web.archive.org

Multivariate statistics: Information from Answers.com

Multivariate statistics is a form of statistics encompassing the simultaneous observation and analysis of more than one statistical variable. The application of multivariate statistics is multivariate analysis. Methods of bivariate statistics, for example ANOVA and correlation, are special cases of multivariate statistics in which two variables are involved.

There are many different models, each with its own type of analysis:

Multivariate analysis of variance (MANOVA) methods extend analysis of variance methods to cover cases where there is more than one dependent variable to be analyzed simultaneously.
Principal components analysis (PCA) finds a set of synthetic variables that summarise the original set. It rotates the axes of variation to give a new set of ordered orthogonal axes that summarise decreasing proportions of the variation.
Factor analysis is similar to PCA but attempts to determine a smaller set of synthetic variables that could explain the original set.
Canonical correlation analysis finds linear relationships among two sets of variables; it is the generalised (i.e. canonical) version of correlation.
Redundancy analysis is similar to canonical correlation analysis but deriving a minimal set of synthetic variables from one set of (independent) variables that explains as much variance as possible in the other (dependent) set. It is a multivariate analogue of regression.
Correspondence analysis (CA), or reciprocal averaging, finds (like PCA) a set of synthetic variables that summarise the original set. The underlying model assumes chi-squared dissimilarities among records (cases). There is also canonical correspondance analysis (CCA) for summarising the joint variation in two sets of variables.
Multidimensional scaling covers various algorithms to determine a set of synthetic variables that best represent the pairwise distances between records. The original method is principal coordinates analysis (based on PCA).
Hotelling's T-square is a generalization of Student's t statistic that is used in multivariate hypothesis testing.
Discriminant function or canonical variate analysis attempts to establish whether a set of variables can be used to distinguish between two or more groups.
Linear discriminant analysis (LDA) computes a linear predictor from two sets of normally distributed data to allow for classification of new observations.
Artificial neural networks extend regression methods to non-linear multivariate models.
Clustering systems assign objects into groups (called clusters) so that objects from the same cluster are more similar to each other than objects from different clusters.
Recursive partitioning creates a decision tree that strives to correctly classify members of the population based on a dichotomous dependent variable