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共同主成分及相关多元模型
Preliminaries principal component analysis relationships between matrices common practical components proportional covariance matrices partial common components and common space analysis how different are several covariance matrices? numerical methods. Appendices: spectral decomposition of symmetric matrices some results from matrix algebra a fortran program for the fg algorithm.
非加性多维分类数据的分析
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 =…
矩阵秩检验及其在方差分析交互作用中的应用
This article develops some general theory for testing the rank of a matrix. Applications include tests of interaction in two-factor experiments that are more powerful than the usual F test for certain reasonable alternatives. The particular tests studied are (a) the likelihood ratio (LR) test of rank(M) = 0 versus rank(M) = r, where M is a matrix of expectations, and (b) the union-intersection (UI) test of rank(M) = 0 versus rank(M) ≥ r. In the two-factor application, M is…