What do factor loadings describe in factor analysis?

What do factor loadings describe in factor analysis?

• A. They describe the strength of the relationship between a variable and a factor.
• B. They are the eigenvalues of the factor.
• C. They indicate the total variance explained by all factors.
• D. They are the same as correlation coefficients between observed variables.

Answer: (A)

Factor loadings describe how strongly each observed variable relates to a latent factor. In the factor-analytic model, every variable is expressed as a combination of the underlying factors plus unique variance, and the loading is the coefficient that links a specific factor to that variable. A larger absolute value means the variable reflects more of the shared variance tied to that factor, and the sign indicates whether the relationship is positive or negative. After standardization and rotation, loadings are often interpreted similarly to correlations between the variable and the factor, and the squared loading shows how much of that variable’s variance is explained by that factor (with the sum across factors giving the variable’s communality). Why the other ideas don’t fit: eigenvalues quantify how much variance a factor explains overall across all variables, not how a single variable relates to a factor, and the total variance explained by all factors is the sum of those eigenvalues. The correlations between observed variables are relationships among the observed items themselves, not with the latent factors.

Factor loadings describe how strongly each observed variable relates to a latent factor. In the factor-analytic model, every variable is expressed as a combination of the underlying factors plus unique variance, and the loading is the coefficient that links a specific factor to that variable. A larger absolute value means the variable reflects more of the shared variance tied to that factor, and the sign indicates whether the relationship is positive or negative. After standardization and rotation, loadings are often interpreted similarly to correlations between the variable and the factor, and the squared loading shows how much of that variable’s variance is explained by that factor (with the sum across factors giving the variable’s communality).

Why the other ideas don’t fit: eigenvalues quantify how much variance a factor explains overall across all variables, not how a single variable relates to a factor, and the total variance explained by all factors is the sum of those eigenvalues. The correlations between observed variables are relationships among the observed items themselves, not with the latent factors.