Iterative principal factor analysis -application on ordinal data

Abstract

This study discusses the procedure of variables reduction that improves assessment of attributes for a subject of interest. Details of how measured variables can be used to obtain a set of unobserved underlying factors are provided. These factors though considered obvious it is shown how they can be quantified. Two ordinal data sets of data are used to discuss the different considerations of the procedure. Starting with results of principal component analysis the study uses iterative principal factor analysis. Assuming orthogonal relationship of possible sets of factors, Varimax rotation is applied to distribute variation among factors. The results show how a better fit of a common factor model can be obtained with the consideration of changes in individual communalities. The model considered to provide the best fit explains 62.5% of the variation and includes measured variables with communalities more than 0.5.