Sparse matrix methods for unbalanced multifactor analysis of variance and covariance
Shu-Yen Ho, Jerome H. Klotz · Journal of Statistical Computation and Simulation · 1992
We apply the contrast algorithm to compute hypothesis sums of squares for complete multifactor unbalanced analysis of variance and covariance. We find a sparse structure for the system of linear equations required by the algorithm. For solution, we find an optimal arrangement of factors that produces a minimum of non zero fills for the triangular decomposition of the sparse equation matrix. We examine several sparse matrix methods that do not improve upon this simple factor arrangement. We also consider iterative methods for solving the linear equations and present a solution for the balanced case that provides an effective initial value for convergence. We present examples indicating a considerable savings in storage and computation time in larger designs.