# PCA/Factor Visualizations

The following tables and options are available for PCA/Factor visualizations.

Scree Plot

Used as an aid in selecting the number of components or factors to extract. Shows the eigenvalues of the observed correlation or covariance matrix of the features on the vertical axis, in decreasing order on the horizontal axis. The eigenvalues are the amounts of variance associated with the respective principal components. In some cases a clear break or “elbow” in the lines connecting the eigenvalues appears, identifying a point beyond which further decreases in values are relatively small and gradual. The number associated with such a point is often chosen as the number of components or factors to extract.

Communalities table

If a correlation matrix is analyzed, shows two columns, one containing proportions of variance retaining all components (labeled Initial, which are always 1) and proportions of variance associated with the extracted factors or components (labeled Extraction). If a covariance matrix is analyzed, these columns are also labeled as Rescaled and are preceded by two columns showing the variances in raw value (labeled Raw).

Total Variance Explained table

The Initial section shows eigenvalues, percentages of variance and cumulative percentages of total variance for each eigenvalue. The Extraction Sums of Squared Loadings section shows sums of squared extracted factor or component loadings and associated percentages of variance, which will be the same as the corresponding values in the Initial section for principal components, but different for factor analysis. If the extracted solution has been rotated, a Rotation Sums of Squared loadings section will also be shown. If the rotation method was orthogonal, this section will contain the same three columns as the other sections, but if the rotation method was oblique, producing correlated factors or pseudo-components, only the sums of squared loadings for the oblique rotation will appear, since proportions of variance for correlated factors cannot be added to obtain the total amount. If a covariance matrix has been analyzed, the table will have all of the information mentioned previously in both Raw and Rescaled metrics.

Image Covariance Matrix

Shown when the image extraction method is specified, this matrix contains estimated variances and covariances of the features that are predictable from regression of each feature on the other features. When a correlation matrix is analyzed, the matrix is shown in a standardized format where elements range in magnitude from 0 to 1.

Component/Factor Matrix

Shows the loadings of the features on the extracted factors or principal components. For analysis of a correlation matrix, these are correlations between the observed features and the factors or components. For analysis of a covariance matrix, the Raw versions provide covariances and the Rescaled versions provide correlations. For a factor analysis model, these are also the regression coefficients for the features on the latent factors, in either raw or standardized metrics.

Goodness-of-fit Test table

If the generalized least squares or maximum likelihood method has been used to extract the factor(s), this table provides a likelihood-ratio test of the null hypothesis that the number of factors extracted is the correct number of factors and that any residual correlation among features is noise, or chance covariation.

Rotated Component/Factor Matrix

For analyses involving orthogonal rotations of factors or principal components, this table shows the loadings of the features on the rotated factors or components. For analysis of a correlation matrix, these are correlations between the observed features and the rotated factors or components. For analysis of a covariance matrix, the Raw versions provide covariances and the Rescaled versions provide correlations. For a factor analysis model, these are also the regression coefficients for the features on the rotated latent factors, in either raw or standardized metrics.

Pattern Matrix

For analyses involving oblique (or non-orthogonal) rotations of factors or principal components, this table shows the loadings of the features on the rotated factors or components in either raw and standardized metrics for analyses involving covariance matrices and in standardized metrics for analyses involving correlation matrices. For a factor analysis model, these are also the regression coefficients for the features on the latent factors, in either raw or standardized metrics.

Structure Matrix

For analyses involving oblique (or non-orthogonal) rotations of factors or principal components, this table shows the covariances (Raw versions) and correlations (Rescaled versions) of the features with the rotated factors or components.

Factor Correlation Matrix

For analyses involving oblique (or non-orthogonal) rotations of factors or principal components, this table shows the estimated correlations among the rotated factors or pseudo-components.

## Next steps

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