Since the early 20th century, the need for multivariate analysis has driven the development of various types of multivariate methods for applications ranging from social science to biomedical research. Multivariate data, as distinguished from univariate and multivariable data, consist of more than one outcome variable measured on a number of subjects. There exist exploratory data analysis methods that aim to extract, summarize, and visualize empirical data information for the purpose of formulating hypotheses as well as confirmatory data analysis methods that allow testing specific research questions and hypotheses. Major exploratory tools for dimension reduction and classification include principal component analysis, canonical correlation, exploratory factor analysis, discriminant, and cluster analysis. Advanced confirmatory modeling techniques encompass general linear multivariate model, mixed model, and structural equation model. This article aims to provide an overview of these methods as well as recent developments in the area of high dimension, low sample size analysis for data from high-throughput bioassays or high-resolution medical images. WIREs Comp Stat 2012, 4:35–47. doi: 10.1002/wics.185
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