Structural analysis of conditional models
Structural analysis is applied to exploit sparsity in the solving of a system of equations [Direct Methods for Sparse Matrices. Monographs on Numerical Analysis (1989)]. Zaher [Conditional modeling (1995)] studied the issues involved in the structural analysis of conditional models and presented a methodology to ensure consistency in a conditional model, the complexity of such an analysis being combinatorial. In that work Zaher considered only cases in which the number of variables and equations of all the alternatives in a conditional model are the same. In this paper, an extension to Zaher's consistency analysis is presented. This extension allows the consistency analysis to be applied to the conditional models in which the number of variables and equations for each of the alternatives may not be the same. Also, we show how, by taking advantage of the structure of the problem, it is sometimes possible to reduce the combinatorial effort required by such an analysis. In particular, the cases of the existence of repeated structures and common incidence pattern among alternatives are discussed. (C) 2002 Elsevier Science Ltd. All rights reserved.
structural analysis conditional models variable partitioning