Discriminant Function Analysis (Statistical Associates Blue Book Series 27)

DISCRIMINANT FUNCTION ANALYSIS

Discriminant function analysis, also known as discriminant analysis or simply DA, is used to classify cases into the values of a categorical dependent, usually a dichotomy. If discriminant function analysis is effective for a set of data, the classification table of correct and incorrect estimates will yield a high percentage correct. Discriminant function analysis is found in SPSS under Analyze>Classify>Discriminant. If the specified grouping variable has two categories, the procedure is considered "discriminant analysis" (DA). If there are more than two categories the procedure is considered "multiple discriminant analysis" (MDA).

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Below is the unformatted table of contents.

Table of Contents

Overview6
Key Terms and Concepts7
Variables7
Discriminant functions7
Pairwise group comparisons8
Output statistics8
Examples9
SPSS user interface9
The "Statistics" button10
The "Classify" button10
The "Save" button13
The "Bootstrap" button13
The "Method" button14
SPSS Statistical output for two-group DA16
The "Analysis Case Processing Summary" table16
The "Group Statistics" table16
The "Tests of Equality of Group Means" table16
The "Pooled Within-Group Matrices" and "Covariance Matrices" tables.18
The "Box's Test of Equality of Covariance Matrices" tables18
The "Eigenvalues" table19
The "Wilks' Lambda" table21
The "Standardized Canonical Discriminant Function Coefficients" table21
The "Structure Matrix" table23
The "Canonical Discriminant Functions Coefficients" table23
The "Functions at Group Centroids" table24
The "Classification Processing Summary" table24
The "Prior Probabilities for Groups" table25
The "Classification Function Coefficients" table25
The "Casewise Statistics" table26
Separate-groups graphs of canonical discriminant functions27
The "Classification Results" table27
SPSS Statistical output for three-group MDA28
Overview and example28
MDA and DA similarities28
The "Eigenvalues" table29
The "Wilks' Lambda" table29
The "Structure Matrix" table30
The "Territorial Map"31
Combined-groups plot34
Separate-groups plots34
SPSS Statistical output for stepwise discriminant analysis35
Overview35
Example35
Stepwise discriminant analysis in SPSS36
Assumptions41
Proper specification41
True categorical dependent variables41
Independence41
No lopsided splits41
Adequate sample size41
Interval data42
Variance42
Random error42
Homogeneity of variances (homoscedasticity)42
Homogeneity of covariances/correlations42
Absence of perfect multicollinearity43
Low multicollinearity of the independents43
Linearity43
Additivity43
Multivariate normality43
Frequently Asked Questions44
Isn't discriminant analysis the same as cluster analysis?44
When does the discriminant function have no constant term?44
How important is it that the assumptions of homogeneity of variances and of multivariate normal distribution be met?44
In DA, how can you assess the relative importance of the discriminating variables?44
Dummy variables45
In DA, how can you assess the importance of a set of discriminating variables over and above a set of control variables? (What is sequential discriminant analysis?)45
What is the maximum likelihood estimation method in discriminant analysis (logistic discriminate function analysis)?45
What are Fisher's linear discriminant functions?46
I have heard DA is related to MANCOVA. How so?46
How does MDA work?46
How can I tell if MDA worked?46
For any given MDA example, how many discriminant functions will there be, and how can I tell if each is significant?47
What are Mahalonobis distances?47
How are the multiple discriminant scores on a single case interpreted in MDA?47
And 5 more pages of topics on MDA.
Coverage: SPSS
Pagecount: 52