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MULTIVARIATE ANALYSIS This note briefly describes some of the common multivariate techniques

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STATISTICAL ANALYSIS – MULTIVARIATE ANALYSIS

• Multiple Regression

• Discriminant Analysis

• Factor Analysis

• Cluster Analysis

• AID (Automatic Interaction Detector)

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MULTIPLE REGRESSION ANALYSIS

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MULTIPLE REGRESSION ANALYSIS

• Method for studying the relationship between

a dependent variable and two or more

independent variables.

• Purposes:

• Prediction

• Explanation

• Theory building

• Y’ = a + b1X1 + b2X2 + …bkXk

• R2 – measure of the proportion of variation

explained ( higher the better)

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DESIGN REQUIREMENTS

• One dependent variable (criterion)

• Two or more independent variables (predictor variables).

• Sample size: >= 50 (at least 10 times as many cases as independent variables)

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SIMPLE VS. MULTIPLE REGRESSION

• One dependent variable Y predicted from

one independent variable X

• One regression coefficient

• R2: proportion of variation in dependent

variable y predictable from x

• One dependent variable Y predicted from

a set of independent variables (X1, X2

….Xk)

• One regression coefficient for each

independent variable

• R2: proportion of variation in dependent

variable Y predictable by set of

independent variables (x’s)

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EXAMPLE: THE MODEL

• Y’ = a + b1x1 + b2x2 + …bkxk

• The b’s are called partial regression coefficients

• x1,x2 etc are the independent variables

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MULTIPLE CORRELATION COEFFICIENT (R) AND COEFFICIENT OF MULTIPLE DETERMINATION (R2)

• R = the magnitude of the relationship between the dependent variable and the

best linear combination of the predictor variables

• R2 = the proportion of variation in Y accounted for by the set of independent

variables (x’s).

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FACTOR ANALYSIS

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FACTOR ANALYSIS

• A variable reduction technique

• Reduces a set of variables in terms of a smaller no of latent factors

(unobservable)

• Factor Analysis is a correlational method used to find and describe

the underlying factors driving data values for a large set of variables

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WHAT IS A FACTOR

• A Factor is a Linear combination of variables. It is a Construct that is

not directly observed but needs to be inferred from the input

variables

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USE OF FACTOR ANALYSIS

• Data Reduction

• Questionnaire Construction

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EXAMPLE

Airline Study On Time Seat Comfortable Love Food Air Hostess Beautiful Boss and Friend fly in Jet Airlines Younger Aircraft Frequent Flyer programme Suits my schedule Mom feels safe in Jet Arlines Complements my lifestyle

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EXAMPLE

Airline Study Factors 1 2 3 On Time 0.954 -0.004 0.153 Seat Comfortable 0.037 0.09 0.962 Love Food 0.912 0.037 -0.052 Air Hostess Beautiful -0.062 0.965 0.096 Boss and Friend fly in Jet Airlines 0.578 0.149 -0.325 Younger Aircraft 0.959 -0.04 0.021 Frequent Flyer programme -0.028 0.985 -0.005 Suits my schedule -0.077 0.175 0.958 Mom feels safe in Jet Arlines -0.184 -0.389 -0.086 Complements my lifestyle -0.016 0.956 0.097

• FACTOR 1

• On time

• Love Food

• Younger Aircraft

• FACTOR 2

• Air Hostess

beautiful

• FF Programme

• Lifestyle

• FACTOR 3

• Seats

• Suits my schedule

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CLUSTER ANALYSIS

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CLUSTER ANALYSIS

• Cluster analysis or clustering is the task of

grouping a set of objects in such a way that

objects in the same group (called a cluster)

are more similar (in some sense) to each

other than to those in other groups (clusters).

• Used to identify similar groups of people

• Used for Consumer segmentation

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SOME APPLICATIONS OF CLUSTER ANALYSIS

• Market Segmentation: Grouping people according to their similarity in several dimensions related

to a product under consideration.

• Purchasing power

• Needs

• Psychographics & Lifestyle

• Attitudes

• Sales Segmentation: Clustering can tell you what types of customers buy what products

• Credit Risk: Segmentation of customers based on their credit history

• City-planning: Identifying groups of houses according to their house type, value, and

geographical location

• Geographical: Identification of areas of similar land use in an earth observation database

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SEGMENTATION – E.G. MOTHERS OF YOUNG BABIES (LESS THAT 3 YEARS)

Pragmatic Mom

Know it All Mom

Dutiful Mom

Profile of these

segments give

direction for

marketing action

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SOME INDICATIVE STATEMENTS FROM THE BATTERY OF STATEMENTS USED (Total statements more than 30)

I pay a lot more attention to the care of my baby’s delicate skin than I care for my own body skin

I tend to compare my baby’s development to other babies

I am very selective in choosing a trusted established brand of baby products that are proven safe for use on my baby

When choosing a baby skin care product for my baby, I am the kind of person who reads product labels about ingredients and functions before buying

I am willing to pay more money to buy baby care products that are proven to be suited for my baby

In general, I feel that a more expensive baby brand means it has better product quality

In general, I believe that baby brands which are less expensive works as well as expensive baby brands

I rely mostly on my mothers information when it comes to advice on baby care

I rely mostly on my friends who are also moms/have babies when it comes to advice on baby care

I like to use the internet for information, connecting with other moms online, etc

I actively keep myself updated about lifestyle and social trends and new baby products that come to the market

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SEGMENTATION – E.G. MOTHERS OF YOUNG BABIES (LESS THAT 3 YEARS)

Example: Dutiful MOM - Profile

Life stage/demographic

26, 2yrs of marriage, SEC B, left her job to

bring up child

Attitudes to baby care products

Try to follow both modern as well as home

tips prescribed by mother and Mother in law.

Attitudes to motherhood

A necessary step in her life. She is proud of

her child as she has completed that step.

Lifestyle

Lives with in-laws. Traditional. Maintains

self. Maintains the house. Good cook. She got

married before her father retired.

Brands & products used

Soap, powder, oil and moisturizing

Key influencers regarding Baby care

Mother, Mother in law, Husband, General

societal norms

Baby care regime

Massaging and bathing in morning and

evening. Applies traditional remedies from

time to time. Uses various brain stimulating

ties

Behaviour regarding child rearing

She will do everything that she has been told

that she needs to do. Will follow a check list.

But she will not indulge her child.

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OTHER – MULTIVARIATE COMMON ANALYSIS METHODS

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OTHER – MULTIVARIATE COMMON ANALYSIS METHODS

• Discriminant Analysis

• DA is a technique for analyzing data when the dependent variable is Nominal and

the independent variables are Interval in nature.

• Discriminant Analyses Applications:

• Market Research: Market segmentation

• Financial Research: Default behavior( Credit Cards, Loans)

• Human resources: High performers

• AID or CHAID (Chi Square Automatic Interaction Detector)

• CHAID (Chi-square Automatic Interaction Detector) analysis is an algorithm used for

discovering relationships between a categorical response variable ( Nominal Scale) and

other categorical ( Nominal Scale) predictor variables. It is useful when looking for patterns

in datasets with lots of categorical variables and is a convenient way of summarizing the data

as the relationships can be easily visualized.