A Biometrics Invited Paper. Factor Analysis: An Introduction to Essentials I. The Purpose and Underlying Models

Factor analysis aims to explain observed relations among numerous variables in terms of simpler relations. The simplification may consist of producing a set of classificatory categories, or creating a smaller number of hypothetical variables. Such resolution is so central to all scientific work that we must pause in a moment to ask about the relation of factor analysis to investigatory methods in general. However, it may be said forthwith that its most valuable functions lie in the biological and behavioral sciences, where a great array of phenomena are multiply determined and where the conceptual independent variables are not easily located and agreed upon. For example, in the behavioral sciences, a student of delinquency or mental disorder may have doubts whether there is such a single thing as delinquency or mental disorder and must have an open mind as to where the important causal influences lie in the bewildering array of possibilities. In such a situation he may take a set of variables, each semantically entitled to be called a form of delinquency, and measure each on members of a population and then seek for the functional unities by computing correlation coefficients for each pair of variables over the list of people concerned. Into this correlation matrix-as we designate the square matrix of coefficients shown in Table 1 below-he may also introduce measures of putative causal influences, seeking in the subsequent factor analysis to find those underlying 'hypothetical variables' or factors among them which are of -theoretical importance. Or again a biologist concerned with nutrition might correlate-over many animals, each fed in a different wayvarious signs of health and disease and various ingredients in the food. The vitamins, for example, might historically have been located-perhaps more economically of research time than they were-as factors each with a certain pattern of deficiency signs and of relative presence in various foods.