Principal Component and Factor Analyses

摘要

Principal component (PCA) and factor analyses (FA) are exploratory multivariatetechniques used in studying the covariance (or correlation) structure of measurements made on individuals. The methods have been used by applied research workers in a variety of ways, from reducing high dimensional data to few functions of variables carrying the maximum possible information, grouping of similar measurements and detecting multicollinearity, to graphical representation of high dimensional data in lower dimensional spaces to visually examine to scatter of the data and detection of outliers. The computations involved in these methods and the interpretation of results in different situations are discussed. The difference between PCA and FA, and the need to choose the appropriate technique in the analysis of given data are stressed. It is shown that there is a close similarity between the growth curve models used in biometric studies and the arbitrage pricing theory model recently introduced in financial statistics.