1997 Fiscal Year Annual Research Report

複雑な統計モデルの感度分析に関する研究とソフトウェアの開発

Research Project

Project/Area Number	08680331
Research Institution	Okayama University
Principal Investigator	田中豊岡山大学, 環境理工学部, 教授 (20127567)
Co-Investigator(Kenkyū-buntansha)	尾高好政倉敷芸術科学大学, 産業科学技術部, 教授 (50109740) 栗原考次岡山大学, 環境理工学部, 助教授 (20170087) 垂水共之岡山大学, 環境理工学部, 教授 (50033915)
Keywords	Multivariate analysis / Sensitivity analysis / Influential observations / Influence function / Local influence / Influential subsets
Research Abstract	平成8-9年度の研究実施計画のうち、1)影響関数法とクックの局所影響の関係の詳細な検討、2)欠損値のある場合の多変量解析の感度分析法の提案、3)一部の変数を用いた主成分分析法とその感度分析の研究、4)多変量解析における感度分析の汎用ソフトウェアの開発、の4つに重点的に取り組んだ。1)については、多くの多変量解析を含み第2世代の多変量解析と呼ばれる共分散構造分析を取り上げ、(あ)全パラメータ/一部のパラメータに関心がある、(い)制約条件がない/ある、の2つの項目を組み合わせた4通りの場合について、影響関数を用いた接近法とクックの局所影響に基づく接近法の間にdualな関係が成り立つことを示した(ISI,51st Session;Technical Report)。この関係の利用は特にinfluential subsetsの探索に有効である。2)の欠損値のある場合の多変量解析における感度分析については、いわゆるignorable missing valuesの場合に関して、EMアルゴリズムに対して陰関数の微分法を適用して影響関数を求め、それを用いて感度分析を行う方法を提案した。日韓統計会議KJCS97および環境理工学部研究報告で報告し、われわれの提案した方法の有効性を示した。ここでも影響関数および局所影響の両方の観点から論じた。3)の一部の変数を用いた主成分分析とは予備調査で求まった沢山の項目に基づく総合指標の情報はできるだけ保存しながら、実際的な観点から項目を少なくする必要が生じた場合に対する方法論で、中規模の詳細な調査で尺度を構成し、大規模な調査でその尺度を利用した研究を使用という場合に最適である。American J.Mathematical & Management SciencesおよびData Science(by Hayashi et al.)で発表した。4)については、Windows 上で感度分析ソフトウェアSAMMIFを開発中で、第1版がCOMPSTAT98(採択)に公表されることになっている。

Research Products
(13 results)

All Other

All Publications (13 results)

[Publications] Shin,J.K.: "Cross-validatory choice for the number of principal components in principal component regression" J.Jpn.Soc.Comp.Statist.9. 53-59 (1996)
[Publications] Tanaka,Y.: "Sensitivity analysis in multivariate methods : General procedure based on influence functions and its robust version" Computer Science and Statistics. 28. 186-195 (1997)
[Publications] Tanaka,Y.: "Principal component analysis based on a subset of variables : Variable selection and sensitivity analysis" American Journal of Mathematical and Management Sciences. 6. 61-89 (1997)
[Publications] Mori,Y.: "Principal component analysis based on a subset of variables for qualitative data" Data Science,Classification,and Related Methods. 547-554 (1997)
[Publications] Kim,H.B.: "Two types of partial least squares methods in linear discriminant analysis" Data Science,Classification,and Related Methods. 261-267 (1997)
[Publications] Kim,H.B.: "Writer identification by using partial least squares linear discriminant function" SERI Journal. 1,2. 31-43 (1997)
[Publications] Tanaka,Y.: "Q-mode and R-mode influence analyses in multivariate methods" Bulletin of The International Statistical Institute,Contributed Papers,51st Session,Book 2. 191-192 (1997)
[Publications] Kim,H.B.: "Criteria to determine the number of components in partial least squares linear discriminant function" Bulletin of The International Statistical Institute,Contributed Papers,51st Session,Book 2. 167-168 (1997)
[Publications] Kim,H.J.: "Influence in multivariate statistical analyses of incomplete data" 9^<th> Korea and Japan Joint Conference of Statistics. 197-202 (1997)
[Publications] Mori,Y.: "Statistical software SAMMIF : Sensitivity analysis in multivariate methods based on influence functions" 9^<th> Korea and Japan Joint Conference of Statistics. 179-185 (1997)
[Publications] Castano-Tostado,E.: "A comparison of canonical correlation analysis and redundancy analysis from the sensitivity viewpoint" Computer Science and Statistics. 28,2. 432-436 (1997)
[Publications] Kim,H.J.: "Assessment of local influence in multivariate analyses of incomplete data" J.Faculty of Environmental Science and Technology. 3. 37-46 (1998)
[Publications] Otake,M.: "Binary data on radiation-related brain damage prenatally exposed and statistical threshold model" J.Faculty of Environmental Science and Technology. 3. 47-62 (1998)

1997 Fiscal Year Annual Research Report

複雑な統計モデルの感度分析に関する研究とソフトウェアの開発

Principal Investigator

田中 豊 岡山大学, 環境理工学部, 教授 (20127567)

Research Products

[Publications] Shin,J.K.: "Cross-validatory choice for the number of principal components in principal component regression" J.Jpn.Soc.Comp.Statist.9. 53-59 (1996)

[Publications] Tanaka,Y.: "Sensitivity analysis in multivariate methods : General procedure based on influence functions and its robust version" Computer Science and Statistics. 28. 186-195 (1997)

[Publications] Tanaka,Y.: "Principal component analysis based on a subset of variables : Variable selection and sensitivity analysis" American Journal of Mathematical and Management Sciences. 6. 61-89 (1997)

[Publications] Mori,Y.: "Principal component analysis based on a subset of variables for qualitative data" Data Science,Classification,and Related Methods. 547-554 (1997)

[Publications] Kim,H.B.: "Two types of partial least squares methods in linear discriminant analysis" Data Science,Classification,and Related Methods. 261-267 (1997)

[Publications] Kim,H.B.: "Writer identification by using partial least squares linear discriminant function" SERI Journal. 1,2. 31-43 (1997)

[Publications] Tanaka,Y.: "Q-mode and R-mode influence analyses in multivariate methods" Bulletin of The International Statistical Institute,Contributed Papers,51st Session,Book 2. 191-192 (1997)

[Publications] Kim,H.B.: "Criteria to determine the number of components in partial least squares linear discriminant function" Bulletin of The International Statistical Institute,Contributed Papers,51st Session,Book 2. 167-168 (1997)

[Publications] Kim,H.J.: "Influence in multivariate statistical analyses of incomplete data" 9^<th> Korea and Japan Joint Conference of Statistics. 197-202 (1997)

[Publications] Mori,Y.: "Statistical software SAMMIF : Sensitivity analysis in multivariate methods based on influence functions" 9^<th> Korea and Japan Joint Conference of Statistics. 179-185 (1997)

[Publications] Castano-Tostado,E.: "A comparison of canonical correlation analysis and redundancy analysis from the sensitivity viewpoint" Computer Science and Statistics. 28,2. 432-436 (1997)

[Publications] Kim,H.J.: "Assessment of local influence in multivariate analyses of incomplete data" J.Faculty of Environmental Science and Technology. 3. 37-46 (1998)

[Publications] Otake,M.: "Binary data on radiation-related brain damage prenatally exposed and statistical threshold model" J.Faculty of Environmental Science and Technology. 3. 47-62 (1998)

田中豊岡山大学, 環境理工学部, 教授 (20127567)