discriminant analysis

Discriminant Analysis

Chapter OutlineChapter Outline1) Overview1) Overview

2) Basic Concept2) Basic Concept

3) Relation to Regression and ANOVA3) Relation to Regression and ANOVA

4) Discriminant Analysis Model4) Discriminant Analysis Model

5) Statistics Associated with Discriminant Analysis 5) Statistics Associated with Discriminant Analysis

6) Conducting Discriminant Analysis 6) Conducting Discriminant Analysis

i. Formulationi. Formulation

ii. Estimationii. Estimation

iii. Determination of Significanceiii. Determination of Significance

iv. Interpretationiv. Interpretation

v. Validationv. Validation

7) Multiple Discriminant Analysis 7) Multiple Discriminant Analysis

i. Formulationi. Formulation

ii. Estimationii. Estimation

iii. Determination of Significanceiii. Determination of Significance

iv. Interpretationiv. Interpretation

v. Validationv. Validation

8) Stepwise Discriminant Analysis8) Stepwise Discriminant Analysis

9) Internet and Computer Applications9) Internet and Computer Applications

10) Focus on Burke10) Focus on Burke

11) Summary11) Summary

12) Key Terms and Concepts12) Key Terms and Concepts

13) Acronyms13) Acronyms

Similarities and Differences between ANOVA, Similarities and Differences between ANOVA, Regression, and Discriminant AnalysisRegression, and Discriminant Analysis ANOVA ANOVA REGRESSION DISCRIMINANT REGRESSION DISCRIMINANT

ANALYSISANALYSIS

SimilaritiesNumber of One One OnedependentvariablesNumber ofindependent Multiple Multiple Multiplevariables

DifferencesNature of thedependent Metric Metric CategoricalvariableNature of theindependent Categorical Metric Metricvariables

Table 18.1Table 18.1

Conducting Discriminant AnalysisConducting Discriminant Analysis Fig. 18.1Fig. 18.1

Estimate the Discriminant Function Coefficients

Assess Validity of Discriminant Analysis

Determine the Significance of the Discriminant Function

Formulate the Problem

Interpret the Results

Information on Resort Visits: Analysis SampleInformation on Resort Visits: Analysis Sample Annual Attitude Importance Household Age of Amount Annual Attitude Importance Household Age of Amount Resort Family Toward Attached Size Resort Family Toward Attached Size Head of Spent on Head of Spent on

No. Visit Income Travel to FamilyNo. Visit Income Travel to Family Household Family Household Family

($000) ($000) Vacation Vacation VacationVacation

1 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 5 36 L (1)5 1 52.7 6 6 4 55 H (3)6 1 75.0 8 7 5 68 H (3)7 1 46.2 5 3 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)


Annual Attitude Importance Household Age of Amount Annual Attitude Importance Household Age of Amount Resort Family Toward Attached Size Resort Family Toward Attached Size Head of Spent on Head of Spent on



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 6 3 42 M (2)21 2 38.3 6 6 2 45 L (1)22 2 55.0 1 2 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 3 2 42 L (1)

Table 18.2 Contd.Table 18.2 Contd.

Information on Resort Visits: Holdout SampleInformation on Resort Visits: Holdout Sample

Annual Attitude Importance Household Age of Amount Annual Attitude Importance Household Age of Amount Resort Family Toward Attached Size Resort Family Toward Attached Size Head of Spent on Head of Spent on



1 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 6 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 3 37 M (2)12 2 38.2 2 2 3 49 L (1)


Results of Two-Group Discriminant AnalysisResults of Two-Group Discriminant Analysis GROUP MEANSGROUP MEANS VISITVISIT INCOMEINCOME TRAVEL VACATION HSIZE AGE TRAVEL VACATION HSIZE AGE

1 60.52000 5.40000 5.80000 4.33333 53.733332 41.91333 4.33333 4.06667 2.80000 50.13333Total 51.21667 4.86667 4.9333 3.56667 51.93333

Group Standard DeviationsGroup Standard Deviations

1 9.83065 1.91982 1.82052 1.23443 8.770622 7.55115 1.95180 2.05171 .94112 8.27101Total 12.79523 1.97804 2.09981 1.33089 8.57395

Pooled Within-Groups Correlation MatrixPooled Within-Groups Correlation MatrixINCOMEINCOME TRAVELTRAVEL VACATION HSIZE AGEVACATION HSIZE AGE

INCOMEINCOME 1.00000TRAVELTRAVEL .19745 1.00000VACATIONVACATION .09148 .08434 1.00000HSIZEHSIZE .08887 -.01681 .07046 1.00000AGEAGE - .01431 -.19709 .01742 -.04301 1.00000

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

VariableVariable Wilks' Wilks' FF SignificanceSignificanceINCOMEINCOME ..45310 33.800 .0000TRAVELTRAVEL .92479 2.277 .1425VACATIONVACATION .82377 5.990 .0209HSIZEHSIZE .65672 14.640 .0007AGEAGE .95441 1.338 .2572 Contd.Contd.


Results of Two-Group Discriminant AnalysisResults of Two-Group Discriminant Analysis

CANONICAL DISCRIMINANT FUNCTIONSCANONICAL DISCRIMINANT FUNCTIONS

% of Cum Canonical After Wilks'% of Cum Canonical After Wilks'FunctionFunction Eigenvalue Variance %Eigenvalue Variance % Correlation Function Correlation Function Chi-square df SignificanceChi-square df Significance

: 0 .3589 26.130 5 .00011* 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 CoefficientsStandard Canonical Discriminant Function Coefficients

FUNC 1FUNC 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 1FUNC 1 INCOMEINCOME .82202 HSIZEHSIZE .54096 VACATIONVACATION .34607 TRAVELTRAVEL .21337 AGEAGE .16354


Contd.Contd.

Results of Two-Group Discriminant AnalysisResults of Two-Group Discriminant Analysis Unstandardized canonical discriminant function coefficientsUnstandardized canonical discriminant function coefficients

FUNC 1FUNC 1INCOMEINCOME .8476710E-01TRAVELTRAVEL .4964455E-01VACATIONVACATION .1202813HSIZEHSIZE .4273893AGEAGE .2454380E-01(constant)(constant) -7.975476

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

GroupGroup FUNC 1FUNC 11 1.291182 -1.29118

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

PredictedPredicted Group MembershipGroup MembershipActual GroupActual Group No. of CasesNo. of Cases 11 22

GroupGroup 1 15 12 380.0% 20.0%

GroupGroup 2 15 0 15.0% 100.0%

Percent of grouped cases correctly classified: 90.00%Percent of grouped cases correctly classified: 90.00%


Contd.Contd.

Results of Two-Group Discriminant AnalysisResults of Two-Group Discriminant Analysis

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)

PredictedPredicted Group MembershipGroup MembershipActual GroupActual Group No. of CasesNo. of Cases 11 22

GroupGroup 1 6 4 266.7% 33.3%

GroupGroup 2 6 0 6.0% 100.0%

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


Results of Three-Group Discriminant AnalysisResults 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 50.300002 50.11000 4.00000 4.20000 3.40000 49.500003 64.97000 6.10000 5.90000 4.20000 56.00000Total 51.21667 4.86667 4.93333 3.56667 51.93333

Group Standard DeviationsGroup Standard Deviations

1 5.29718 1.71594 1.88856 1.19722 8.097322 6.00231 2.35702 2.48551 1.50555 9.252633 8.61434 1.19722 1.66333 1.13529 7.60117Total 12.79523 1.97804 2.09981 1.33089 8.57395

Pooled Within-Groups Correlation MatrixPooled Within-Groups Correlation MatrixINCOMEINCOME TRAVEL TRAVEL VACATION HSIZE AGE VACATION HSIZE AGE

INCOMEINCOME 1.00000TRAVELTRAVEL .05120 1.00000VACATIONVACATION .30681 .03588 1.00000HSIZEHSIZE .38050 .00474 .22080 1.00000AGEAGE -.20939 -.34022 -.01326 -.02512 1.00000


Contd.Contd.

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.

VariableVariable Wilks' LambdaWilks' Lambda FF SignificanceSignificance

INCOMEINCOME .26215 38.00 .0000TRAVELTRAVEL .78790 3.634 .0400VACATIONVACATION .88060 1.830 .1797HSIZEHSIZE .87411 1.944 .1626AGEAGE .88214 1.804 .1840

CANONICAL DISCRIMINANT FUNCTIONSCANONICAL DISCRIMINANT FUNCTIONS

% of Cum Canonical After Wilks'% of Cum Canonical After Wilks'FunctionFunction Eigenvalue Variance %Eigenvalue Variance % Correlation Function Correlation Function Chi-square df Significance Chi-square df Significance

: 0 .1664 44.831 10 .001* 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 CoefficientsStandardized Canonical Discriminant Function Coefficients

FUNC 1FUNC 1 FUNC 2 FUNC 2INCOMEINCOME 1.04740 -.42076TRAVELTRAVEL .33991 .76851VACATIONVACATION -.14198 .53354HSIZEHSIZE -.16317 .12932AGEAGE .49474 .52447


Contd.Contd.

Results of Three-Group Discriminant AnalysisResults of Three-Group Discriminant Analysis

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 1FUNC 1 FUNC 2 FUNC 2INCOMEINCOME .85556* -.27833HSIZEHSIZE .19319* .07749VACATIONVACATION .21935 .58829*TRAVELTRAVEL .14899 .45362*AGEAGE .16576 .34079*

Unstandardized canonical discriminant function coefficientsUnstandardized canonical discriminant function coefficientsFUNC 1FUNC 1 FUNC 2 FUNC 2

INCOMEINCOME .1542658 -.6197148E-01TRAVELTRAVEL .1867977 .4223430VACATIONVACATION -.6952264E-01 .2612652HSIZEHSIZE -.1265334 .1002796AGEAGE .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)GroupGroup FUNC 1FUNC 1 FUNC 2 FUNC 21 -2.04100 .418472 -.40479 -.658673 2.44578 .24020


Contd.Contd.

Results of Three-Group Discriminant AnalysisResults of Three-Group Discriminant Analysis

Classification Results:Classification Results:PredictedPredicted Group MembershipGroup Membership

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

GroupGroup 1 10 9 1 090.0% 10.0% .0%

GroupGroup 2 10 1 9 010.0% 90.0% .0%

GroupGroup 3 10 0 2 8.0% 20.0% 80.0%


Classification results for cases not selected for use in the analysisClassification results for cases not selected for use in the analysisPredictedPredicted Group MembershipGroup Membership

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

GroupGroup 1 4 3 1 075.0% 25.0% .0%

GroupGroup 2 4 0 3 1.0% 75.0% 25.0%

GroupGroup 3 4 1 0 325.0% .0% 75.0%


Table 18.5Table 18.5Results of Three-Group Discriminant AnalysisResults of Three-Group Discriminant Analysis

-4.0

Across: Function 1 Across: Function 1 Down: Function 2Down: Function 2

All-Groups ScattergramAll-Groups Scattergram Fig. 18.2Fig. 18.2

4.0

0.0

-6.0 4.0 0.0-2.0-4.0 2.0 6.0

1 1

1 1

1

1 1 1

1

2 1 2

2 2 2

2 3 3 3 3

3

3 3

2

3*

* *

* indicates a group centroid

-4.0

Across: Function 1 Across: Function 1 Down: Function 2Down: Function 2

Territorial MapTerritorial Map Fig. 18.3Fig. 18.3

4.0

0.0

-6.0 4.0 0.0-2.0-4.0 2.0 6.0

1

1 3

*

-8.0

-8.0

8.0

8.0

1 3

1 3

1 3

1 3 1 3 1 3 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 2 2

1 1 1 2 2

1 1 2 2

1 1 2 2

1 1 1 2 2 1 1 1 2 2

1 1 2 2 2

2 2 32 3 3

2 2 3 3

2 2 3

2 2 3

2 2 3

2 2 3 3

2 3 3

2 3 3

2 3 3

* *

* Indicates a group centroid

Satisfactory Results Of Satisfaction Programs In Europe

RIP 18.1RIP 18.1

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.

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.RIP 18.1 Contd.

Discriminant Analysis Discriminates Discriminant Analysis Discriminates Ethical and Unethical FirmsEthical and Unethical Firms

RIP 18.2RIP 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.

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.

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.RIP 18.2 Contd.

discriminant analysis

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multiple discriminant

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