Discriminant Analysis

Testing latent variables as predictors of groups

Discriminant Analysis – Discussion

DefinitionVocabularySimple ProcedureSPSS example ICPSR and hands on

Definition of Discriminant Analysis

In clustering, the classification categories of the respondents are unknown. However, we know the rule to classify (usually based upon distance) and we also have specified the Independent Variables that can best derive the classification of the respondents.

In discriminant analysis, the goal is to define group differences. The groupings of respondents have been specified. The model of classification is also given and we want to find the parameters of the model that can best separate the respondents based on these classifications

Assumptions of the Analysis

1. The group classifications must be independent of each other.

2. The combination of independent variables used to predict are normal with respect to each other.

3. The variance of the population distributions are homogeneous.

4. The independent variables are all linearly related.

Vocabulary and Procedure

First is to create the categories of respondents the researcher is interested in differentiating. The researcher then introduces a list of Independent Variables that s/he thinks best differentiates these respondents across the categories or groupings.

This list is not unlike a set of IVs in a regression equation. That is, each IV has a “weight” that is used to, together with the raw score yields a discriminant score, not unlike a factor score.

The logic is to find the best combination of linearly related IV’s that “maximize” the between vs. within association on the Groupings.

Vocabulary and Procedure (cont.)

Next, a correlation is computed which measures the relationship between the discriminant function scores and levels of the dependent variable (called a canonical correlation).

Structure Coefficients are also calculated and can be thought of much as we would factor loadings, but for groups as opposed to variables.

Output

Each independent function is determined, subject to the constraint that there will be the fewer of k-1 (where k is the number of categories) or p (where p is the number of independent variables).

Output gives:

1) means and s.d. for each variable on each group and an ANOVA for group scores across IVs that shows the significance of each IV in the discriminant function;

2) signficance test for each function is presented in Eigenvallues, together with the canonical correlation;

3) a table of classification is generated

Steps in the Analysis

Input the data Choose the method for grouping Generate the Output Interpret the results

Input the data

Generate the Procedure

Generate the Output

Generate the Output (cont.)