Constrained three-mode factor analysis as a tool for parameter estimation with second-order instrumental data

Three-mode factor analysis models are often used in exploratory analysis of three-way data. However, in some situations it is a priori known that a particular constrained three-mode factor analysis (C3MFA) model describes an underlying process exactly. In such situations, fitting a C3MFA model to a data set can be used for both quantitative analysis (e.g. estimating concentrations of a chemical substance in a mixture) and qualitative analysis (e.g. on the basis of certain subsets of parameters one can identify the substances present in a mixture). In this paper a general algorithm for fitting a range of such C3MFA models is proposed. Whether C3MFA is used for qualitative or quantitative analysis, in both cases it is crucial that the relevant parameter estimates are uniquely determinable. In the present paper it is discussed how and to what extent uniqueness of certain model parameters can be assessed. (C) 1998 John Whey & Sons, Ltd.