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

Overview 6
Key Terms and Concepts 7
Variables 7
Discriminant functions 7
Pairwise group comparisons 8
Output statistics 8
Examples 9
SPSS user interface 9
The "Statistics" button 10
The "Classify" button 10
The "Save" button 13
The "Bootstrap" button 13
The "Method" button 14
SPSS Statistical output for two-group DA 16
The "Analysis Case Processing Summary" table 16
The "Group Statistics" table 16
The "Tests of Equality of Group Means" table 16
The "Pooled Within-Group Matrices" and "Covariance Matrices" tables. 18
The "Box's Test of Equality of Covariance Matrices" tables 18
The "Eigenvalues" table 19
The "Wilks' Lambda" table 21
The "Standardized Canonical Discriminant Function Coefficients" table 21
The "Structure Matrix" table 23
The "Canonical Discriminant Functions Coefficients" table 23
The "Functions at Group Centroids" table 24
The "Classification Processing Summary" table 24
The "Prior Probabilities for Groups" table 25
The "Classification Function Coefficients" table 25
The "Casewise Statistics" table 26
Separate-groups graphs of canonical discriminant functions 27
The "Classification Results" table 27
SPSS Statistical output for three-group MDA 28
Overview and example 28
MDA and DA similarities 28
The "Eigenvalues" table 29
The "Wilks' Lambda" table 29
The "Structure Matrix" table 30
The "Territorial Map" 31
Combined-groups plot 34
Separate-groups plots 34
SPSS Statistical output for stepwise discriminant analysis 35
Overview 35
Example 35
Stepwise discriminant analysis in SPSS 36
Assumptions 41
Proper specification 41
True categorical dependent variables 41
Independence 41
No lopsided splits 41
Adequate sample size 41
Interval data 42
Variance 42
Random error 42
Homogeneity of variances (homoscedasticity) 42
Homogeneity of covariances/correlations 42
Absence of perfect multicollinearity 43
Low multicollinearity of the independents 43
Linearity 43
Additivity 43
Multivariate normality 43
Frequently Asked Questions 44
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 variables 45
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