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Unformatted text preview: Multivariate Analysis. Herv´ e Abdi 1 The University of Texas at Dallas Introduction As the name indicates, multivariate analysis comprises a set of techniques dedicated to the analysis of data sets with more than one variable. Several of these techniques were developed recently in part because they require the computational capabilities of modern computers. Also, because most of them are recent, these techniques are not always unified in their presentation, and the choice of the proper technique for a given problem is often difficult. This article provides a (non-exhaustive) catalog in order to help decide when to use a given statistical technique for a given type of data or statistical question and gives a brief description of each technique. This paper is organized according to the number of data sets to analyze: one or two (or more). With two data sets we consider two cases: in the first case, one set of data plays the role of predictors (or independent) variables (IV’s) and the second set of data corresponds to measurements or dependent variables (DV’s); in the second case, the different sets of data correspond to different sets of DV’s. One data set Typically, the data tables to be analyzed are made of several measurements collected on a set of units (e.g., subjects). In general, the units are rows and the variables columns. Interval or ratio level of measurement: principal component analysis (PCA) This is the oldest and most versatile method. The goal of PCA is to decom- pose a data table with correlated measurements into a new set of uncorrelated (i.e., orthogonal) variables. These variables are called, depending upon the con- text, principal components, factors, eigenvectors, singular vectors, or loadings. Each unit is also assigned a set of scores which correspond to its projection on the components. The results of the analysis are often presented with graphs plotting the projections of the units onto the components, and the loadings of the variables 1 In: Lewis-Beck M., Bryman, A., Futing T. (Eds.) (2003). Encyclopedia of Social Sciences Research Methods. Thousand Oaks (CA): Sage. Address correspondence to Herv´ e Abdi Program in Cognition and Neurosciences, MS: Gr.4.1, The University of Texas at Dallas, Richardson, TX 75083–0688, USA E-mail: [email protected] http://www.utdallas.edu/ ∼ herve 1 (the so-called “circle of correlations”). The importance of each component is expressed by the variance (i.e., eigenvalue) of its projections or by the proportion of the variance explained. In this context, PCA is interpreted as an orthogonalof the variance explained....
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- Spring '10
- Multivariate statistics, data sets