多変量解析
WordNet
- an investigation of the component parts of a whole and their relations in making up the whole
- the abstract separation of a whole into its constituent parts in order to study the parts and their relations (同)analytic thinking
- a branch of mathematics involving calculus and the theory of limits; sequences and series and integration and differentiation
- a form of literary criticism in which the structure of a piece of writing is analyzed
- the use of closed-class words instead of inflections: e.g., `the father of the bride instead of `the brides father
- pertaining to any procedure involving two or more variables
PrepTutorEJDIC
- (内容・状況などの)『分析』,分解;(詳細な)検討 / (化学・物理で)分析;《米》(心理学で)[精神]分析;(数学で)解析
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出典(authority):フリー百科事典『ウィキペディア(Wikipedia)』「2017/06/09 13:53:27」(JST)
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This article is about statistics. For multivariate analysis in mathematics, see multivariable calculus.
Multivariate analysis (MVA) is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical outcome variable at a time. In design and analysis, the technique is used to perform trade studies across multiple dimensions while taking into account the effects of all variables on the responses of interest.
Uses for multivariate analysis include:
- design for capability (also known as capability-based design)
- inverse design, where any variable can be treated as an independent variable
- Analysis of Alternatives (AoA), the selection of concepts to fulfil a customer need
- analysis of concepts with respect to changing scenarios
- identification of critical design-drivers and correlations across hierarchical levels.
Multivariate analysis can be complicated by the desire to include physics-based analysis to calculate the effects of variables for a hierarchical "system-of-systems". Often, studies that wish to use multivariate analysis are stalled by the dimensionality of the problem. These concerns are often eased through the use of surrogate models, highly accurate approximations of the physics-based code. Since surrogate models take the form of an equation, they can be evaluated very quickly. This becomes an enabler for large-scale MVA studies: while a Monte Carlo simulation across the design space is difficult with physics-based codes, it becomes trivial when evaluating surrogate models, which often take the form of response-surface equations.
Contents
- 1 Factor analysis
- 2 History
- 3 Commercial
- 4 See also
- 5 References
- 6 Further reading
- 7 External links
Factor analysis
Main article: Factor analysis
Overview: Factor analysis is used to uncover the latent structure (dimensions) of a set of variables. It reduces attribute space from a larger number of variables to a smaller number of factors. Factor analysis originated a century ago[when?] with Charles Spearman's attempts to show that a wide variety of mental tests could be explained by a single underlying intelligence factor.
Applications:
- To reduce a large number of variables to a smaller number of factors for data modeling
- To validate a scale or index by demonstrating that its constituent items load on the same factor, and to drop proposed scale items which cross-load on more than one factor.
- To select a subset of variables from a larger set, based on which original variables have the highest correlations with some other factors.
- To create a set of factors to be treated as uncorrelated variables as one approach to handling multi-collinearity in such procedures as multiple regression
- To integrate different data in earth sciences and geo-modeling. For example, integration of drilling and seismic data [1]
Factor analysis is part of the general linear model (GLM) family of procedures and makes many of the same assumptions as multiple regression, but it uses multiple outcomes.
History
Anderson's 1958 textbook, An Introduction to Multivariate Analysis, educated a generation of theorists and applied statisticians; Anderson's book emphasizes hypothesis testing via likelihood ratio tests and the properties of power functions: Admissibility, unbiasedness and monotonicity.[2][3]
Commercial
- NCSS (statistical software) includes multivariate analysis.
- The Unscrambler® X is a multivariate analysis tool.
See also
|
Wikimedia Commons has media related to Multivariate analysis. |
- Bivariate analysis
- Design of experiments (DoE)
- Dimensional analysis
- Envelope model
- Exploratory data analysis
- OLS
- Partial least squares regression
- Pattern recognition
- Principal component analysis (PCA)
- Regression analysis
- Soft independent modelling of class analogies (SIMCA)
- Statistical interference
- Univariate analysis
References
- ^ Tahmasebi, Pejman; Sahimi, Muhammad (18 February 2015). "Geostatistical Simulation and Reconstruction of Porous Media by a Cross-Correlation Function and Integration of Hard and Soft Data" (PDF). Transport in Porous Media. 107 (3): 871–905. doi:10.1007/s11242-015-0471-3.
- ^ Sen, Pranab Kumar; Anderson, T. W.; Arnold, S. F.; Eaton, M. L.; Giri, N. C.; Gnanadesikan, R.; Kendall, M. G.; Kshirsagar, A. M.; et al. (June 1986). "Review: Contemporary Textbooks on Multivariate Statistical Analysis: A Panoramic Appraisal and Critique". Journal of the American Statistical Association. 81 (394): 560–564. ISSN 0162-1459. JSTOR 2289251. doi:10.2307/2289251. (Pages 560–561)
- ^ Schervish, Mark J. (November 1987). "A Review of Multivariate Analysis". Statistical Science. 2 (4): 396–413. ISSN 0883-4237. JSTOR 2245530. doi:10.1214/ss/1177013111.
Further reading
- T. W. Anderson, An Introduction to Multivariate Statistical Analysis, Wiley, New York, 1958.
- KV Mardia; JT Kent & JM Bibby (1979). Multivariate Analysis. Academic Press,. ISBN 0124712525. (M.A. level "likelihood" approach)
- Feinstein, A. R. (1996) Multivariable Analysis. New Haven, CT: Yale University Press.
- Hair, J. F. Jr. (1995) Multivariate Data Analysis with Readings, 4th ed. Prentice-Hall.
- Johnson, Richard A.; Wichern, Dean W. (2007). Applied Multivariate Statistical Analysis (Sixth ed.). Prentice Hall. ISBN 978-0-13-187715-3.
- Schafer, J. L. (1997) Analysis of Incomplete Multivariate Data. CRC Press. (Advanced)
- Sharma, S. (1996) Applied Multivariate Techniques. Wiley. (Informal, applied)
External links
- Discriminant Correlation Analysis (DCA)
- M. Haghighat, M. Abdel-Mottaleb, & W. Alhalabi (2016). Discriminant Correlation Analysis: Real-Time Feature Level Fusion for Multimodal Biometric Recognition. IEEE Transactions on Information Forensics and Security, 11(9), 1984-1996.
UpToDate Contents
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English Journal
- Combination of C-reactive protein, procalcitonin and sepsis-related organ failure score for the diagnosis of sepsis in critical patients.
- Yang Y1, Xie J1, Guo F1, Longhini F1,2, Gao Z1, Huang Y1, Qiu H3.
- Annals of intensive care.Ann Intensive Care.2016 Dec;6(1):51. doi: 10.1186/s13613-016-0153-5. Epub 2016 Jun 10.
- OBJECTIVE: To measure the ability of a new bioscore to diagnose sepsis in a general critical care population.METHODS: The study was done at an intensive care unit (ICU) from April to December 2012. Demographic and clinical patient information were recorded on admission to the ICU with blood samples
- PMID 27287669
- Practice of hemodynamic monitoring and management in German, Austrian, and Swiss intensive care units: the multicenter cross-sectional ICU-CardioMan Study.
- Funcke S1, Sander M2, Goepfert MS3, Groesdonk H4, Heringlake M5, Hirsch J6, Kluge S3, Krenn C7, Maggiorini M8, Meybohm P9, Salzwedel C3, Saugel B3, Wagenpfeil G10, Wagenpfeil S11, Reuter DA3; ICU-CardioMan Investigators.
- Annals of intensive care.Ann Intensive Care.2016 Dec;6(1):49. doi: 10.1186/s13613-016-0148-2. Epub 2016 May 31.
- BACKGROUND: Hemodynamic instability is frequent and outcome-relevant in critical illness. The understanding of complex hemodynamic disturbances and their monitoring and management plays an important role in treatment of intensive care patients. An increasing number of treatment recommendations and g
- PMID 27246463
- Prognostic value of PCT in septic emergency patients.
- Peschanski N1, Chenevier-Gobeaux C2, Mzabi L3, Lucas R1, Ouahabi S4, Aquilina V1, Brunel V5, Lefevre G4, Ray P3,6.
- Annals of intensive care.Ann Intensive Care.2016 Dec;6(1):47. doi: 10.1186/s13613-016-0146-4. Epub 2016 May 21.
- BACKGROUND: An accurate assessment of septic patients at risk for poor clinical outcomes is challenging for clinicians in the emergency department (ED).OBJECTIVES: We aimed to evaluate the prognostic value of procalcitonin (PCT) in septic patients in the ED for predicting death.RESULTS: In a retrosp
- PMID 27207179
Japanese Journal
- Risk Factors for Pancreatic Cancer in China: A Multicenter Case-Control Study
- 構成要素の有無に着目した多変量解析による茶室意匠様式の分析 : 茶室の形態構成に関する基礎的研究(その1)
Related Links
- Multivariate Data Analysis are powerful statistical techniques for analyzing data with many variables simultaneously to identify patterns & relationships ... Multivariate Data Analysis refers to any statistical technique used to analyze ...
- Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly... ... Journal Metrics Source Normalized Impact per Paper (SNIP): 1.165 ℹ Source ...
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[★]
- 関
- anal、analyse、analyses、analytical、analyze、assay、dissect、-metry、solve
[★]
- (主に統計分析で)独立したいくつかの変数のある、多変数の、多変量の
- 関
- univariate
- multivariable