MAPF and MAPS: Subroutines for the Number of Prineipal Components

One of the key issues in the use of principal components analysis in exploratory applications is the determination of how many components to retain. The problem is one of finding how many components are sufficient for capturing the systematic variance in the observations. Although a number of criteria are available, Velicefs (1976) residual partial correlation 1~I~P test is probably the best test available in terms of statistical and computational characteristics (Reddon, in press). To the extent that covariance represents systematic variance, a condition that is generally true asymptotically and even in moderate sized samples, the MAP test retains components until additional components represent proportionately