Analysis of Nonadditive Multiway Classifications
Analysis of Nonadditive Multiway Classifications
复制标题
非相加多路分类分析
DOI：
10.1080/01621459.1989.10478872
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发表时间：
1989
影响因子：
3.7
通讯作者：
Mervyn G. Marasinghe
中科院分区：
文献类型：
--
作者：
R. J. Boik;Mervyn G. Marasinghe
摘要本文研究了无重复多向分类中的可加性检验和σ2估计问题。为了对非可加性建模并联合估计σ2，必须限制交互作用参数空间;否则模型将饱和。我们使用的参数化是Mandel（1971）和约翰逊和Graybill（1972 a）的双向倍增相互作用模型的多向扩展。例如，在三向分类中，我们将交互作用建模为θijk = λδ 1 i δ 2 j δ 3 k。这种结构是k模式主成分模型的一个特例，在心理测量学文献中受到了相当大的关注（Kapteyn，Neudecker和Wansbeek 1986）。我们构造了一个λ = 0的精确检验，并提出了一个σ2的估计量，当检测到相互作用时可以使用。我们的检验近似于Ho：λ = 0的似然比检验（LRT）。建议的测试基本上具有相同的功率的LRT，但更容易计算，和准确的零分布的测试…
Abstract 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 = λδ 1i δ2j δ3k . This structure is a special case of the k-mode principal components model, which has received considerable attention in the psychometric literature (Kapteyn, Neudecker, and Wansbeek 1986). We construct an exact test of λ = 0 and propose an estimator of σ2 that can be used when interaction has been detected. Our test is an approximation to the likelihood ratio test (LRT) of Ho : λ = 0. The proposed test has essentially the same power as the LRT but is easier to compute, and the exact null distribution of the test...