In factor analysis, which term refers to the matrix used during rotation that encodes the orientation of the factors?

In factor analysis, which term refers to the matrix used during rotation that encodes the orientation of the factors?

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

Answer: (D)

During factor rotation, you reorient the latent factor axes by applying a rotation (transformation) matrix to the unrotated factor loading matrix. This transformation matrix encodes how the factors are oriented in relation to the observed variables. By multiplying the original loadings by this matrix, you obtain the rotated loadings that reflect the new orientation and typically reveal a simpler structure. In orthogonal rotation, this matrix is orthogonal, preserving the amount of variance attributed to each factor while changing their directions. The specific term used for this matrix is the factor transformation matrix, ∧. The other options don’t capture the idea of reorienting the factor axes: a fixed coefficient is just a constant, a factor score is the estimated factor value for each case, and Fisher's exact test is unrelated to rotation.

During factor rotation, you reorient the latent factor axes by applying a rotation (transformation) matrix to the unrotated factor loading matrix. This transformation matrix encodes how the factors are oriented in relation to the observed variables. By multiplying the original loadings by this matrix, you obtain the rotated loadings that reflect the new orientation and typically reveal a simpler structure. In orthogonal rotation, this matrix is orthogonal, preserving the amount of variance attributed to each factor while changing their directions. The specific term used for this matrix is the factor transformation matrix, ∧. The other options don’t capture the idea of reorienting the factor axes: a fixed coefficient is just a constant, a factor score is the estimated factor value for each case, and Fisher's exact test is unrelated to rotation.