Using Factor Analysis to Estimate Parameters

Abstract

Abstract Factor analysis has been traditionally utilized for three broad purposes: First, as a data reduction technique which will hopefully simplify a multivariate situation to a smaller set of dimensions and enable the researcher to utilize data on a large number of variables; second, as an indexing device in which overtly manifested data are transformed to provide the latent or unobservable trait of a phenomenon; finally, as a cluster technique which helps the researcher to classify a variety of observations into a small set of clusters which are also generally ordered. All three approaches have used a common starting point, namely, a matrix of correlations either among the variables (R type factor analysis) or among the observations (Q type factor analysis). In other words, factor analysis has been limited to associative relations. The same technique can be used in functional relations, especially to estimate parameters of all linear and several nonlinear functions. It, therefore, essentially seems to serve the same function as curve fitting techniques but with two important distinctions. First, the procedure outlined here provides estimates of parameters for each observation (individual) in the sample as well as aggregate parameters. Second, it provides decision rules for various types of functions where aggregation of observations (individuals) assumed to have certain functional relations is or is not legitimate.