The defining characteristic that distinguishes between PCA and factor analysis is that in PCA we assume that all variability in an item should be used in the analysis, while in factor analysis, we define a priori the number of factors that we want to extract, and the extracted axes will be scaled to the variance along the new improved axes.
- In factor analysis, it is often difficult to interpret the loadings, because they may show intermediate correlations with a large number of variables. Rotation of extracted factors attempts to put the factors in a simpler position with respect to the original variables in a manner that either minimizes (move towards one) or maximizes (moves towards zero) individual variable loadings. Aabel provides the Kaiser varimax rotation, which is the most commonly used.
- The R-mode factor analysis considers the inter-relationships in a matrix of correlation between variables. The Q-mode analyzes the inter-object relationships.
The factor analysis output includes the scores, loadings, and correlation matrices.
- To represent the factor loadings graphically, you can for example, use the binary scatter chart while using the option of plotting the X and Y axes through zero and connecting the data points to origo.
- To compare the fraction of variance of the variables explained by the model and the fraction that is not, you can also use the multiple-Y column graphs.
- For a graphical representation of the correlation matrices, you can use the heatmap diagram.
Pre-Processing the Data
PCA and factor analysis methods allow optional pre-processing of the data prior to the main analysis. Examples of data transformations that can be used (as part of PCA or factor analysis) are:
- Log centering
- Mean centering
- Taking square root
- Ranking variables individually
- Ranking variables jointly