Rotational Tools for Factor Analytic Models

Rotational ambiguity is a major problem in the application of factor analysis to a variety of multivariate mixture resolution problems and particularly important in the analysis of environmental data. As part of the development of an implementation of positive matrix factorization for the U.S. Environmental Protection Agency to distribute in support of airborne particle source identification and apportionment, several tools have been developed to control the rotations and explore the extent of rotational solution space. This discussion of the nature of the rotational tools provides an understanding of these rotational tools as well as the basis for their incorporation into other implementations of least-squares based solutions to the factor analysis problem. Several example algorithms are presented. Copyright (C) 2008 John Wiley & Sons, Ltd.