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非加性多维分类数据的分析AI 解读

This article considers the problems of testing additivity and estimating σ2 in unreplicated multiway classifications. To model nonadditivity and jointly estimate σ2, the interaction parameter space must be restricted; otherwise the model is saturated. The parameterization we use is a multiway extension of the two-way multiplicative interaction model of Mandel (1971) and Johnson and Graybill (1972a). For example, in a three-way classification, we model interaction as θijk =…

乘法交互模型中不完全可加性的检验AI 解读

Consider the multiplicative interaction model defined by yij = μ + τ i + β j + λα i γ j + ∈ ij , i = 1, 2, …, t, j = 1, 2, …, b, where it is assumed that Σ i τ i = Σ j β j = Σ i α i = σ j γ j = 0 and γ i α i 2 = γ j γ j 2 = 1. It is also assumed that the ∈ ij are distributed NID (0, σ2). This article derives the likelihood ratio test of H 0: Hα = 0 and Gγ = 0 vs. Ha :Hα ≈ 0 or Gγ ≈ 0, where H is a q × t matrix of row contrasts of rank q and G is a r × b matrix of row…