Factor Analysis

as a linear combination Xi·B of the q columns of X, plus some mean-zero random error Ui·. Perhaps fewer than q terms would suffice to predict Y adequately or, more realistically, perhaps some number m < q of linear combinations of the columns ofX would suffice. That is the essence of Factor Analysis, a method proposed in 1904 by psychologist Charles Spearman in his effort to show that all measures of mental ability (mathematical skill, vocabulary, other verbal skills, artistic skills, logical reasoning ability, etc.) could be explained by a single quantity he called g for “general intelligence” (also the idea behind IQ). The same goal comes up in many application areas— to explain some rather large number q of measurements in terms of a much smaller number m. An extreme example of recent importance is the search for “genes” within DNA sequence data where q might be many thousands, much larger than the number n of subjects— a challenge for the traditional multivariate tools, leading to the development of “data mining” methodology.