CONSTRAINED 3-MODE FACTOR-ANALYSIS AS A TOOL FOR PARAMETER-ESTIMATIONWITH 2ND-ORDER INSTRUMENTAL DATA

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