Factor Analysis by MINRES

Abstract

The basic idea of exploratory factor analysis is the following. For a given set of observed response variables one wants to find a set of latent factors, fewer in number than the observed variables. These factors are supposed to account for the intercorrelations of the response variables in the sense that when the factors are partialed out from the observed variables, there should no longer remain any correlations between these. The term exploratory means that one does not know how many factors are needed nor does one know the factorial nature of the observed variables. Before 1970 the term factor analysis was used without the word exploratory; this term was added later to distinguish it from confirmatory factor analysis introduced around 1969 (see, e.g.,J oreskog, 1969) The term MINRES (MINimum RESiduals) was first introduced by Harry Harman (1960) as a way of doing factor analysis by least squares. This was at a time when nobody cared about where the data came from or what distributions it had. It was only a matter of fitting a matrix of factor loadings to the correlation matrix.