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A psychometric study of generalized nonmetric principal components anlysis for ordered categorical data

Research Project

Project/Area Number 24530926
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Experimental psychology
Research InstitutionChukyo University

Principal Investigator

MURAKAMI Takashi  中京大学, 現代社会学部, 教授 (70093078)

Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords数量化 / 多重対応分析 / メトリック / ノンメトリック / 直交回転 / 斜交回転 / 直交多項式 / Likert 尺度 / 主成分分析 / Likert尺度 / カテゴリカルデータ / 数量化理論 / 主クラスター成分分析 / 余剰次元の解釈 / 負荷行列の回転 / 量的データと質的データ / 心理学的尺度構成
Outline of Final Research Achievements

A procedure for analyzing ordered categorical variables is developed based on a relationship between Multiple Correspondence Analysis (MCA) and Principal Components Analysis (PCA), which has not been found so far. By metric scaling of categories using orthogonal polynomials, and Harris-Kaiser type rotation, MCA is transformed into PCA without changing the size of explained variances and quantified scores given to individual up to orthogonal transformations. The metamorphosed PCA can be used to evaluate the appropriateness of Likert-type scoring as simple sums of category numbers, and the interpretability of nonlinear components which are usually considered to be spurious dimensions. Rotation attaining the simple structure makes it possible to treat far more numbers of dimensions than MCA by separating contents of dimensions each other.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (11 results)

All 2014 2013 2012

All Journal Article (5 results) Presentation (6 results) (of which Invited: 1 results)

  • [Journal Article] なぜプロ野球ファンは球場で観戦するのか 「3つの人間関係」の提案2014

    • Author(s)
      村上 隆
    • Journal Title

      中京大学現代社会学部紀要

      Volume: 8 Pages: 149-181

    • Related Report
      2014 Annual Research Report
  • [Journal Article] 完全単純構造・主クラスター成分分析・resampling による確認: 心理測定尺度構成のための単純な分析方法試論2014

    • Author(s)
      村上 隆
    • Journal Title

      中京大学現代社会学部紀要

      Volume: 9 Pages: 47-89

    • NAID

      40020231065

    • Related Report
      2014 Annual Research Report
  • [Journal Article] なぜプロ野球ファンは球場で観戦するのか?『3つの人間関係」の提案2014

    • Author(s)
      村上 隆
    • Journal Title

      中京大学現代社会学部紀要

      Volume: 7 Pages: 175-207

    • Related Report
      2013 Research-status Report
  • [Journal Article] 発達障碍者の援助に役立つ数量的アセスメント(2)2013

    • Author(s)
      村上 隆・行廣隆次・安永和央・伊藤大幸・谷伊織・平島太郎
    • Journal Title

      アスペハート

      Volume: 35 Pages: 108-121

    • Related Report
      2013 Research-status Report
  • [Journal Article] 数量化3類と多重対応分析2012

    • Author(s)
      村上 隆
    • Journal Title

      社会と調査

      Volume: 9 Pages: 48-62

    • Related Report
      2012 Research-status Report
  • [Presentation] A simple exploratory method to obtain the linear composites with a very simple pattern2013

    • Author(s)
      Takashi Murakami
    • Organizer
      Psychometric society
    • Place of Presentation
      Musis Sacre Arnhem, the Netherland
    • Related Report
      2013 Research-status Report
  • [Presentation] セミメトリック主成分分析と3値データへの応用2013

    • Author(s)
      村上 隆
    • Organizer
      日本行動計量学会
    • Place of Presentation
      東邦大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 極端な単純構造をもつ合成変量を生成する探索的「因子分析」2013

    • Author(s)
      村上 隆
    • Organizer
      日本心理学会
    • Place of Presentation
      北海道医療大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 測定の理論・方法の観点から2013

    • Author(s)
      村上 隆
    • Organizer
      日本心理学会
    • Place of Presentation
      北海道医療大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] A simple procedure for scale construction with both characteristics of Principal components analysis and Cluster analysis2013

    • Author(s)
      Murakami, T.
    • Organizer
      International Meeting of Psychometric Society, 2012
    • Place of Presentation
      Arnhem, NL
    • Related Report
      2012 Research-status Report
  • [Presentation] Semi-metric principal components analysis for ordered ternary variables2012

    • Author(s)
      Murakami, T.
    • Organizer
      International Meeting of Psychometric Society, 2012
    • Place of Presentation
      Lincoln, Nebraska, US.
    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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