Factor Analysis

Factor Analysis

Need of factor analysis The difficulties in a having too many independent variables in predicting the response variable are :  Increased computational time to get solution .  Increased time in data collection .  Too much expenditure in data collection  Presence of redundant independent variables.  Difficulty in making inference .

These can be avoided using Factor Analysis

What is Factor Analysis ?

Factor analysis aims at grouping the original input variables into factors which underlie the input variables

Theoretically

The total no of factors = total no of input variables

But after performing Factor Analysis

The total no of factors in the study can be reduced by dropping the insignificant factors 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 number of 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 involvement across a number of product categories, 19 items were reduced to four factors of : 1. Perceived product importance/ perceived importance s of negative consequences of a mispurchase 2. Subjective probability of a mispurchase 3. Pleasure of owing/using product. The value of the product as a cue to the type of person who owns it Each of these factors 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 the variables in a data set come from a specifies number of factors.

Example Customer feedback about a two wheeler – on the basis of 6 variables are –  Fuel efficiency  Life of two wheeler  Handling convenience  Quality of original spare parts  Breakdown rate  Price

Assigning variables      

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

Factor Analysis can group these variables as 

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



X6 -Factor 2(Price Factor )



X3- Factor 3( Personal Factor)

Essence 

In future while conducting a detailed study ,it is sufficient to get opinion of the customers on the three factors which are 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 or interrelationships among data. The analysis begins by observing the correlation and determining whether there are significant correlations between them.

Terminology 1.Factor Loading –  A set of correlation of the original variable with the factor .  A measure of the importance of a variable in measuring a factor ,  A means for interpreting and labeling a factor .

2.Factor Score 



A number that represents each observations calculated value on each factor in a factor analysis. At the initial stage ,the respondents assign scores for the variables. After performing factor analysis ,each factor assigns a score for each respondent .Such score are called factor score.

3.Communality 



In factor Analysis ,a measure of the percentage of a variable’s variation that is explained by the factors . A relative high communality indicates that a variable has much in common with the other variables taken as a group.

Cluster Analysis 

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

Multidimensional scaling 



A technique that measures attitudes about objects in multidimensional space on the basis of respondents judgments of similarity of objects . MDS is the extension of multivariate techniques for measuring human perception & preference.

MDS is used to measure human perception and preferences towards some stimuli (object ) , like product, organizations ,places ,events and positioning them in a perceptual space .