Factor Analysis by Limited Scales: Which Factors to Analyze?

Factor Analysis (FA) and Principal Component Analysis (PCA) are well-known main tools of the multivariate statistics for data analysis, reduction, and visualization. Commonly, the analysis and interpretation of their solutions is performed for each of several main eigenvectors with variances explaining a big part of the total variability in data. The recommendation is to determine if all the main vectors are really needed in the analysis, or some of them should be skipped if they correspond to the absence of the analyzing features. A simple criterion for identifying redundant vectors of loadings is their negative correlation with the vector of mean values of the original variables. Limited Likert scales of measurements are considered, and it is shown variables correlations and variances are connected to the mean values. FA and PCA structures defined by subsets of highly related variables can correspond to the lower levels of Likert scales meaning the absence of the measured features, so these loading vectors could be senseless for interpretation. Numerical examples are discussed on marketing research data