Saturday, 3 September 2011

Descriptive Discriminant Analysis

If you have two or more groups of subjects and several variables about each subject and you want to determine how the groups differ on the variables, you will use descriptive discriminant analysis. Descriptive discriminant analysis shows which variables are best at distinguishing one group from the other.

Function: Descriptive discriminant analysis allows you to describe two or more groups of subjects (e.g. people) in terms of the variables that you have available and in ways that make the differences between the groups as large as possible. It uses information on the means and standard deviations of the variables to create weighted combinations of variables that distinguish the groups.

Types: The two broad types of discriminant analysis are parametric and nonparametric. Parametric discriminant analysis assumes the distribution of each group is multivariate normal. Nonparametric discriminant analysis relaxes this assumption, at some cost in power.

Types of Parametric Discriminant Analysis: The most common type of parametric discriminant analysis is Fisher's linear discriminant analysis, which creates linear combinations of the variables. That is the value of each variable is multiplied by a constant, and then these products are added together to create a discriminant score. An alternative is quadratic discriminant analysis, which adds quadratic terms.

Types of Nonparametric Discriminant Analysis: Two common types of nonparametric discriminant analysis are kernel and k-nearest neighbor. Kernel discriminant analysis estimates the distribution of variables in each group using one of a variety of complex functions known as kernel density estimates. These are needed because when the distribution of variables is not normal, the mean and standard deviation are not enough to describe the distribution.

K-nearest neighbor methods first define "nearness" and then attempt to find groups of subjects that are as near as possible to each other.