Shifted multiplicative models for nonadditive two-way tables

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Abstract
This paper presents analysis of a two-way table of data using a "shifted multiplicative model (SHMM) of the form The least squares estimates of the multiplicative terms are obtained from singular value decomposition of the matrix where but the least squares estimate of the shift parameter depends on estimates of parameters contained in the multiplicative terms. The sum of squares can be minimized as a function only of for which iterative Newton-Raphson and generalized En algorithms are developed. Expectations of sums of squares owing to sequentially increasing the number, t, of multiplicative terms (presented in an AMOVA format) were obtained by Monte Carlo simulation for the case where errors are i.i.d.N(0,σ2) and all The analysis is illustrated with several examples from the literature.