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. Typically, MVA is used to address the situations where multiple measurements are made on each experimental unit and the relations among these measurements and their structures are important. A modern, overlapping categorization of MVA includes:
- Normal and general multivariate models and distribution theory
- The study and measurement of relationships
- Probability computations of multidimensional regions
- The exploration of data structures and patterns
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.
Anderson's 1958 textbook, An Introduction to Multivariate Statistical 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. MVA once solely stood in the statistical theory realms due to the size, complexity of underlying data set and high computational consumption. With the dramatic growth of computational power, MVA now plays an increasingly important role in data analysis and has wide application in OMICS fields.
- Multivariate hypothesis testing
- Dimensionality reduction
- Latent structure discovery
- Multivariate regression analysis
- Classification and discrimination analysis
- Variable selection
- Multidimensional Scaling
- Data mining
- NCSS (statistical software) includes multivariate analysis.
- The Unscrambler® X is a multivariate analysis tool.
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- Bivariate analysis
- Design of experiments (DoE)
- Dimensional analysis
- Exploratory data analysis
- Partial least squares regression
- Pattern recognition
- Principal component analysis (PCA)
- Regression analysis
- Soft independent modelling of class analogies (SIMCA)
- Statistical interference
- Univariate analysis
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- 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 978-0124712522. (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)
- Izenman, Alan J. (2008). Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning. Springer Texts in Statistics. New York: Springer-Verlag. ISBN 9780387781884.
- "Handbook of Applied Multivariate Statistics and Mathematical Modeling | ScienceDirect". Retrieved 2019-09-03.
- 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.