Multivariate Methods
Introduction to Multivariate Analysis
Overview of Multivariate Techniques
Multivariate Methods describes the following techniques for analyzing several variables simultaneously:
• The Multivariate platform examines multiple variables to see how they relate to each other. See “Correlations and Multivariate Techniques”.
• The Principal Components platform derives a small number of independent linear combinations (principal components) of a set of measured variables that capture as much of the variability in the original variables as possible. It is a useful exploratory technique and can help you create predictive models. See “Principal Components”.
• The Discriminant platform looks to find a way to predict a classification (X) variable (nominal or ordinal) based on known continuous responses (Y). It can be regarded as inverse prediction from a multivariate analysis of variance (MANOVA). See “Discriminant Analysis”.
• The Partial Least Squares platform fits linear models based on factors, namely, linear combinations of the explanatory variables (Xs). PLS exploits the correlations between the Xs and the Ys to reveal underlying latent structures. See “Partial Least Squares Models”.
• The Multiple Correspondence Analysis (MCA) platform takes multiple categorical variables and seeks to identify associations between levels of those variables. MCA is frequently used in the social sciences particularly in France and Japan. It can be used in survey analysis to identify question agreement. See “Multiple Correspondence Analysis”.
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The Structural Equation Models platform enables you to fit a variety of models, including confirmatory factor analysis, path models with or without latent variables, measurement error models, and latent growth curve models. See “Structural Equation Models”.
• The Factor Analysis platform enables you to construct factors from a larger set of observed variables. These factors are expressed as linear combinations of a subset of the observed variables. Factor analysis enables you to explore the number of factors that are explained by a set of measured, observed variables, and the strength of the relationship between factors and variables. See “Factor Analysis”.
• The Multidimensional Scaling (MDS) platform enables you to create a visual representation of the pattern of proximities (similarities, dissimilarities, or distances) among a set of objects. See “Multidimensional Scaling”.
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The Multivariate Embedding platform enables you to map data from very high dimensional spaces to a low dimensional space. See “Multivariate Embedding”.
• The Item Analysis platform enables you to fit item response theory models. The Item Response Theory (IRT) method is used for the analysis and scoring of measurement instruments such as tests and questionnaires. IRT uses a system of models to relate a trait or ability to an individual’s probability of endorsing or correctly responding to an item. IRT can be used to study standardized tests, cognitive development, and consumer preferences. See “Item Analysis”.
• The Hierarchical Cluster platform groups rows together that share similar values across a number of variables. It is a useful exploratory technique to help you understand the clumping structure of your data. See “Hierarchical Cluster”.
• The KMeans Clustering platform groups observations that share similar values across a number of variables. See “K Means Cluster”.
• The Normal Mixtures platform enables you to cluster observations when your data come from overlapping normal distributions. See “Normal Mixtures”.
• The Latent Class Analysis platform finds clusters of observations for categorical response variables. The model takes the form of a multinomial mixture model. See “Latent Class Analysis”.
• The Cluster Variables platform groups similar variables into representative groups. You can use Cluster Variables as a dimension-reduction method. Instead of using a large set of variables in modeling, the cluster components of the most representative variable in the cluster can be used to explain most of the variation in the data. See “Cluster Variables”.