Multivariate statistics - Definition and Overview

Multivariate statistics or multivariate statistical analysis in statistics describes a collection of procedures which involve observation and analysis of more than one statistical variable at a time.

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

1. Canonical correlation analysis tries to establish whether or not there are linear relationships among two sets of variables (covariates and response).
2. Regression analysis attempts to determine a linear formula that can describe how some variables respond to changes in others.
3. Principal components analysis attempts to determine a smaller set of synthetic variables that could explain the original set.
4. Discriminant function or canonical variate analysis attempt to establish whether a set of variables can be used to distinguish between two or more groups.
5. 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 coordinate analysis.
6. Linear discriminant analysis (LDA) computes a linear predictor from two sets of normally distributed data to allow for classification of new observations.
7. Logistic regression allows to perform a regression analysis to estimate and test the influence of covariates on a binary response.
8. Multivariate analysis of variance (MANOVA) methods extend analysis of variance methods to cover cases where there is more than one dependent variable and where the dependent variables cannot simply be combined.

See also

• Multivariate normal distribution
• Estimation of covariance matrices
• Wishart distribution
• Hotelling's T-square distribution
• Important publications in multivariate statistics