Download ppt - Chapter Fifteen Overview of Other Multivariate Techniques and Data Mining

Chapter Fifteen

Overview of Other Multivariate Techniques

and Data Mining

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Dependence and Interdependence Techniques

• Dependence technique– One variable is designated as the dependent

variable and the rest are treated as independent variables

• Interdependence technique– There are no dependent and independent

variable designations, all variables are treated equally in a search for underlying patterns of relationships


Dependence Technique –Regression Analysis

• Input Data – Dependent variable(s) - metric – Independent variable(s) - metric

• Primary Purpose of the Technique– Ascertain the relative importance of

independent variable(s) in explaining variation in the dependent variable

– Predict dependentvariable values for given values of the independent variable(s)


Table 15.1 Overview of Multivariate Techniques


Analysis of Variance

• ANOVA is appropriate in situations where the independent variable is set at certain specific levels (called treatments in an ANOVA context) and metric measurements of the dependent variable are obtained at each of those levels


Example

24 Stores Chosen randomly for the study

8 Stores randomly chosen for each treatment

Treatment 1

Store brand sold at the regular price

Treatment 2Store brand sold at 50¢ off the regular price

Treatment 3

Store brand sold at 75¢ off the regular

price

monitor sales of the store brand for a week in each store


Table 15.2 Unit Sales Data Under Three Pricing Treatments


EG1(R) X1 O1

EG2(R) X2 O2

EG3(R) X3 O3

EG1 -- Experiment Group 1, X1-- Regular Price

EG2 -- Experiment Group 2, X2-- 50c off


O1 -- Observation (monitoring unit sales data in each store)



After Only Design


EG1(R) X1 O1

EG2(R) X2 O2

EG3(R) X3 O3

After Only Design

EG1 -- Experiment Group 1, X1-- Regular Price







ANOVA –Grocery Store Hypothesis

• Grocery Store Example– Ho 1 = 2 = 3 – Ha At least one is different from one or

more of the others • Hypotheses for K Treatment groups or

samples – Ho 1 = 2 = . . . = k – Ha At least one is different from one or

more of the others


Exhibit 15.1 SPSS Computer Output for ANOVA Analysis


Bank Customers

Gender

Male Female

< 35 Years

35-64 Years

> 64 Years

< 35 Years

35-64 Years

> 64 Years

Measure Overall Perceptions

Bank Customer Perceptions Study


Tests Between-Subjects EffectsDependent Variable:Overall Quality of the Company’s Services

Source Type IIISum ofSquares

df MeanSquare

F Sig.

CorrectedModel

2156.112a 5 431.222 438.891 .000

Intercept 20665.912 1 20665.912 1033.424 .000

Gender 382.436 1 382.436 389.237 .000

Age 1311.623 2 655.811 667.474 .000Gender * Age 260.433 2 30.216 132.532 .000

Error 459.823 468 .983

Total 24341.000 474

Corrected Total 2615.935 473

a. R Squared = .824 (Adjusted R Squared = .822)

Bank Customer Perceptions Study (Cont’d)



Descriptive Statistics

Dependent Variable: Overall Quality of the company's services

2.54 1.31 79

6.72 1.17 88

8.08 .82 85

5.87 2.57 252

6.49 1.39 55

6.95 .58 79

9.36 .48 88

7.79 1.53 222

4.16 2.36 134

6.83 .94 167

8.73 .93 173

6.77 2.35 474

Age<35

35-64

>64

Total

<35

35-64

>64

Total

<35

35-64

>64

Total

GenderMale

Female

Total

Mean Std. Deviation N

Male and female

customers differed in their

overall perceptions

Customers' perceptions differed

according to their ages


Estimated Marginal Means of Overall Quality of the company's services

Age

>6435-64<35

Estim

ate

d M

arg

ina

l M

ea

ns

10

8

6

4

2

Gender

Male

Female

Sex and age interacted in influencing perceptions



Factorial Anova

• The Factorial ANOVA is used to analyze data from a factorial design experiment variable– Using the grocery store example

• Add in the impact of an in-store, point of purchase display on orange juice

• In addition to the pricing factor


Exhibit 15.2 Illustrations of Main and Interaction Effects


Factorial ANOVA

• The interaction effect is calculated and F-tested

• SST=SSTR + SSE

• = SSA + SSB + SSAB + SSE

• SSA = Effect of Treatment A

• SSB = Effect of Treatment B

• SSAB= Interaction Effect


Discriminant Analysis

• Identifies the distinguishing features of prespecified subgroups of units that are formed on the basis of some dependent variable

• Examples of subgroups– Heavy, moderate, and light users of a product– Homeowners and renters– Viewers and nonviewers of a television

program


Discriminant Analysis (Cont’d)

• Dependent Variable– Categorical: as many categories as there are

subgroups

• Heavy, moderate, and light users: 3 categories• Independent Variable

– Metric-scaled

• Purpose of discriminant analysis is to classify new units into one of the subgroups given the new units’ values of the independent variable


Example

Computer Manufacturer

Household

income

Number of years of formal education

PC Ownership Not Owning A PC


Exhibit 15.3 Scatter Plot of Income and Education Data for Personal Computer Owners and Nonowners


Using the Discriminant Function

• Y = v1X1 + v2X2

– Discriminant weights v1 and v2 can be interpreted as signifying the relative importance of X1 and X2 in being able to discriminate between the two groups

• Ynew = v1X1,new + v2X2, new

– The program assigns either to the owner group or to the non-owner group based on the criterion value


Evaluating a Discriminant Function

• Confusion Matrix – Indicates the degree of correspondence, or

lack thereof, between the actual groupings of the sample units and the predicted groupings obtained by classifying the same units through the discriminant function


Table 15.3 Confusion Matrix


Usefulness of Discriminant Analysis

• Discriminant analysis is very useful for– Defining customer segments

– Identifying critical characteristics capable of distinguishing among them

– Classifying prospective customers into appropriate segments


Factor Analysis

• A data and variable reduction technique that attempts to partition a given set of variables into groups of maximally correlated variables


Intuitive Explanation

• Consider two statements from the Star Brand Inc.(SBI) survey

– S1. “I have been satisfied with the Star products I have purchased”

– S2. “When I have to purchase a home appliance in the future, it will likely be a Star product”


Exhibit 15.6 Situation in Which Factor Analysis Will Be Beneficial: S1 and S2 Highly Correlated


Exhibit 15.7 Situation in Which Factor Analysis Will Not Be Beneficial: S1 and S2 Poorly Correlated


Factor Analysis Output and Its Interpretation

• Primary output of factor analysis is a factor-loading matrix

• Achieved Communality– represents the proportion of variance in an

original variable accounted for by all the extracted factors.

– Each original variable will have an achieved communality value in the factor analysis output


Factor Analysis Output (cont)

• The eigenvalue for a given factor measures the variance in all the variables which is accounted for by that factor. – Note that the eigenvalue is not the percent of variance

explained but the amount of variance in relation to total variance

– (since variables are standardized to have means of 0 and variances of 1, total variance is equal to the number of variables).

– SPSS will output a corresponding column titled '% of variance'. A factor's eigenvalue may be computed as the sum of its squared factor loadings for all the variables.


Table 15.4 Factor-Loading Matrix Based on Data from Study of Star Customers


Reducing Star Data

• X1, X4, and X6 can be combined into one factor

• X2, X3, and X5 can be into a second factor

• 6 variables can be reduced to two factors


Potential Applications of Factor Analysis

• Used to – Develop concise but comprehensive, multiple-

item scales for measuring various marketing constructs

– Illuminate the nature of distinct dimensions underlying an existing data set

– Convert a large volume of data into a set of factor scores on a limited number of uncorrelated factors


Cluster Analysis

• Segment objects into groups so that members within each group are similar to one another in a variety of ways

• Useful for segmenting customers, market areas, and products


Use of Cluster Analysis

• Firm offering recreational services wanted to enter a new region of the country

• They gathered data on more than 100 characteristics including– Demographics– Expenditures on recreation– Leisure time activities– Interests of household members

• The firm identified one or several household segments that are likely to be most responsive to its advertising and to its services


How Does Cluster Analysis Work?

• Cluster analysis measures the similarity between objects on the basis of their values on the various characteristics


Exhibit 15.8 Clusters Formed by Using Data on Two Characteristics


Multidemensional Scaling

• Uncovers key dimensions underlying customers' evaluations from a series of similarity and/or preference judgments provided by customers about products or brands within a given set


Multi-Dimensional Scaling on SUV’s

• A customer is asked to compare pairs of SUVs and rank the pairs from most similar to least similar


Table 15.5 Similarity Rankings of Six 2005 SUVs


Exhibit 15.9 Multidimensional Map of 2005 SUVs Based on Similarity Rankings


Conjoint Analysis

• Technique for deriving the utility values that customers presumably attach to different levels of an object's attributes

• Requires respondents to compare hypothetical product profiles or, brands– The hypothetical stimuli are descriptive

profiles formed by systematically combining varying levels of certain key attributes


Personal Computer Study

• To assess the role played by attributes in customer evaluations of personal compters – Price: 3 levels - $299, $649, $999

– Processor: 2 levels – 2.6 GHz , 2.8 GHz

– Hard Drive: 4 levels - 80 GB, 120 GB, 160 GB, 200 GB


Personal Computer Study (Cont’d)

• 3 Levels of Price X, 2 Levels of Processor Speed X, 4 Levels of Hard Drive Capacity = 24 different descriptive profiles of personal computers are possible

• Data Collection in Conjoint Analysis– Two-Factors-at-a-Time Approach

– Full-Profile Approach


Note: This rating procedure would be repeated for the 12 price-versatility combinations and the 8 memory-versatility combinations

Price

Processing Speed

$299 $649 $999

2.6 GHx

2.8 ghZ

Personal Computer Study: Two-Factors-At-a-Time Approach


PERSONAL COMPUTER –

DESKTOP

Price$299

Speed2.6 GHz

Hard Drive80 GB

PERSONAL COMPUTER –

DESKTOP

Price$299

Speed2.6 GHz

Hard Drive120 GB

PERSONAL COMPUTER - DESKTOP

Price$299

Speed2.6 GHz

Hard Drive160 GB

PERSONAL COMPUTER -DESKTOP

Price$299

Speed2.6 GHz

Hard Drive200 GB

Note: Customers are asked to rank order their preferences for the 24 different profiles representing all possible combinations of the three attributes

Personal Computer Study: Full-Profile Approach


Exhibit 15.10 Utility Values for Three

Personal -Computer Attributes


Exhibit 15.10 Utility Values for Three Personal - Computer Attributes (Cont’d)


Relative Attributes of the 3 Attributes

• Range for price = 0.8 - 0.3 = 0.5 – Price is the most critical

• Range for hard drive capacity = 0.8 - 0.4 = 0.4 – Hard drive capacity is the next most critical

• Range for processor speed = 0.9 - 0.6 = 0.3 – Processor speed Ii the least critical


Potential Attractiveness of Different Personal Computer Configurations

• PC Configuration A– 2.6 GHz, 120 GB, $649

– Total utility for the personal computer = 0.6 + 0.7 + 0.4 = 1.7

• PC Configuration B – 2.8 GHz, 160 GB, $999

– Total utility for the personal computer = 0.9 + 0.8 + 0.3 = 2.0

• Personal Computer B is more attractive


Data Mining

• Is an analytic process designed to explore data to find consistent patterns or systematic relationships between variables

• Data mining is sometimes referred to as knowledge discovery in databases (KDD) or predictive analytics


Data Mining Procedures

• Association: Looking for patterns that connect one event or characteristic

• Sequence or path analysis: Looking for patterns in which one event leads to a later event

• Classification: Looking for new patterns by segmenting the data into groups.


Data Mining Procedures (Cont’d)

• Clustering: Finding and visually documenting groups of facts or groups of customers not previously known to be similar

• Scoring Models: Developing propensity scores for individual customers

• Forecasting/Prediction: Discovering patterns in data that can lead to reasonable predictions about the future


Data Mining Analysis

• The various data mining procedures are used in different types of data mining analysis

• For example, association and sequence or path analysis is used in market basket analysis, whereas classification and clustering are used for segmentation analysis


Market Basked Analysis

• Examines customers’ shopping carts to determine items that are most frequently purchased together

• From an analysis of 8 million market baskets, Mind Meld, Inc. has found that beauty care items, greeting cards, and seasonal candies were often bought together by “beauty conscious” customers


Market Basked Marketing Implications

1. Ability to place products that sell together in close proximity

2. Knowing which products potentially increase impulse purchasing

3. Suggest products to customers based on purchase by previous customers

4. Separate goods to ensure maximum coverage of the store


Classification Models

• Decision trees are one of the most popular classification algorithms

• The basic idea underlying the decision tree technique is to hierarchically segment individuals included in the database on the basis of a designated categorical dependent variable


Sample Decision Tree

• The first split is based on income variable. All users of the product are high-income customers

• The second split is based on education and shows that 100% of customers have a college degree

• Thus the firm should target high income customers with college degrees


15.12 Sample Decision Tree (Cont’d)


Scoring Models and RFM Analysis

• A score (typically a numerical value) is assigned to each record in the database and indicates the likelihood that the specific customer will exhibit a particular behavior

• Recency, Frequency and Monetary Value Analysis (RFM) is one of the most commonly used scoring models


RFM Analysis

1. Customers who purchased recently are more likely to buy again than customers who have not purchased in a while

2. Customers who purchase frequently are more likely to buy again than customers who have made just one or two purchases

3. Customers who spent the most money in total are more likely to buy again. The most valuable customers tend to continue to become even more valuable.


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Forecasting or Prediction Models

• Logistic Regression is a type of regression analysis in which the dependent variable is dichotomous coded as either 1 or 0, to represent the occurrence or nonoccurrence of some outcome event.

• Where p is the probability that Y-1 and X1, X2…Xn are the independent variables and Beta sub 0, Beta sub 1….Beta sub N are the regression coefficients.


Logistic Regression

• Does not assume that the relationship between the independent and dependent variable is linear

• Does not assume that the dependent variable or error terms are normally distributed


Neural Networks

• Neural network models mimic the functioning of the human brain and basically work on the principle of biological neurons


Neural Network Analysis

• Like the human brain, neural networks can learn. New information is assimilated and used to make decisions.

• Neural network analysis has been shown to make superior predictions over other more traditional forecasting techniques such as discriminant analysis and logistic regression.


New Trends in Data Mining

• New data sources such as audio or video data are leading to new techniques for analyzing that data

• Text mining analysis is used to uncover patterns and relationships within thousands of documents

• The same techniques are now being adapted to search audio and video files


Case Study- Athenaeum Booksellers—Part B• Case objectives:

• Opportunity to analyze the factor analysis output for an actual research study.

• Learn some of the technical aspects of factor analysis

• Infer matters of managerial significance.

• Review and interpret the eigenvalues contained in the output.

• analyze and interpret the different factors that arise out of the analysis.

• consider the managerial implications of the findings.


Case Discussion• Address the information in the first table,

specifically the interpretation of the eigenvalues. • Interpret the percent of variance explained• Interpret the factor loadings for the two factors• What do these factors represent?• What are the managerial implications to Mr.

Karvonides• The factor analysis tables are in the textbook• Copy of the customer satisfaction survey is in the

textbook.


First Factor• Eigenvalue of 3.110 (out of a total of 7),• Explains roughly 44 percent of the variance. • It represents aspects of service and variety. • The implications of these findings are that

– Mr. K should be sure to provide good levels of service and a wide variety of products in order to satisfy customers.

• The following variables load heavily on the first factor:


CASE DISCUSSION