Multivariate Methods

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Multivariate statistical methods are designed to evaluate more than 1 variable at a time. Many of the most common methods are derived from models in which all the variables are assumed to follow a multivariate normal distribution.

Comparing the numbers of dependent and independent variables

The diverse array of multivariate methods are easier to understand in terms of the number (and types) of dependent (or "response") variables on one side of the equation and the number of independent (or "predictor") variables on the other.

Comparison of statistical methods

Sometimes it's easiest to understand how a method works by comparing it with a related method. This link compares all the multivariate methods to each other .

Discriminant function analysis (DFA)

DFA uses multiple variables to divide cases into meaningful and similar groups. Multiple regression is a related method which uses multiple variables to predict values for another variable.

Multivariate ANOVA (MANOVA)

Multivariate analysis of variance is DFA turned around. Rather than predict group membership, MANOVA tests whether the groups are significantly different in terms of the independent variables.

Principal components analysis (PCA)

PCA takes multiple variables and defines a smaller number of new variables by constructing linear combinations of the original variables. The new variables are combined in such a way to separate the cases as much as possible.

Canonical correlation

Canonical correlation uses two sets variables. Like PCA, it creates linear combinations of the initial variables in each set so that the number of variables are reduced. The new linear combinations are selected such that they maximize the correlation between the pairs of variables, one from each set.

Cluster analysis

Although typically included with multivariate methods, analysis is based on a very different type of model. The multivariate normal distribution is not assumed, rather, a distance measure is used to cluster similar cases together.

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