chapter18.ppt 519KB Dec 31 1997 01:50:00 PM

Discriminant
Analysis

Chapter Outline
1) Overview
2) Basic Concept
3) Relation to Regression and ANOVA
4) Discriminant Analysis Model
5) Statistics Associated with Discriminant Analysis
6) Conducting Discriminant Analysis
i. Formulation
ii. Estimation
iii. Determination of Significance
iv. Interpretation
v. Validation

7) Multiple Discriminant Analysis
i. Formulation
ii. Estimation
iii. Determination of Significance
iv. Interpretation

v. Validation
8) Stepwise Discriminant Analysis
9) Internet and Computer Applications
10) Focus on Burke
11) Summary
12) Key Terms and Concepts
13) Acronyms

Similarities and Differences between ANOVA,
Table 18.1 Regression, and Discriminant Analysis
ANALYSIS
Similarities
Number of
dependent
variables
Number of
independent
variables
Differences
Nature of the

dependent
variable
Nature of the
independent
variables

ANOVA

REGRESSION

DISCRIMINANT

One

One

One

Multiple


Multiple

Multiple

Metric

Metric

Categorical

Categorical

Metric

Metric

Fig. 18.1

Conducting Discriminant Analysis
Formulate the Problem

Estimate the Discriminant Function Coefficients
Determine the Significance of the Discriminant Function
Interpret the Results
Assess Validity of Discriminant Analysis

Information on Resort Visits: Analysis Sample
Annual
Attitude Importance Household Age of
Resort Family
Toward Attached
Size
Head of
No.
Visit
Income
Travel
to Family
Household Family
($000)
Vacation


Table 18.2

1
2
3
4
5
6
7
8
9
10
11
12
13
14

1
1

1
1
1
1
1
1
1
1
1
1
1
1

50.2
70.3
62.9
48.5
52.7
75.0
46.2

57.0
64.1
68.1
73.4
71.9
56.2
49.3

5
6
7
7
6
8
5
2
7
7
6
5

1
4

8
7
5
5
6
7
3
4
5
6
7
8
8
2

3
4

6
5
4
5
3
6
4
5
5
4
6
3

43
61
52
36
55
68
62

51
57
45
44
64
54
56

Amount
Spent on
Vacation

M (2)
H (3)
H (3)
L (1)
H (3)
H (3)
M (2)
M (2)

H (3)
H (3)
H (3)
H (3)
M (2)
H (3)

Table 18.2 Contd.
Annual
Attitude Importance Household Age of
Resort Family
Toward Attached
Size
Head of
No.
Visit
Income
Travel
to Family
Household Family
($000)
Vacation

16
17
18
19
20
21
22
23
24
25
26
27
28
29

2
2
2
2
2
2
2
2
2
2
2
2
2
2

32.1
36.2
43.2
50.4
44.1
38.3
55.0
46.1
35.0
37.3
41.8
57.0
33.4
37.5

5
4
2
5
6
6
1
3
6
2
5
8
6
3

4
3
5
2
6
6
2
5
4
7
1
3
8
2

3
2
2
4
3
2
2
3
5
4
3
2
2
3

58
55
57
37
42
45
57
51
64
54
56
36
50
48

Amount
Spent on
Vacation

L (1)
L (1)
M (2)
M (2)
M (2)
L (1)
M (2)
L (1)
L (1)
L (1)
M (2)
M (2)
L (1)
L (1)

Information on Resort Visits: Holdout Sample
Table 18.3

Annual
Attitude Importance Household Age of
Resort Family
Toward Attached
Size
Head of
No.
Visit
Income
Travel
to Family
Household Family
($000)
Vacation

1
2
3
4
5
6
7
8
9
10
11

1
1
1
1
1
1
2
2
2
2
2

50.8
63.6
54.0
45.0
68.0
62.1
35.0
49.6
39.4
37.0
54.5

4
7
6
5
6
5
4
5
6
2
7

7
4
7
4
6
6
3
3
5
6
3

3
7
4
3
6
3
4
5
3
5
3

45
55
58
60
46
56
54
39
44
51
37

Amount
Spent on
Vacation

M (2)
H (3)
M (2)
M (2)
H (3)
H (3)
L (1)
L (1)
H (3)
L (1)
M (2)

Table 18.4

Results of Two-Group Discriminant Analysis

GROUP MEANS
VISIT
1
2
Total

INCOME TRAVEL VACATION HSIZE
60.52000
41.91333
51.21667

5.40000
4.33333
4.86667

AGE

5.80000
4.06667
4.9333

4.33333
2.80000
3.56667

53.73333
50.13333
51.93333

1.82052
2.05171
2.09981

1.23443
.94112
1.33089

8.77062
8.27101
8.57395

Group Standard Deviations
1
2
Total

9.83065
7.55115
12.79523

1.91982
1.95180
1.97804

Pooled Within-Groups Correlation Matrix
INCOME TRAVEL VACATION

INCOME
TRAVEL
VACATION
HSIZE
AGE

1.00000
.19745
.09148
.08887
- .01431

1.00000
.08434
-.01681
-.19709

1.00000
.07046
.01742

HSIZE

1.00000
-.04301

AGE

1.00000

Wilks' (U-statistic) and univariate F ratio with 1 and 28 degrees of freedom
Variable
INCOME
TRAVEL
VACATION
HSIZE
AGE

Wilks'
.45310
.92479
.82377
.65672
.95441

F
33.800
2.277
5.990
14.640
1.338

Significance
.0000
.1425
.0209
.0007
.2572

Contd.

Table 18.4

Results of Two-Group Discriminant Analysis
CANONICAL DISCRIMINANT FUNCTIONS

Function Eigenvalue
1*

1.7862

% of
Cum Canonical After
Wilks'
Variance %
Correlation Function 
Chi-square df Significance
: 0
.3589
26.130
5
.0001
100.00 100.00
.8007
:

* marks the 1 canonical discriminant functions remaining in the analysis.
Standard Canonical Discriminant Function Coefficients
FUNC 1
INCOME
TRAVEL
VACATION
HSIZE
AGE

.74301
.09611
.23329
.46911
.20922

Structure Matrix:
Pooled within-groups correlations between discriminating variables & canonical discriminant functions
(variables ordered by size of correlation within function)
FUNC 1
INCOME
HSIZE
VACATION
TRAVEL
AGE

.82202
.54096
.34607
.21337
.16354

Contd.

Table 18.4

Results of Two-Group Discriminant Analysis
Unstandardized canonical discriminant function coefficients
FUNC 1
.8476710E-01
.4964455E-01
.1202813
.4273893
.2454380E-01
-7.975476

INCOME
TRAVEL
VACATION
HSIZE
AGE
(constant)

Canonical discriminant functions evaluated at group means (group centroids)
Group
1
2

FUNC 1
1.29118
-1.29118

Classification results for cases selected for use in analysis
Actual Group

Predicted Group Membership
No. of Cases
1
2

Group

1

15

12
80.0%

3
20.0%

Group

2

15

0
.0%

15
100.0%

Percent of grouped cases correctly classified: 90.00%

Contd.

Table 18.4

Results of Two-Group Discriminant Analysis
Classification Results for cases not selected for use in the analysis (holdout sample)
Actual Group

Predicted Group Membership
No. of Cases
1
2

Group

1

6

4
66.7%

2
33.3%

Group

2

6

0
.0%

6
100.0%

Percent of grouped cases correctly classified: 83.33%.

Table 18.5

Results of Three-Group Discriminant Analysis
Group Means
AMOUNT INCOME TRAVEL VACATION HSIZE
1
2
3
Total

38.57000
50.11000
64.97000
51.21667

4.50000
4.00000
6.10000
4.86667

AGE

4.70000
4.20000
5.90000
4.93333

3.10000
3.40000
4.20000
3.56667

50.30000
49.50000
56.00000
51.93333

1.88856
2.48551
1.66333
2.09981

1.19722
1.50555
1.13529
1.33089

8.09732
9.25263
7.60117
8.57395

Group Standard Deviations
1
2
3
Total

5.29718
6.00231
8.61434
12.79523

1.71594
2.35702
1.19722
1.97804

Pooled Within-Groups Correlation Matrix
INCOME TRAVEL VACATION HSIZE
INCOME
TRAVEL
VACATION
HSIZE
AGE

1.00000
.05120
.30681
.38050
-.20939

1.00000
.03588
.00474
-.34022

1.00000
.22080
-.01326

AGE

1.00000
-.02512 1.00000

Contd.

Table 18.5

Results of Three-Group Discriminant Analysis
Wilks' (U-statistic) and univariate F ratio with 2 and 27 degrees of freedom.
Variable

Wilks' Lambda

INCOME
TRAVEL
VACATION
HSIZE
AGE

.26215
.78790
.88060
.87411
.88214

F

Significance

38.00
3.634
1.830
1.944
1.804

.0000
.0400
.1797
.1626
.1840

CANONICAL DISCRIMINANT FUNCTIONS
Function Eigenvalue
1*

3.8190

2*

.2469

% of
Cum Canonical After
Wilks'
Variance %
Correlation Function  Chi-square df Significance
: 0
.1664
44.831 10
.00
93.93 93.93
.8902
: 1
.8020
5.517
4
.24
6.07

100.00

.4450

:

* marks the two canonical discriminant functions remaining in the analysis.
Standardized Canonical Discriminant Function Coefficients
INCOME
TRAVEL
VACATION
HSIZE
AGE

FUNC 1
1.04740
.33991
-.14198
-.16317
.49474

FUNC 2
-.42076
.76851
.53354
.12932
.52447

Contd.

Table 18.5

Results of Three-Group Discriminant Analysis

Structure Matrix:
Pooled within-groups correlations between discriminating variables and canonical discriminant
functions (variables ordered by size of correlation within function)
INCOME
HSIZE
VACATION
TRAVEL
AGE

FUNC 1
.85556*
.19319*
.21935
.14899
.16576

FUNC 2
-.27833
.07749
.58829*
.45362*
.34079*

Unstandardized canonical discriminant function coefficients
FUNC 1
FUNC 2
INCOME
.1542658
-.6197148E-01
TRAVEL
.1867977
.4223430
VACATION
-.6952264E-01 .2612652
HSIZE
-.1265334
.1002796
AGE
.5928055E-01 .6284206E-01
(constant)
-11.09442
-3.791600
Canonical discriminant functions evaluated at group means (group centroids)
Group
FUNC 1
FUNC 2
1
-2.04100
.41847
2
-.40479
-.65867
3
2.44578
.24020

Contd.

Table 18.5

Results of Three-Group Discriminant Analysis

Classification Results:
Actual Group

Predicted Group Membership
No. of Cases 1
2
3

Group

1

10

9
90.0%

1
10.0%

0
.0%

Group

2

10

1
10.0%

9
90.0%

0
.0%

Group

3

10

0
2
.0%
20.0%
Percent of grouped cases correctly classified: 86.67%

8
80.0%

Classification results for cases not selected for use in the analysis
Predicted Group Membership
Actual Group No. of Cases 1
2
3
Group

1

4

3
75.0%

1
25.0%

0
.0%

Group

2

4

0
.0%

3
75.0%

1
25.0%

Group

3

4

1
0
25.0%
.0%
Percent of grouped cases correctly classified: 75.00%

3
75.0%

All-Groups Scattergram

Fig. 18.2

Across: Function 1
Down: Function 2

4.0

1

1

1

23
*1
1 1 12
1
1 *2 2
2 2
1
2

0.0

3 3 3
3* 3
3

3

-4.0
* indicates a group centroid
-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

Territorial Map

Fig. 18.3

13
13
Across: Function 1
13
13
Down: Function 2
13
* Indicates a
13
group centroid
13
113
112 3
112233
*1 1 1 2 2 2 2 3 3 *
1 1 2 2*
223
233
1122
2233
1122
223
11122
233
11222
223
1122
233
11122
2233
11122
223
1122
11122
233

8.0
4.0

0.0

-4.0

-8.0
-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

RIP 18.1

Satisfactory Results Of Satisfaction
Programs In Europe

These days more and more computer companies are emphasizing
customer service programs rather than their erstwhile emphasis on
computer features and capabilities. Hewlett-Packard learned this
lesson while doing business in Europe. Research conducted on
the European market revealed that there was a difference in
emphasis on service requirements across age segments. Focus
groups revealed that customers above 40 years of age had a hard
time with the technical aspects of the computer and greatly
required the customer service programs. On the other hand,
young customers appreciated the technical aspects of the product
which added to their satisfaction. Further research in the form of
a large single cross-sectional survey was done to uncover the
factors leading to differences in the two segments.

RIP 18.1 Contd.

A two group discriminant analysis was conducted with satisfied
and dissatisfied customers as the two groups and several
independent variables such as technical information, ease of
operation, variety and scope of customer service programs, etc.
Results confirmed the fact that the variety and scope of customer
satisfaction programs was indeed a strong differentiating factor.
This was a crucial finding since HP could better handle
dissatisfied customers by focusing more on customer services than
technical details. Consequently, HP successfully started three
programs on customer satisfaction - customer feedback, customer
satisfaction surveys, and total quality control. This effort resulted
in increased customer satisfaction.

RIP 18.2

Discriminant Analysis Discriminates
Ethical and Unethical Firms

In order to identify the important variables that predict ethical and
unethical behavior, discriminant analysis was used. Prior research
suggested that the variables that impact ethical decisions are
attitudes, leadership, the presence or absence of ethical codes of
conduct, and the organization's size.

To determine which of these variables are the best predictors of
ethical behavior, 149 firms were surveyed and respondents
indicated how their firms operate in 18 different ethical situations.
Of these 18 situations, nine related to marketing activities. These
activities included using misleading sales presentations, accepting
gifts for preferential treatment, pricing below out-of-pocket
expenses, etc. Based on these nine issues, the respondent firms
were classified into two groups: never practice and practice
unethical marketing.

RIP 18.2 Contd.

An examination of the variables that influenced classification
indicated that attitudes and a company's size were the best
predictors of ethical behavior. Smaller firms tend to
demonstrate more ethical behavior on marketing issues.