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

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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

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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

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Similarities and Differences between ANOVA,

Regression, and Discriminant Analysis

ANOVA

REGRESSION DISCRIMINANT

ANALYSIS

Similarities

Number of

One

dependent

variables

Number of

independent

Multiple

variables

Differences

Nature of the

dependent

Metric

Categorical

variable

Nature of the

independent

Categorical

Metric

[image:4.720.6.720.28.500.2]

variables

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Conducting Discriminant Analysis

[image:5.720.0.716.74.484.2]

Conducting Discriminant Analysis

Fig. 18.1

Estimate the Discriminant Function Coefficients

Assess Validity of Discriminant Analysis

Determine the Significance of the Discriminant Function

Formulate the Problem

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Information on Resort Visits: Analysis Sample

Annual Attitude Importance Household Age of Amount

Resort Family Toward Attached Size

Head of Spent on

No. Visit Income Travel to Family

Household Family

[image:6.720.40.711.41.527.2]

($000)

Vacation

1

50.2

5

8

3

43 M (2)

2

1

70.3

6

7

4

61 H (3)

3

1

62.9

7

5

6

52 H (3)

4

1

48.5

7

5

36 L (1)

5

1

52.7

6

4

55 H (3)

6

1

75.0

8

7

5

68 H (3)

7

1

46.2

5

3

62 M (2)

8

1

57.0

2

4

6

51 M (2)

9

1

64.1

7

5

4

57 H (3)

10

1

68.1

7

6

5

45 H (3)

11

1

73.4

6

7

5

44 H (3)

12

1

71.9

5

8

4

64 H (3)

13

1

56.2

1

8

6

54 M (2)

14

1

49.3

4

2

3

56 H (3)

15

1

62.0

5

6

2

58 H (3)

Table 18.2

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Resort Family Toward Attached Size

Head of Spent on

Household Family

($000)

Vacation

[image:7.720.4.714.37.524.2]

16

2

32.1

5

4

3

58 L (1)

17

2

36.2

4

3

2

55 L (1)

18

2

43.2

2

5

2

57 M (2)

19

2

50.4

5

2

4

37 M (2)

20

2

44.1

6

3

42 M (2)

21

2

38.3

6

2

45 L (1)

22

2

55.0

1

2

57 M (2)

23

2

46.1

3

5

3

51 L (1)

24

2

35.0

6

4

5

64 L (1)

25

2

37.3

2

7

4

54 L (1)

26

2

41.8

5

1

3

56 M (2)

27

2

57.0

8

3

2

36 M (2)

28

2

33.4

6

8

2

50 L (1)

29

2

37.5

3

2

3

48 L (1)

30

2

41.3

3

2

42 L (1)

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Information on Resort Visits: Holdout Sample

Annual Attitude Importance Household Age of Amount

Head of Spent on

Household Family

($000)

Vacation

1

50.8

4

7

3

45 M (2)

2

1

63.6

7

4

7

55 H (3)

3

1

54.0

6

7

4

58 M (2)

4

1

45.0

5

4

3

60 M (2)

5

1

68.0

6

46 H (3)

6

1

62.1

5

6

3

56 H (3)

7

2

35.0

4

3

4

54 L (1)

8

2

49.6

5

3

5

39 L (1)

9

2

39.4

6

5

3

44 H (3)

10

2

37.0

2

6

5

51 L (1)

11

2

54.5

7

3

37 M (2)

12

2

38.2

2

3

49 L (1)

Table 18.3

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Results of Two-Group Discriminant Analysis

GROUP MEANS

VISITVISIT INCOMEINCOME TRAVEL VACATION HSIZE AGE TRAVEL VACATION HSIZE AGE 1 60.52000 5.40000 5.80000 4.33333 53.73333 2 41.91333 4.33333 4.06667 2.80000 50.13333 Total 51.21667 4.86667 4.9333 3.56667 51.93333

Group Standard Deviations

1 9.83065 1.91982 1.82052 1.23443 8.77062 2 7.55115 1.95180 2.05171 .94112 8.27101 Total 12.79523 1.97804 2.09981 1.33089 8.57395

Pooled Within-Groups Correlation Matrix

INCOME

INCOME TRAVELTRAVEL VACATION HSIZE AGEVACATION HSIZE AGE INCOME

INCOME 1.00000 TRAVEL

TRAVEL .19745 1.00000 VACATION

VACATION .09148 .08434 1.00000 HSIZE

HSIZE .08887 -.01681 .07046 1.00000 AGE

AGE - .01431 -.19709 .01742 -.04301 1.00000

Wilks' (U-statistic) and univariate F ratio with 1 and 28 degrees of freedom

Variable

Variable Wilks' Wilks' FF SignificanceSignificance INCOME

INCOME .45310. 33.800 .0000 TRAVEL

TRAVEL .92479 2.277 .1425 VACATION

VACATION .82377 5.990 .0209 HSIZE

HSIZE .65672 14.640 .0007 AGE

[image:9.720.52.691.85.523.2]

AGE .95441 1.338 .2572

Contd.

Table 18.4

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CANONICAL DISCRIMINANT FUNCTIONS

% of Cum Canonical After Wilks'% of Cum Canonical After Wilks' Function

Function Eigenvalue Variance %Eigenvalue Variance % Correlation Function Correlation Function  Chi-square df SignificanceChi-square df Significance

: 0 .3589 26.130 5 .0001 1* 1.7862 100.00 100.00 .8007 :

* marks the 1 canonical discriminant functions remaining in the analysis. * marks the 1 canonical discriminant functions remaining in the analysis.

Standard Canonical Discriminant Function Coefficients

FUNC 1 FUNC 1

INCOMEINCOME .74301

TRAVELTRAVEL .09611

VACATIONVACATION .23329

HSIZEHSIZE .46911

AGEAGE .20922 Structure Matrix:

Structure Matrix:

Pooled within-groups correlations between discriminating variables & canonical discriminant functions Pooled within-groups correlations between discriminating variables & canonical discriminant functions (variables ordered by size of correlation within function)

(variables ordered by size of correlation within function) FUNC 1

FUNC 1

INCOMEINCOME .82202

HSIZEHSIZE .54096

VACATIONVACATION .34607

TRAVELTRAVEL .21337

AGEAGE .16354 Table 18.4

Table 18.4

Contd.

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Unstandardized canonical discriminant function coefficients Unstandardized canonical discriminant function coefficients

FUNC 1 FUNC 1 INCOME INCOME .8476710E-01 TRAVEL TRAVEL .4964455E-01 VACATION VACATION .1202813 HSIZE HSIZE .4273893 AGE AGE .2454380E-01 (constant)

(constant) -7.975476

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

Group FUNC 1FUNC 1 1 1.29118 2 -1.29118

Classification results for cases selected for use in analysis Classification results for cases selected for use in analysis

Predicted

Predicted Group MembershipGroup Membership Actual Group

Actual Group No. of CasesNo. of Cases 11 22 Group

Group 1 15 12 3

80.0% 20.0% Group

Group 2 15 0 15

.0% 100.0% Percent of grouped cases correctly classified: 90.00%

[image:11.720.105.686.223.504.2]

Percent of grouped cases correctly classified: 90.00% Table 18.4

Table 18.4

Contd.

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Classification Results for cases not selected for use in the analysis (holdout sample) Classification Results for cases not selected for use in the analysis (holdout sample)

Predicted

Actual Group No. of CasesNo. of Cases 11 22 Group

Group 1 6 4 2 66.7% 33.3%

Group

Group 2 6 0 6

.0% 100.0%

[image:12.720.278.689.124.529.2]

Percent of grouped cases correctly classified: 83.33%. Percent of grouped cases correctly classified: 83.33%. Table 18.4

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Results of Three-Group Discriminant Analysis

Group MeansGroup Means

AMOUNT INCOMEAMOUNT INCOME TRAVEL VACATION HSIZE AGETRAVEL VACATION HSIZE AGE 1 38.57000 4.50000 4.70000 3.10000 50.30000 2 50.11000 4.00000 4.20000 3.40000 49.50000 3 64.97000 6.10000 5.90000 4.20000 56.00000 Total 51.21667 4.86667 4.93333 3.56667 51.93333 Group Standard Deviations

Group Standard Deviations

1 5.29718 1.71594 1.88856 1.19722 8.09732 2 6.00231 2.35702 2.48551 1.50555 9.25263 3 8.61434 1.19722 1.66333 1.13529 7.60117 Total 12.79523 1.97804 2.09981 1.33089 8.57395

Pooled Within-Groups Correlation Matrix Pooled Within-Groups Correlation Matrix

INCOME

INCOME TRAVEL TRAVEL VACATION HSIZE AGE VACATION HSIZE AGE

INCOME

INCOME 1.00000 TRAVEL

TRAVEL .05120 1.00000 VACATION

VACATION .30681 .03588 1.00000 HSIZE

HSIZE .38050 .00474 .22080 1.00000 AGE

[image:13.720.85.585.70.500.2]

AGE -.20939 -.34022 -.01326 -.02512 1.00000 Table 18.5

Table 18.5

Contd.

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Wilks' (U-statistic) and univariate Wilks' (U-statistic) and univariate FF ratio with 2 and 27 degrees of freedom. ratio with 2 and 27 degrees of freedom. Variable

Variable Wilks' Lambda Wilks' Lambda FF SignificanceSignificance INCOME

INCOME .26215 38.00 .0000 TRAVEL

TRAVEL .78790 3.634 .0400 VACATION

VACATION .88060 1.830 .1797 HSIZE

HSIZE .87411 1.944 .1626 AGE

AGE .88214 1.804 .1840 CANONICAL DISCRIMINANT FUNCTIONS CANONICAL DISCRIMINANT FUNCTIONS

% of Cum Canonical After Wilks'% of Cum Canonical After Wilks' Function

Function Eigenvalue Variance %Eigenvalue Variance % Correlation Function Correlation Function  Chi-square df Significance_{Chi-square df Significance}

: 0 .1664 44.831 10 .00 1* 3.8190 93.93 93.93 .8902 : 1 .8020 5.517 4 .24 2* .2469 6.07 100.00 .4450 :

* marks the two canonical discriminant functions remaining in the analysis. * marks the two canonical discriminant functions remaining in the analysis.

Standardized Canonical Discriminant Function Coefficients Standardized Canonical Discriminant Function Coefficients

FUNC 1

FUNC 1 FUNC 2 FUNC 2 INCOME

INCOME 1.04740 -.42076 TRAVEL

TRAVEL .33991 .76851 VACATION

VACATION -.14198 .53354 HSIZE

HSIZE -.16317 .12932 AGE

AGE .49474 .52447 Table 18.5

Table 18.5

Contd.

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Structure Matrix: Structure Matrix:

Pooled within-groups correlations between discriminating variables and canonical discriminant Pooled within-groups correlations between discriminating variables and canonical discriminant functions (variables ordered by size of correlation within function)

functions (variables ordered by size of correlation within function) FUNC 1

FUNC 1 FUNC 2 FUNC 2 INCOME

INCOME .85556* -.27833

HSIZE

HSIZE .19319* .07749

VACATION

VACATION .21935 .58829*

TRAVEL

TRAVEL .14899 .45362*

AGE

AGE .16576 .34079*

Unstandardized canonical discriminant function coefficients Unstandardized canonical discriminant function coefficients

FUNC 1

FUNC 1 FUNC 2 FUNC 2 INCOME

INCOME .1542658 -.6197148E-01

TRAVEL

TRAVEL .1867977 .4223430

VACATION

VACATION -.6952264E-01 .2612652

HSIZE

HSIZE -.1265334 .1002796

AGE

AGE .5928055E-01 .6284206E-01

(constant)

(constant) -11.09442 -3.791600

Canonical discriminant functions evaluated at group means (group centroids) Canonical discriminant functions evaluated at group means (group centroids)

Group

Group FUNC 1FUNC 1 FUNC 2 FUNC 2

[image:15.720.45.713.139.454.2]

1 -2.04100 .41847 2 -.40479 -.65867 3 2.44578 .24020

Table 18.5 Table 18.5

Contd.

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Classification Results: Classification Results:

Predicted

Predicted Group MembershipGroup Membership

Actual GroupActual Group No. of CasesNo. of Cases 1 1 22 33

GroupGroup 1 10 9 1 0 90.0% 10.0% .0%

GroupGroup 2 10 1 9 0 10.0% 90.0% .0%

GroupGroup 3 10 0 2 8

.0% 20.0% 80.0% Percent of grouped cases correctly classified: 86.67%

Percent of grouped cases correctly classified: 86.67%

Classification results for cases not selected for use in the analysis Classification results for cases not selected for use in the analysis

Predicted

Actual Group No. of CasesNo. of Cases 11 22 33

GroupGroup 1 4 3 1 0 75.0% 25.0% .0%

.0% 75.0% 25.0%

25.0% .0% 75.0% Percent of grouped cases correctly classified: 75.00%

[image:16.720.39.711.81.511.2]

Percent of grouped cases correctly classified: 75.00% Table 18.5

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-4.0

Across: Function 1

Down: Function 2

All-Groups Scattergram

[image:17.720.55.702.20.526.2]

All-Groups Scattergram

Fig. 18.2

4.0

0.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

1

2

1 2

2

3

2

3

*

indicates a group centroid

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-4.0

Across: Function 1

Down: Function 2

[image:18.720.44.693.17.526.2]

Territorial Map

Fig. 18.3

4.0

0.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

1

1 3

*

-8.0

8.0

1 3

1 1 2 3

1 1 2 2 3 3

1 1 2 2

1 1 1 2 2 2 2 3 3

1 1 1 2 2

1 1 2 2

1 1 1 2 2

1 1 2 2

1 1 1 2 2

1 1 2 2 2

2 2 3

2 3 3

2 2 3 3

2 2 3

2 2 3 3

2 3 3

*

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Satisfactory Results Of Satisfaction

Programs In Europe

RIP 18.1

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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 18.1 Contd.

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Discriminant Analysis Discriminates

Ethical and Unethical Firms

RIP 18.2

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.

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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.

RIP 18.2 Contd.