Principal components analysis and canonical correlations analysis for three-mode data and their applications to questionnaire data
| Project/Area Number |
14510132
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
教育・社会系心理学
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| Research Institution | Nagoya University |
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Principal Investigator |
MURAKAMI Takashi Nagoya University, Graduate school of education and human development, Professor, 大学院・教育発達科学研究科, 教授 (70093078)
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| Project Period (FY) |
2002 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2003: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2002: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | Principal components analysis / Canonical correlation analysis / Three-mode data / Procrustes method / Questionnaire data / Linear composites / Psychological measurement / Construct validity / 一般化正準分析 / 潜在方程式モデル / 3相データ解析 / シミュレーション |
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| Research Abstract |
The traditional procedure of scale construction for measuring psychological individual differences by the use of factor analytical method has two distinctive drawbacks:
(1)It is based on internal consistency between items and ignores the relationships with external information. As the results, scores of (sub)scales sometimes lack of constructive validity although they have sufficiently high reliability.
(2)Items with elaborated wordings tend to be removed from the definitions of subscales as 'remainder items' due to relatively low correlations with questions with simple wordings although they could contribute to increasing validity by reflecting some subtle aspects of intended constructs.
These two propositions suggest that one should explore different optimization criteria which generate more or less different weights for linear composites of item responses from ones obtained from standard principal components analysis (PCA). We proposed two newly developed psychometric techniques, and d
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emonstrated their possibility to overcome drawbacks mentioned above. The first one, modified tucker2 (a simplified version of three-mode principal components analysis), showed that it generates remarkably different sets of weights from ordinary PCA when a subset of internally consistent items have higher correlations with external variables than others. In addition, it was also shown that one can balance the 'bandwidth-fidelity dilemma' caused by the differences of correlations by changing the number of the second-order components. The second (set of) methods, orthogonal and oblique direct procrustes techniques, demonstrated that one may obtain (sub)scales whose pattern approximate the theoretically specified target matrix in any conditions while the amount of explained variances would be very small if the target is not congruent to the correlational structure of the given data. Oblique method optimizing the pattern (the matrix of standard regression weights) rather than structure (the matrix of correlations) worked better than orthogonal one. Less
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Report
(3 results)
Research Products
(8 results)
