General term for the structure matrix in principal components analysis.

General term for the structure matrix in principal components analysis.

• A. Covariance matrix
• B. Communality
• C. Factor loading
• D. Component matrix

Answer: (D)

In PCA, the matrix that packages how each original variable relates to each extracted component is captured by the component matrix. This matrix holds the loadings, which are essentially the correlations between variables and components (often identical to the loadings when variables are standardized). So the structure matrix, describing these relationships, is best labeled the component matrix because it centralizes all variable–component relationships in one place. Thinking of the alternatives helps: the covariance matrix shows how variables covary with each other, not how they relate to components; communality is about how much of a variable’s variance is explained by all components together; a factor loading is the term typical for factor analysis for a single variable–factor relationship, whereas the component matrix sums up these loadings across all components.

In PCA, the matrix that packages how each original variable relates to each extracted component is captured by the component matrix. This matrix holds the loadings, which are essentially the correlations between variables and components (often identical to the loadings when variables are standardized). So the structure matrix, describing these relationships, is best labeled the component matrix because it centralizes all variable–component relationships in one place.

Thinking of the alternatives helps: the covariance matrix shows how variables covary with each other, not how they relate to components; communality is about how much of a variable’s variance is explained by all components together; a factor loading is the term typical for factor analysis for a single variable–factor relationship, whereas the component matrix sums up these loadings across all components.