Factor Analysis Factor Analysis

Need of factor analysis Need of factor analysis

The difficulties in a having too many The difficulties in a having too many independent variables in predicting the independent variables in predicting the response variable are :response variable are :

Increased computational time to get Increased computational time to get solution .solution .

Increased time in data collection .Increased time in data collection . Too much expenditure in data collection Too much expenditure in data collection Presence of redundant independent Presence of redundant independent

variables.variables. Difficulty in making inference .Difficulty in making inference .

These can be avoided These can be avoided using Factor Analysisusing Factor Analysis

What is Factor Analysis ?What is Factor Analysis ?

Factor analysis aims at Factor analysis aims at grouping the original grouping the original input variables into input variables into

factors which underlie factors which underlie the input variables the input variables

TheoreticallyTheoretically

The total no of factors = total no of The total no of factors = total no of input variables input variables

But after performing Factor But after performing Factor Analysis Analysis

The total no of factors in The total no of factors in the study can be reduced the study can be reduced

by dropping the by dropping the insignificant factors insignificant factors

based on Certain Criteria based on Certain Criteria ..

objective of Factor analysis

The main objective of Factor analysis is to summarize a large number of underlying factors

into a smaller number of variables or factors which represent the basic factors underlying the data.

Factor analysis is used to uncover the latent structure (dimensions) of a set of variables.

It reduces attribute space from a larger numberof variables to a smaller number of factors and as

such is a “nondependent" procedure (that is, it does not assume a dependent variable is specified).

Applications

The main applications of factor analysis are in marketing research.

Some of the application are as follows:

1.Developing perceptual maps

Factor analysis is often used to determine the dimensions or criteria by which consumers evaluate brands and how each brand is seen on each dimension.

2.Determining the underlying dimensions of

the data

A factor analysis of data on TV viewing indicates that there are seven different types of programmers that are independent of

the network offering as perceived by the viewers: movies, adult entertainment, westerns, family entertainment, adventure plots, unrealistic events ,songs .

3. Identifying market segments; and positioning

of products;An example of this : In a study of consumer involvementacross a number of product categories, 19 items were reducedto four factors of :1. Perceived product importance/ perceived importance s ofnegative consequences of a mispurchase2. Subjective probability of a mispurchase3. Pleasure of owing/using product. The value of the productas a cue to the type of person who owns it Each of thesefactors was independent and there was no multicollinearity.4. Testing of hypotheses about the structure of a data set.Confirmatory factor analysis can be used to test whether thevariables in a data set come from a specifies number of factors.

Example Example

Customer feedback about a two Customer feedback about a two wheeler – on the basis of 6 variables wheeler – on the basis of 6 variables are –are –

Fuel efficiency Fuel efficiency Life of two wheeler Life of two wheeler Handling convenience Handling convenience Quality of original spare partsQuality of original spare parts Breakdown rateBreakdown rate Price Price

Assigning variables Assigning variables

Fuel efficiency -X1Fuel efficiency -X1 Life of two wheeler- X2 Life of two wheeler- X2 Handling convenience –X3Handling convenience –X3 Quality of original spare parts-X4Quality of original spare parts-X4 Breakdown rate-X5Breakdown rate-X5 Price –X6Price –X6

Factor Analysis can group Factor Analysis can group these variables asthese variables as

X1,X2,X4 and X5 – Factor 1 X1,X2,X4 and X5 – Factor 1 (Technical factor)(Technical factor)

X6 -Factor 2(Price Factor )X6 -Factor 2(Price Factor )

X3- Factor 3( Personal Factor)X3- Factor 3( Personal Factor)

Essence Essence

In future while conducting a In future while conducting a detailed study ,it is sufficient to detailed study ,it is sufficient to get opinion of the customers on get opinion of the customers on the three factors which are the three factors which are obtained through factor analysis. obtained through factor analysis.

Factor Analysis-The Theory

Factor analysis is a complex statistical technique which works on the basis of consumer responses to identify similarities or associations across factors. It analyzes correlations between

variables, reduces their numbers by grouping them in to fewer factors.

How it Works

Factor analysis applies an advanced form of correlation analysis to a no. of factors / statements or attributes. If several of the statements are highly correlated, it is thought that these statements measure some factor common to all of them.

A typical study will throw up many such factors. For each such the researchers have to use their judgment to determine what a particular factor represents. Factor analysis can only be applied to continuous or intervally scaled variables.

Factor Analysis - The Process

We now take the case of a marketing research study where factor

analysis is most popularly used. We begin by administering a

questionnaire to all consumers. What factor analysis does is it

identifies two or more questions that result in responses that are

highly correlated. Thus it looks at interdependencies orinterrelationships among data. The analysis begins by

observingthe correlation and determining whether there are

significantcorrelations between them.

Terminology Terminology

1.Factor Loading – 1.Factor Loading – A set of correlation of the original A set of correlation of the original

variable with the factor .variable with the factor . A measure of the importance of a A measure of the importance of a

variable in measuring a factor ,variable in measuring a factor , A means for interpreting and A means for interpreting and

labeling a factor .labeling a factor .

2.Factor Score 2.Factor Score

A number that represents each A number that represents each observations calculated value on observations calculated value on each factor in a factor analysis.each factor in a factor analysis.

At the initial stage ,the respondents At the initial stage ,the respondents assign scores for the variables. After assign scores for the variables. After performing factor analysis ,each performing factor analysis ,each factor assigns a score for each factor assigns a score for each respondent .Such score are called respondent .Such score are called factor score. factor score.

3.Communality 3.Communality

In factor Analysis ,a measure of the In factor Analysis ,a measure of the percentage of a variable’s variation percentage of a variable’s variation that is explained by the factors .that is explained by the factors .

A relative high communality A relative high communality indicates that a variable has much in indicates that a variable has much in common with the other variables common with the other variables taken as a group.taken as a group.

Cluster AnalysisCluster Analysis

An Analysis that classifies An Analysis that classifies individuals or objects into a smaller individuals or objects into a smaller number of mutually exclusive groups number of mutually exclusive groups ,ensuring there will be as much ,ensuring there will be as much likeness within groups and as much likeness within groups and as much difference among groups as difference among groups as possible .possible .

Multidimensional scaling Multidimensional scaling

A technique that measures attitudes A technique that measures attitudes about objects in multidimensional about objects in multidimensional space on the basis of respondents space on the basis of respondents judgments of similarity of objects .judgments of similarity of objects .

MDS is the extension of multivariate MDS is the extension of multivariate techniques for measuring human techniques for measuring human perception & preference.perception & preference.

MDS is used to measure MDS is used to measure human perception and human perception and preferences towards preferences towards

some stimuli (object ) , some stimuli (object ) , like product, like product,

organizations ,places ,evorganizations ,places ,events and positioning ents and positioning them in a perceptual them in a perceptual

space .space .