An iterative algorithm for analysis of variance

In this paper, an iterative algorithm is proposed for computing estimates of parameters and sums of squares in non-orthogonal multivariate analysis of variance, without inverting any matrix. It is useful in the case of a large design matrix for it saves memory and computation time. It was first proposed by Stevens (1948) for 3 factors and is here generalised to any number of factors and interactions of any order. Convergence properties are studied. The more orthogonal is the design, the faster is the convergence. Several examples are provided.