Factor analysis

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Presented by

RangeGowda .R

I Ph.D (Agril. Economics)

UAS ,GKVK

Bengaluru

Factor analysis is an interdependence technique in that an entire set of interdependent relationships is examined.

Factor Analysis: a statistical technique used to,

1. Estimate factors variables

2. Reduce the dimensionality of a large number of variables to a fewer number of factors.

o Helps in Data Summarization and Reduction

Introduction

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Applications of factor analysis in marketing research

Market segmentation

Product research

Advertising studies

Pricing studies

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The factor model may be represented as

Where, Xi = A i1

Xi = ith standardized variable.Aij = Standardized multiple regression coefficient of variable i on

common factor j, F = Common FactorVi= Standardized regression coefficient of variable i on unique

factor i,Ui = The unique factor for variable i,m = Number of common factors.

i i1 1 i 2 2 i 3 3 im m i iX = A F + A F + A F + ...... + A F + V U

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Assumptions in Factor analysis

Observed variables should be linear combinations.

Some underlying structure does exist in the set of selectedvariables

Sample is homogenous

variables should be normality, homoscedasticity and linearityapply only to the extent that they diminish the observedcorrelations

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Steps in factor analysis

Formulate the problem

Construct the correlation matrix

Determine the method of factor analysis.

Determine the number of factors

Estimate the factor matrix

Rotate the factors

Estimating practical significance 7

Steps in factor analysis

Formulate the problem

The variables to be included in the factor analysis should be specified

Variables should be appropriately measured on an interval or ratio scale

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Construct the correlation matrix

The variables must be correlated

Formal statistics are available for testing appropriateness of the factor model, they are

Bartlett’s test

1. Chi-square transformation of the determinant of thecorrelation matrix

Kaiser- Meyer-Olkin (KMO) measure of sampling adequacy

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Kaiser- Meyer-Olkin (KMO) measure of sampling adequacy

o Ranges between 0 and 1o Value greater than 0.5 is desirable

oThe measure can be interpreted with the following guidelines:

0.8 or above- admirable0.7 or above –medium 0.6 or above-moderate0.5 or above- miserable or negligibleBelow 0.5-unacceptable

o Values above 0.5 for either the entire matrix or an individual variable indicate appropriateness

There are two approaches to factor analysis

1. Principal component analysis and

2. Common factor analysis

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The total variance of any variable can be divided into three types of variance

• Common varianceIs defined as that variance in a variable that is shared

with all other variables in the analysis

• Specific variance- Unique variancevariance associated with only a specific variable

• Error varianceUnreliable variation in a variable

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The selection of one of the method over the other is based on two criteria

• The objectives of the factor analysis

• The amount of prior knowledge about the variance in the variables

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Determine the number of factors

a. Apriori determination : Based on prior knowledge

b. Determination based on eigen values

o Only factors with eigen value greater than 1.0are retained

o All factors which less than 1 are considered

insignificant

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Based on significance tests

• Statistical significance of the separateeigen values

• Retain only those factors that arestatistically significant

• When sample size is large many will havesignificant values

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Interpreting the factors

Estimate the factor matrix

1. Factor loadings are the correlation of each

variable and the factor

2. Higher loadings making the variable

representative of the factor

3. Values greater than +0.50 are generally

considered necessary for practical

significance. 16

Case Study-I

Supply Chain Management of Organic Products in Karnataka

Gayatri, Y.P., (2007)

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o Studied the Factors influencing the consumer

preference for organic products

o Author has selected randomly 50 respondents from

four outlets

o Factors influencing the purchase of organic products

are examined with the help of factor analysis

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A total of twenty variables are considered encompassing different aspects of organic products VariablesOrganic food is more tastierIt is free of pesticide residuesIt is safe food for children and sickIt is nutritiousOrganic fruits and vegetables are larger than the conventional onesIt is less attractive than the conventional produceIt is eco-friendlyIt stays more fresh It can be stored for long periodHealth benefitsConsumers fall sick less oftenOrganic fruits are more sweeterProduced without using chemicalsIts high price confers better qualityIt is certifiedCertification is a quality assuranceNo genuinity between labeled & non-labeledFree from blemishesMeant for only high end users Organic consumption is status symbol

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Variables

Factor Loadings

Factor 1 Factor 2 Factor 3

Organic food is more tastier 0.839 0.022 -0.147

It is free of pesticide residues 0.780 -0.095 0.200

It is safe food for children and sick 0.688 -0.335 0.264

It is nutritious 0.705 -0.186 -0.248

Organic fruits and vegetables are larger than the

conventional ones

-0.672 0.150 -0.247

It is less attractive than the conventional produce 0.079 0.114 -0.047

It is eco-friendly 0.007 -0.158 0.713

It stays more fresh 0.969 -0.094 -0.214

It can be stored for long period 0.874 -0.195 -0.037

Health benefits 0.382 -0.167 -0.130

Consumers fall sick less often 0.551 -0.385 0.245

Organic fruits are more sweeter 0.144 0.137 0.202

Produced without using chemicals -0.020 0.459 -0.078

Its high price confers better quality 0.224 0.036 -0.009

It is certified -0.557 0.346 -0.005

Certification is a quality assurance -0.291 -0.066 -0.123

No genuinity between labeled & non-labeled -0.221 -0.222 0.121

Free from blemishes -0.005 0.020 -0.251

Meant for only high end users -0.297 0.766 0.116

Organic consumption is status symbol 0.100 0.607 -0.061

Rotated factor Matrix

Source: Gayatri, 2007 20

Factor 1 captured the quality of organic food free from

pesticide residues and its associated health benefits

Factor 2 was highly related to organic consumption as a prestige

issue

Factor 3 represented the consumer’s perception of eco friendly

nature organic products

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Sl.no

FactorsEigenvalues

% ofvariance

Cumulativevariance

1 Health benefits andpesticide free food

7.078 35.38 35.38

2 Prestige symbol 1.747 8.73 44.12

3 Eco-friendly natureof organic products

1.547 7.73 51.85

4Production withoutfertilizers

0.902 4.51 56.36

5 Price 0.770 3.84 60.21

Table 14: Total Variance Explained by Factor Analysis

Source: Gayatri, 2007 22

The results of factor analysis revealed three distinct factors

viz., health benefits, prestige issue and eco friendly nature

of organic products are found to influence in order the

purchase of organic products

Health benefits associated with the consumption of organic

products is the driving factor influencing their decision to

purchase

The eco friendly nature of these products is another factor

that influences the consumer’s preference

Results

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Conclusions

1. It provides the researcher to Data Summarization and

Reduction

2. The general purpose of factor analysis techniques is to

summarize the information

3. This requires large sample size and if the measurement

variables are in ratio scale we can get very good results

4. Factors scores calculated from this analysis can be used in

subsequent multivariate analysis

5. This can be used in market research (consumer preference)