PERFORMANCE OF MODIFIED PRINCIPAL COMPONENTS

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  • Iizuka Masaya
    Faculty of Law, Okayama University
  • Mori Yuichi
    Department of Socio-Information, Okayama University of Science
  • Tarumi Tomoyuki
    Department of Environmental and Mathematical Sciences, Okayama University
  • Tanaka Yutaka
    Department of Environmental and Mathematical Sciences, Okayama University

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Other Title
  • 拡張主成分の性能の評価
  • カクチョウ シュセイブン ノ セイノウ ノ ヒョウカ

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Modified principal component analysis (M.PCA) derives principal components (PCs) which are computed using only a selected subset but which represent all the variables including those not selected as well as possible. When we apply ordinary principal component analysis (O.PCA) to the same selected variables, the derived PCs represent only information of the subset of variables. This means that PCs obtained by M.PCA are expected to contain more information about the latent structure behind the whole variables than those obtained by O.PCA. To confirm this, a simulation study is conducted in which the performance of M.PCA and that of O.PCA are compared: 1) several 100 artificial data sets are generated based on one- or two-factor model with a couple of loading patterns; 2) M.PCA and O.PCA are applied to the data sets after performing variable selection; 3) the reproducibility of PCs computed by M.PCA and that by O.PCA are measured by the closeness between the derived PCs and the latent factors of each of the data sets. From the results that the reproducibility of M.PCA are better than that of O.PCA for most of 100 data sets, it can be stated that M.PCA can derive more reasonable PCs than O.PCA in the sense of reproducing the latent factors/structures.

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