Multivariate analysis

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Multivariate analysis (MVA) is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical 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, the selection of concepts to fulfill 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 See also 3 Software and tools 4 References

[edit] 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 with Charles Spearman's attempts to show that a wide variety of mental tests could be explained by a single underlying intelligence factor (a notion now rejected, by the way).

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 the principal component 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

Factor analysis is part of the general linear model (GLM) family of procedures and makes many of the same assumptions as multiple regression

[edit] See also

• Pattern recognition
• Exploratory data analysis
• Principal component analysis(PCA)
• Design of experiments (DoE)
• Soft independent modelling of class analogies (SIMCA)
• Regression analysis
• OLS
• Partial least squares regression

[edit] Software and tools

• The Unscrambler (free-to-try commercial MVA software for Windows)
• ControlMV, PharmaMV and WaterMV from Perceptive Engineering
• SIMCA-P+ (Professional MVA Software, free demo)

[edit] References

• KV Mardia, JT Kent, and JM Bibby (1979). Multivariate Analysis. Academic Press,. http://www.amazon.com/dp/0124712525/. 

• Feinstein, A. R. (1996) Multivariable Analysis. New Haven, CT: Yale University Press.

• Gould, S. J. (1996) The Mismeasure of Man, rev. exp. ed. New York: W. W. Norton.

• Hair, J. F. Jr. (1995) Multivariate Data Analysis with Readings, 4th ed. Prentice-Hall.

• Schafer, J. L. (1997) Analysis of Incomplete Multivariate Data. CRC Press.

• Sharma, S. (1996) Applied Multivariate Techniques. Wiley.

• Bryant and Yarnold (1994). "Principal components analysis and exploratory and confirmatory factor analysis". In: Grimm and Yarnold, Reading and understanding multivariate analysis. American Psychological Association Books. ISBN 978-1-55798-273-5

• Garson, G. David, “Factor Analysis,” from Statnotes: Topics in Multivariate Analysis. Retrieved on April 13, 2009 from http://www2.chass.ncsu.edu/garson/pa765/statnote.htm

• Gorsuch, R. L. (1983). Factor Analysis. Hillsdale, NJ: Lawrence Erlbaum. (Orig. ed. 1974.) ISBN 089859202X

• Raubenheimer, J. E. (2004). "An item selection procedure to maximize scale reliability and validity". South African Journal of Industrial Psychology, 30 (4), 59–64.

• Professor Kim H. Esbensen. Multivariate Data Analysis in Practice (5th Edition). http://www.camo.com/introducer/.