Principal Components and Classification Analysis Results - Variables Tab

Principal Components and Factor Analysis

Select the Variables tab of the Principal Components and Classification Analysis Results dialog box to access options to produce PCCA results pertaining to variables in the current analysis. Various plotting options are available to provide a visual aid for interpretation of the results and classification of variables.

Factor coordinates of variables

Click the Factor coordinates of variables button to display a spreadsheet with the factor coordinates of the active and supplementary variables (if selected through the Variables button of the Principal Components Classification Analysis Startup Panel - Quick tab). To distinguish between the two types of variables in the current analysis, the supplementary variables are marked with an asterisk (*). The factor coordinates are commonly referred to as factor loadings, and provide useful information for the interpretation of the factors. Refer to the Introduction for additional details.

Plot var. factor coordinates, 2D.

Click the Plot var. factor coordinates, 2D button to produce a 2D scatterplot of the current set of factor coordinates for the selected pair of factors. After you click this button the Select Two Factors for the Plot dialog box gets displayed through which you can select factors for the factor axes. After you select this button, you can use one of the Options for plot of factor coord.

Options for plot of factor coord

The options in the Options for plot of factor coord. group box can be used for including objects, such as the correlation (unit) circle, the vector lines, and so on, in the Plot of factor coordinates. Note that, by default, a plot with the unit circle and the vector lines is produced, as are the names (or numbers, if names are not available) of the variables.

Vectors (points to origin)

Select the Vectors check box to plot the vector lines from the origin to the factor coordinates.

Unit circle

Select the Unit circle check box to plot the unit circle, encircling the factor coordinates. If the current analysis is based on the correlation matrix, then the area inside the unit circle represents the region of the valid (possible) factor coordinates (loadings). The closer a plotted variable is to the border of the circle, the better is its representation by the factors in the plot. The option of unit circle is not available if the current analysis is based on the covariance matrix rather than the correlation matrix (see the Analysis based on group box on the Principal Components Classification Analysis Startup Panel - Advanced tab). However, the vector lines can still be produced, if required.

Variable names

Select the Variables names option button to display the names of the variables projected on the factor-plane.

Variable numbers

Select the Variables numbers option button to display the numbers of the variables projected on the factor-plane.

No Names/Numbers

Select the No Names/Numbers option button to plot the points for the factor coordinates without displaying the names or the numbers of the variables projected on the factor-plane.

Factor & variable correlations

Click the Factor & variable correlations button to display a spreadsheet that displays the correlations between the factors and the variables in the current analysis. These correlations are identical to the factor coordinates, if the current analysis is based on the correlation matrix. However, if the current analysis is based on the covariances, then these values can be interpreted analogously to the factor loadings in a traditional factor analysis (see the Analysis based on group box on the Principal Components Classification Analysis Startup Panel - Advanced tab). Refer to the Introduction for additional details.

Communalities (Cosine²).

Click the Communalities (Cosine²) button to display a spreadsheet with the communalities. Communalities represent the proportion of variance accounted for in the respective variables by the given number of factors.

Contributions of variables

Click the Contributions of variables button to display a spreadsheet presenting the contributions of factors to the variance. These values are computed for the active cases only, and are helpful in interpreting the factor axes.

Eigenvalues

Click the Eigenvalues button to display a spreadsheet with the positive eigenvalues of the correlation or covariance matrix (depending on which was chosen for the analysis in the Analysis based on group box on the PCCA Startup Panel - Advanced tab). Note that the displayed eigenvalues are computed from the correlations or covariances of the active variables only, even if supplementary variables were selected through the Variables button on the Principal Components Classification Analysis Startup Panel - Quick tab.

Scree plot

Click the Scree plot button to produce a simple line plot of the eigenvalues, called a Scree plot (Cattell, 1966). The eigenvalues in this plot seem to level off at certain point. It is recommended that no more than the number of factors to the left of this point should be computed. Note that the scree plot plots all the eigenvalues of the correlation or covariance matrix, irrespective of the numbers of factors chosen for the current analysis (see the Principal Components and Classification Analysis Results dialog box).

Eigenvectors

Click the Eigenvectors button to display a spreadsheet with the eigenvectors corresponding to each eigenvalue.