Which term describes a matrix used in factor analysis that contains the angles through which factors are rotated in factor rotation?

Which term describes a matrix used in factor analysis that contains the angles through which factors are rotated in factor rotation?

• A. Fixed coefficient
• B. Factor score
• C. Factorial ANOVA
• D. Factor transformation matrix, ∧

Answer: (D)

In factor analysis, rotation is used to make the factor structure easier to interpret by redefining the axes of the factor space. This redefinition is accomplished by applying a transformation matrix to the unrotated factor loadings, and the matrix that contains the angles of rotation between the factors is the factor transformation matrix, often denoted by ∧. In simple terms, this matrix specifies how much to tilt or rotate each factor toward new directions, and multiplying it by the original loadings yields the rotated loadings. This concept is distinct from fixed coefficients, which are constants in a model, from factor scores, which are the estimated factor values for observations, and from factorial ANOVA, which is a different statistical technique.

In factor analysis, rotation is used to make the factor structure easier to interpret by redefining the axes of the factor space. This redefinition is accomplished by applying a transformation matrix to the unrotated factor loadings, and the matrix that contains the angles of rotation between the factors is the factor transformation matrix, often denoted by ∧. In simple terms, this matrix specifies how much to tilt or rotate each factor toward new directions, and multiplying it by the original loadings yields the rotated loadings. This concept is distinct from fixed coefficients, which are constants in a model, from factor scores, which are the estimated factor values for observations, and from factorial ANOVA, which is a different statistical technique.