Which term is the regression coefficient of a variable for the linear model that describes a latent variable or factor in factor analysis?

Which term is the regression coefficient of a variable for the linear model that describes a latent variable or factor in factor analysis?

• A. Factor score
• B. Factor loading
• C. Factor transformation matrix, ∧
• D. Fisher's exact test

Answer: (B)

In factor analysis, observed variables are modeled as linear functions of one or more latent factors plus error. The coefficient that links a specific observed variable to a latent factor is the factor loading. This loading acts as the regression coefficient of that variable on the factor: it tells how much the observed variable is expected to change when the latent factor changes by one unit. If you standardize the variables and the factor, the standardized loading becomes the correlation between the variable and the factor, clarifying the strength of their relationship. Factor scores are the estimated values of the latent factors for each case, computed from the loadings and observed data, not the regression coefficients themselves. The transformation matrix collects all such loadings to transform between observed-variable space and factor space, but the single-variable regression coefficient on the latent factor is the loading.

In factor analysis, observed variables are modeled as linear functions of one or more latent factors plus error. The coefficient that links a specific observed variable to a latent factor is the factor loading. This loading acts as the regression coefficient of that variable on the factor: it tells how much the observed variable is expected to change when the latent factor changes by one unit. If you standardize the variables and the factor, the standardized loading becomes the correlation between the variable and the factor, clarifying the strength of their relationship. Factor scores are the estimated values of the latent factors for each case, computed from the loadings and observed data, not the regression coefficients themselves. The transformation matrix collects all such loadings to transform between observed-variable space and factor space, but the single-variable regression coefficient on the latent factor is the loading.