2005 Fiscal Year Final Research Report Summary
Applications of asymptotic theory to factor analysis and structural equation modeling
| Project/Area Number |
16500167
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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 |
Statistical science
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| Research Institution | Otaru University of Commerce |
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Principal Investigator |
OGASAWARA Haruhiko Otaru University of Commerce, Faculty of Commerce, Professor, 商学部, 教授 (70271731)
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| Project Period (FY) |
2004 – 2005
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| Keywords | factor analysis / principal component analysis / structural eauation modeling / Edgeworth expansion / Studentized statistics / higher-order asymptotic SE / asymptotic bias / asymptotic robustness |
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| Research Abstract |
(1)Derivation of the asymptotic bias in factor analysis (FA)
In factor analysis, the estimators of factor loadings are of primary interest. So, the asymptotic biases of the estimators of factor loadings are derived under nonnormality, where the loadings are possibly orthogonally rotated.
(2)Derivation of the asymptotic bias in principal component analysis (PCA)
In principal component analysis, the asymptotic biases of the orthogonally or obliquely rotated component loading estimators are derived under nonnormality.
(3)Asymptotic expansion of the parameter estimators
Edgeworth expansions of the parameter estimators in covariance structures are given under nonnormality. To have the confidence intervals of the parameters, the Cornish-Fisher expansions of the Studentized estimators are derived.
(4)Higher-order asymptotic standard error
Higher-order asymptotic standard errors of the parameter estimators are provided using an extended formula in implicit functions in structural equation modeling.
(5)Derivation of the asymptotic robustness of the asymptotic biases in structural equation modeling
The asymptotic robustness of the normal-theory asymptotic biases of the parameter estimators in structural models are derived under some conditions against the violation of the assumption of normality.
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Research Products
(10 results)
