Principal Components and Factor Analysis

Select the Quick tab of the Factor Analysis Results dialog box to access the most commonly used options. The remaining tabs (Explained variance, Loadings, Factor scores, and Descriptives tabs) contain options to explore the results of your analyses in more detail.

Eigenvalues. Click the Eigenvalues button to produce a spreadsheet with the eigenvalues. The relative (percent) and cumulative eigenvalues are also reported. The interpretation of eigenvalues is described in the Introductory Overviews. In general, the eigenvalues reflect the amount of common variance accounted for by the respective number of factors.

Factor rotation. Use the Factor rotation box to select an orientation of axes. As discussed in the Introductory Overviews, the rotational orientation of axes in factor analysis is more or less arbitrary. However, numerous rotational strategies have been proposed to choose an orientation of axes that is most interpretable (i.e., approximates simple structure). You have access to several of these strategies in the Factor rotation box.

Summary: Factor loadings. Click the Summary: Factor loadings button to produce a spreadsheet with the current factor loadings, that is, rotated in the manner indicated in the Factor rotation box (see above). The default statistical plots for this spreadsheet are the 2D or 3D scatterplots of factor loadings. Factor loadings can be interpreted as correlations between the respective variables and factors; thus, they represent the most important information for the interpretation of factors. Refer to the Introductory Overviews for additional details. The default specifies that factor loadings greater than 0.7 are highlighted in the spreadsheet.

Note: Computation details for Explained Variance and Proportion of Total Variance:

Explained Variance for a given factor is the square of the loadings across the variables for the given factor.

Proportion of Total Variance is Explained Variance divided by the Total Variance in the data set.

In Factor Analysis, the analysis works on the correlation matrix or equivalently the standardized variables so that each variable is a variance of 1, thus, you can divide the explained variance by the total number of variables to get the proportion of total variance.

Plot of factor loadings, 2D. Click the Plot of factor loadings, 2D button to produce a 2D scatterplot of the current factor loadings. Visual inspection of loadings often suggests a clearer interpretation of factors.