Comparison of Multivariate Methods

Number of Variables

Most of the differences in multivariate methods can be understood in terms of the underlying model which can be defined by the number of independent and dependent variables on each side of the equation and the type of variables included in the model. The tables on this page compare the number and types of variables used in each method.

The tables below use a very simplified form for a multivariate statistical model:

Dependent variable(s) = f(independent variables).

Where f represents some function.

Table 1. Type of multivariate method, number of dependent (DV), independent (IV) variables, and icon showing number of DV's (orange) and number of IV's (blue). Cross-hatching indicates a categorical variable; solid circles indicate continuous variables.

Table 1. Type of multivariate method, number of dependent (DV), independent (IV) variables, and icon showing number of DV's (orange) and number of IV's (blue). Cross-hatching indicates a categorical variable; solid circles indicate continuous variables.
Method	No. of DV	No. of IV
Multiple regression	1	many
DFA	1	many
Manova	many	1 or many
PCA	many *	---------
Canonical	many *	many *

* "Dependent" and "independent" aren't exactly appropriate terms for these models because they are more exploratory than predictive.

Type of Variables

Another difference relates to the type of variables, for example, multiple regression and DFA have a similar set-up regarding number of variables, but multiple regression tries to predict values for a continuous dependent variable while the groups DFA tries to predict are categorical. An example of a categorical variable is ecoregion, the ecoregion aren't typically ranked in terms of which is more "ecoregional." In contrast, elevation or latitude are examples of continuous variables. For this table, continuous might also include what is more properly called ordinal. Stream order would be an example of an ordinal variable.

Table 2. Type of multivariate method, type of dependent and independent variables, and icon illustrating whether continuous (whole circles) or categorical (partitioned circles) variables are typically used.
Method	Dependent	Independent
Multiple regression	continuous	either
DFA	categorical	continuous
Manova	continuous	categorical
PCA	continuous	---------
Canonical	continuous	continuous

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Comparison of Multivariate Methods

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