Principal Components and Factor Analysis

Select the Loadings tab of the Factor Analysis Results dialog to access the options described here.

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 containing the current factor loadings, that is, rotated in the manner indicated in the Factor rotation box. 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. By default, factor loadings greater than 0.7 (and less than -1) are highlighted in the spreadsheet.

Highlight factor loadings greater than. Use the Highlight factor loadings greater than box to enter the cut-off value for factor loadings that are to be highlighted in the spreadsheet. 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.

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

Plot of loadings, 3D. Click the Plot of loadings, 3D button to produce a 3D scatterplot of the current factor loadings. Visual inspection of loadings often suggests a clearer interpretation of factors. This button is only available if three or more factors are extracted via the Define Method of Factor Extraction dialog box - Advanced tab.

Hierarchical analysis of oblique factors. Click the Hierarchical analysis of oblique factors to perform a hierarchical factor analysis (see Thompson, 1951; Schmid & Leiman, 1957; Wherry, 1959, 1975, 1984) and display spreadsheets with the complete results. In short, STATISTICA will first identify clusters of marker variables (with high unique factor loadings, and low cross-loadings) and rotate axes through those clusters. If no such clear clusters of "marker variables" can be identified for each oblique factor, the hierarchical analysis will not be performed. Next, the correlations between those (oblique) factors is computed, and that correlation matrix of oblique factors is further factor-analyzed to yield a set of orthogonal factors that divide the variability in the items into that due to shared or common variance (secondary factors), and unique variance due to the clusters of similar variables (items) in the analysis (primary factors). This option is only available if more than one factor was extracted via the Define Method of Factor Extraction dialog box - Advanced tab.