A psychometric study of generalized nonmetric principal components anlysis for ordered categorical data
| Project/Area Number |
24530926
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Experimental psychology
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| Research Institution | Chukyo University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| 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)
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| 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 |
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| 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.
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Report
(4 results)
Research Products
(11 results)
