factor analysis (1)

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EXPLORATORY

FACTOR ANALYSIS:USING SPSS

Dr. Vipul Patel

A researcher is interested to study the consumer

motivation to shop in shopping malls. He developed the

research instrument after conducting in depth review of

the literature. The instrument contained 35 statements on

seven point likert type scale.

After conducting exploratory factor analysis, the

researcher summarized the 35 statements in six

motivational factors to shop in Shopping Malls.

Economic Incentives, Aesthetic Ambience, Diversion/Browsing,

Social Experience, Convenient Service Availability, Meal /

Snack Consumption

Source: Kang, Kim and Taun (1993) Motivational Factors of Mall Shoppers Effects of Ethnicity and Age Journal

of Shopping Center Research, Vol. 3(1), pp.7-31


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A researcher is interested to measure the image of the

bank. Respondents were asked to rate the importance of

15 bank attributes. A five point likert scale ranging from

not important to very important was employed.

After conducting exploratory factor analysis, a four

factor solution resulted: Traditional Services (6),

convenience (4), visibility(4) and competence (2).

Source: Sinukula , J.M. and Lowtor, L (1987), Positioning in the Finanacial Service Industry: A Look at the

Decompossion of Image, i n Jon. M. Hawes and George B Glisan, eds., Development in Marketing Science, Vol. 10

(Akron, OH, Academy of Marketing Science, 1987): pp.439-42.

Brand Personality Scale

A researcher is interested to develop the scale for brand

personality. At the initial stage, 309 personality traits

were identified. These were reduced to 114 personality

traits for study.

Using exploratory factor analysis, five dimensions with 15

traits of brand personality were identified.

Sincerity (4), Excitement (4), Competence (3), Sophistication

(2), Ruggedness (2)

Further, the researcher used CFA to check validity and

reliability of Brand personality scale.

Source: Aaker, J.L. (1997), Dimensions of Brand Personality, Journal of Marketing Research, Vol. 34 (3), pp.347-

356.


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SERVQUAL Scale A researcher is interested to measure perceived service

quality. Ninety seven statements were originally

developed.

These ninety seven statements were reduced to 34

statements using factor analysis. These 34 statements

were further reduced to 22 statements, reflecting five

dimensions of service quality.

Tangibility, reliability, responsiveness, assurance andempathy.

Source: Parasuraman, A; Zeithaml, V. A and Berry, L.L. (1988), SERVQUAL: A Multiple-Item Scale For Measuring

Consumer Perceptions of Service Quality, Journal of Retailing, Vol. 64 (1), pp.12-40.

Job Satisfaction of Industrial Salesperson

The researcher is interested to develop the scale to measure

the job satisfaction of industrial sales person.

Through an extensive literature review and open ended

questions with salespeople and a work psychologist, 185 items

were generated. These items were reduced to 117 items andfurther reduced to 95 items using factor analysis techniques.

During this procedure, seven dimensions of job satisfaction

were identified: (1) the job itself, (2) fellow worker, (3)

supervisors (4) company policy and support (5) pay (6)

promotion and advancement (7) customers.

Source: Churchil, Ford and Walker (1974), Measuring the Job Satisfaction of Industrial Salesmen, Journal of

Marketing Res earch, Vol. 11, pp.254-260


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Perceived Leadership Behavior

Researcher is interested to classified the leadership behavior.

Based on path goal theory and extensive literature review, a

pool of 35 items were generated. Data were collected from

206 employees of two electronic firms and consisted of

manager, professionals, foremen, blue collar workers,

technicians and others.

Principal Components Factor Analysis revealed three types of

leadership behavior : Instrumental leadership (7), Supportive

Leadership (10) and Participative leadership (5).

Source: House, Robert, J and Dessler Gary (1974) The Path Goal Theory of Leadership: Some Post Hoc and A

Priori Tests, In James G Hunt and Lars L Larson (Eds), Contingency Approaches to Leadership. Carbondale:

Southern Illinois University Press.

In a study, a researcher is interested to study the customer

preference for life insurance in Northern Region of India.

Data were collected from 600 customers on 20 reasons

(i.e., variables) for preference of life insurance on five

point likert scale from 1 = least important to 5 = mostimportant

Using Factor Analysis, five factors are derived: Core

Product, Promotional, Consumer Expectation, Service

Quality, and Risk Return.


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What is Factor Analysis? Factor analysis is a method of data reduction and

summarisation: take many variables and explain them

with a few factors or components or dimensions

The common objective of factor analysis is to

represent a set of variables in terms of a smaller

number of latent variables.

The primary function of factor analysis is to definethe underlying structure among the variables in the

analysis.

SERVQUAL

R-Matrix:

V1 V2 V4 V3 V5 V6

V1: Prevention of Cavities 1.000V2: Fighting againstGerms

0.837 1.000

V4: Prevention of toothdecay

0.858 0.672 1.000

V3: Shiny teeth 0.053 0.002 -0.248 1.000

V5: Fresh Breath 0.004 -0.155 0.018 0.778 1.000

V6: Attractive teeth -0.086 0.0001 0.007 0.596 0.779 1.000

Underlying benefits Consumers seek from the purchase

of toothpaste

Health Benefit Factor

Social Benefit Factor


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Factor analysis is foundation for other univariate or

multivariate analysis like t test, ANOVA, MANOVA,

Regression Analysis, Cluster Analysis, etc.

Factor Analysis can be used for checking reliability

and validity of scales designed to measure latent

variables.

(CFA using AMOS)

EFA v/s CFA

Exploratory Factor Analysis (EFA):

The researcher may not have any idea as to how many

underlying dimensions there are for the given data.

Factor analysis may be used a means of exploring the

data for possible data reduction.

Confirmatory Factor Analysis

The researcher may anticipate or hypothesize that

there are n different underlying dimensions and that

certain variables belong to one dimension while others

belong to the second.


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Assumptions of Factor Analysis Sample should be homogeneous with respect to the

underlying factor structure.

Normality

Kolmogorove-Smirnove Test

Skewness and Kurtosis

Multicollinearity

Determinant of the R-Matrix should be greater than0.00001.

Procedure for EFA

Stage 1: Conceptual Consideration

Stage 2: Appropriateness of Data for Factor

Analysis

Stage 3: Method of Factor Analysis Stage 4: Extraction, Interpretation and Naming the

Factors.


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Stage 1: Conceptual Consideration R factor Analysis v/s Q factor Analysis

Variable Selection

Garbage in, Garbage out

Metric variables (continuous variables)

Five or more variables per factor

Sample Size

The sample must have more observation than variables.

The minimum sample size should be 50.

Preferable sample size should be 100 or more. As a general rule, the minimum sample size is to have at

least five times as many observations as the number of

variables to be analyzed, and the more acceptable

sample size would have a 10:1 ratio.

Some researchers even propose a minimum of 20 cases

for each variable.


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Stage 2: Appropriateness of Data for

Factor Analysis

Kaiser-Meyer-Olkin (KMO) Measure of Sampling

Adequacy

Values of of KMO between 0.5 and 0.7 are mediocre,

values between 0.7 and 0.8 are good, values between

0.8 and 0.9 are great and values above 0.9 are superb

(Hutcheson & Sofroniou, 1999).

Bartletts test of sphericity

Stage 3: Method of Factor Extraction

Principal Component Analysis

Common Factor Analysis


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Stage 4: Number of Factors Determination based on Eigenvalue

Determination based on Scree Plot

Determination based on Percentage of Variance

A priori Determination

Scree Plot

Point of Inflexion


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Stage 5: Interpret and Name the

Factors Factor Loading

Factor loadings are the weights and correlations between each

variable and the factor.

The higher the load the more relevant in defining the factors

dimensionality.

Factor loading in the range of 0.30 to 0.40 are considered

to meet the minimum level for interpretation of structure.

Loadings 0.50 or greater are considered practicallysignificant.

Loadings exceeding 0.70 are considered indicative of wee

defined structure and are the goal of any factor analysis.

Factor Rotation

Orthogonal Rotation & Oblique Rotation

Interpretation of factor Structure

Step1: Examine factor loadingsCross loading

Step 2: Assess the communality of variables

Step 3 : Label the Factors


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Interpretation of a Hypothetical Factor Loading

Matrix

Unrotated Factor Loading Matrix VARIMAX Rotated Factor Loading Matrix

Factor Factor

1 2 3 1 2 3 Communality

V1 0.511 0.250 -0.204 V1 0.462 0.099 0.505 0.324

V2 0.614 -0.446 0.264 V2 0.101 0.778 0.173 0.644

V3 0.295 -0.447 0.107 V3 -0.134 0.517 0.114 0.477

V4 0.561 -0.176 -0.550 V4 -0.005 0.184 0.784 0.648

V5 0.589 -0.467 0.314 V5 0.087 0.801 0.119 0.664

V6 0.630 -0.102 -0.285 V6 0.180 0.302 0.605 0.548

V7 0.498 0.611 0.160 V7 0.795 -0.032 0.120 0.647

V8 0.310 0.300 0.649 V8 0.623 0.293 -0.366 0.608

V9 0.492 0.597 -0.094 V9 0.694 -0.147 0.323 0.608

*Factor loading more than 0.4 is considered for interpretation

Simplified Rotated Factor Loading Matrix

Factor

1 2 3

V2 0.807

V5 0.803V3 0.524

V7 0.802

V9 0.686

V8 0.655

V4 0.851

V6 0.717

*Factor loading less than 0.40 are not shown.

**Variables are shorted by highest loadings.


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SPSS Exercise

Case Study: HBAT

SPSS File: Case_HBAT.sav

Uses of Factor Analysis Results

Surrogate Variable

Summated Scales

Reliability Analysis

Cronbach Alpha should be greater than 0.7, althougha 0.60 level can be used in exploratory research.


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Thank You!!!

Dr. Vipul Patel

([email protected])

factor analysis (1)

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