Which statement about the structure matrix and pattern matrix under orthogonal rotation is true?

Which statement about the structure matrix and pattern matrix under orthogonal rotation is true?

• A. The structure matrix is the same as the pattern matrix under orthogonal rotation.
• B. The structure matrix is always unrelated to the pattern matrix.
• C. The pattern matrix includes residual correlations.
• D. The structure matrix contains regression coefficients.

Answer: (C)

Under orthogonal rotation, the factors are uncorrelated, so the correlation between each observed variable and a factor is the same as the regression loading of that variable on that factor. In other words, the structure matrix and the pattern matrix become identical because the factor correlation matrix is the identity. The pattern matrix shows the standardized regression coefficients (loadings) of variables on the factors, while the structure matrix shows the correlations between variables and factors. When rotation is orthogonal, those two sets of numbers match, so they are the same. Residual correlations or error-related terms aren’t what the pattern matrix carries, and the structure matrix isn’t a matrix of regression coefficients.

Under orthogonal rotation, the factors are uncorrelated, so the correlation between each observed variable and a factor is the same as the regression loading of that variable on that factor. In other words, the structure matrix and the pattern matrix become identical because the factor correlation matrix is the identity.

The pattern matrix shows the standardized regression coefficients (loadings) of variables on the factors, while the structure matrix shows the correlations between variables and factors. When rotation is orthogonal, those two sets of numbers match, so they are the same.

Residual correlations or error-related terms aren’t what the pattern matrix carries, and the structure matrix isn’t a matrix of regression coefficients.