only one observed variable. Factor loadings are correlation coefficients between observed variables and latent common factors.

Factor loadings can also be viewed as standardized regression coefficients, or regression weights. Because an observed variable is a linear combination of latent common factors plus a unique component, such a structure is analogous to a multiple linear regression model where each observed variable is a response and common factors are predictors. From this perspective, factor loadings are viewed as standardized regression coefficients when all observed variables and common factors are standardized to have unit variance. Stated differently, factor loadings can be thought of as an optimal set of regression weights that predicts an observed variable using latent common factors.

Factor loadings usually take the form of a matrix, and this matrix is a standard output of almost all statistical software packages when factor analysis is performed. The factor loading matrix is usually denoted by the capital Greek letter Λ, or lambda, whereas its matrix entries, or factor loadings, are denoted by λij with i being the row number and j the column number. The number of rows of the matrix equals that of observed variables and the number of columns that of common factors.

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