Exploring \(N\)-way tables with sums-of-products models (Q689450)

The paper deals with the following model (a variant of the analysis of variance model): let \(A_ 1,\dots, A_ N\) be a collection of finite sets, \(A\) their Cartesian product, \(G\) a finite set of integers, \(\{I_ i\): \(i\in G\}\) a collection of subsets of \(1,\dots, N\) and \(H_{ij}\) a mapping of \(A_ j\) into the reals. Then a mapping \(F\) from \(A\) into the reals is a sum-of-product model if \(F(a_ 1,\dots, a_ N)= \sum_{i\in G} \prod_{j\in I_ i} H_{ij} (a_ j)\). It is also supposed that the index sets \(I_ i\) must be unique and that the factor scales \((H_{ij})\) must satisfy a property called joint non-constancy. The key concept is the concept of multifactor residuals with respect to a set of factors. The paper presents a way of using these models to explore \(N\)-way tables and studies their theoretical properties.