Factor Analysis - 360 Degree View ( Karanbir Singh , 12141 , Marketing)

INTRODUCTION

Factor analysis is a statistical technique to study the inter-relationships among the variables in an effort to find a new set of factors, fewer in number than the original variables so that the factors are common among the original variables. In factor analysis a small number of common factors are extracted so that these common factors are sufficient to study the relationships of original variables.

In many real-life applications, the number of independent variables used in predicting a response variable will be too many. The difficulties in having too many independent variables in such exercise are as follows,

•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 inferences.
These can be avoided using factor analysis.

AIMS OF FACTOR ANALYSIS

• Factor analysis helps the researcher to reduce the number of variables to be analyzed, thereby making the analysis easier.
• Analysis based on a wide range of variables can be tedious and time consuming.
• For example, consider a market researcher at a credit card company who wants to evaluate the credit card usage and behaviour of customers, using various variables. The variables include age, gender, marital status, income level, education, employment status, credit history and family background.
•Using Factor Analysis, the researcher can reduce the large number of variables into a few dimensions called factors that summarize the available data.
• Its aims at grouping the original input variables into factors which underlying the input variables.
• For example, age, gender, marital status can be combined under a factor called demographic characteristics. The income level, education, employment status can be combined under a factor called socio-economic status. The credit card and family background can be combined under factor called background status.

BENEFITS OF FACTOR ANALYSIS

¨ To identify the hidden dimensions or construct which may not be apparent from direct analysis

¨ To identify relationships between variables

¨ It helps in data reduction

¨ It helps the researcher to cluster the product and population being analyzed.

TERMINOLOGY IN FACTOR ANALYSIS

•· Factor: A factor is an underlying construct or dimensions that represent a set of observed variables. In the credit card company example, the demographic characteristics, socio economic status and background status represent a set of variables.
•· Factor Loadings: Factor loading help in interpreting and labeling the factors. It measures how closely the variables in the factor are associated. It is also called factor-variable correlation. Factor loadings are correlation coefficients between the variables and the factors.
•· Eigen Values: Eigen values measure the variance in all the variables corresponding to the factor. Eigen values are calculated by adding the squares of factor loading of all the variables in the factor. It aid in explaining the importance of the factor with respect to variables. Generally factors with Eigen values more than 1.0 are considered stable. The factors that have low Eigen values (<1.0) may not explain the variance in the variables related to that factor.
•· Communalities: Communalities, denoted by h2, measure the percentage of variance in each variable explained by the factors extracted. It ranges from 0 to 1. A high communality value indicates that the maximum amount of the variance in the variable is explained by the factors extracted from the factor analysis.
•· Total Variance explained: The total variance explained is the percentage of total variance of the variables explained. This is calculating by adding all the communality values of each variable and dividing it by the number of variables.
•· Factor Variance explained: The factor variance explained is the percentage of total variance of the variables explained by the factors. This is calculating by adding the squared factor loadings of all the variables and dividing it by the number of variables.


PROCEDURE FOLLOWED FOR FACTOR ANALYSIS

• Define the problem
• Construct the correlation matrix that measures the relationship between the factors and the variables.
•Select an appropriate factor analysis method
•Determine the number of factors
•Rotation of factors
•Interpret the factors
•Determine the factor scores


APPLICATION AREAS

Factor analysis is by far the most often used multivariate technique of research studies, specially pertaining to social and behavioral science.

It is a technique applicable when there is a systematic interdependence among a set of observed or manifest variables and the researcher is finding out something more fundamental or latent which creates this commonality.



Example

Consider the problem of studying the customer's feedback about a two-wheeler produced by a company as explained below;

The marketing manager of a two-wheeler company designed a questionnaire to study the customer's feedback about its two-wheeler and in turn he is keen in identifying the factors of his study. He has identified six variables, which are:

1.Fuel Efficiency (X1)
2. Life of the Two-Wheeler (X2)
3.Handling Convenience (X3)
4.Quality of Original Spares (X4)
5.Breakdown Rate (X5)
6.Price (X6)

MEHTODS OF FACTOR ANALYSIS Centroid Method of Factor Analysis

This method of factor analysis, developed by L.L Thurstone, was quite frequently used until about 1950 before the advent of large capacity high-speed computers. The centroid method tends to maximize the sum of loadings, disregarding signs; it is method, which extracts the largest sum of absolute loadings for each factor in turn. It is defined by linear combinations in which all weights are either + 1.0 or -1.0. The main merit of this method is that it is relatively simple, can be easily understood and involves simpler computations. If one understands this method, it becomes easy to understand the mechanics involved in other method of factor analysis.

Principal Component Method

Principal-components method (or simply P.C. method) of factor analysis, developed by H.Hotelling, seeks to maximize the sum of squared loadings of each factor extracted in turn. Accordingly PC factor explains more variance than would the loadings obtained from any other method of factoring.

The aim of the principal components method is the construction out of a given set of variables X's (j=1, 2, 3… k) of new variables (pi) called principal components, which are linear combinations of the Xs.

ROTATION IN FACTOR ANALYSIS

One often talks about the rotated solutions in the context of factor analysis. This is done (i.e., a factor matrix is subjected to rotation) to attain what is technically called "simple structure" in data. Simple structure according to L.L Thurstone is obtained by rotating the axes** until:

(i) Each row of the factor matrix has one zero.

(ii) Each column of the factor matrix has p zeros, where p is the number of factors.

(iii) For each pair of factors, there are several variables for which the loadings on one is virtually zero and the loading on the other is substantial

(iv) If there are many factors, then for each pair of factors there are many variables for which both loadings are zero.

(v) For every pair of factors, the number of variables with non-vanishing loadings on both of them is small.

All these criteria simply that the factor analysis should reduce the complexity of all the variables.

R-TYPE AND Q-TYPE FACTOR ANALYSES

Factor analysis may be R-type factor analysis or it may be Q-type factor analysis. In R-type factor analysis, high correlations occur when respondents who score high on variable1 also score high on variable2 and respondents who score low on variable1 also score low on variable2. Factors emerge when there are high correlations within groups of variables.

In Q-type factor analysis, the correlations are computed between pairs of respondents instead of pairs of variables. High correlations occur when respondent 1's pattern of responses on all the variables is much like respondent 2's pattern of responses. Factor emerges when there are high correlations within groups of people. Q-type analysis is useful when the object is to sort out people into groups based on their simultaneous responses to all the variables.

Factor analysis is has been mainly used in developing psychological tests (such as IQ tests, personality tests, and the like) in the realm of psychology. In marketing, this technique has been used to look at media readership profiles of people.

MERITS

The main merits of factor analysis can be stated thus:

(i) The techniques of the factor analysis are quite useful when we want to condense and simplify the multivariate data.

(ii) The technique is helpful in pointing out important and interesting, relationship among observed data that were there all the time, but not easy to see from the data alone.

(iii) The technique can reveal the latent factors (i.e. underlying factors not directly observed) that determine relationships among several variable concerning a research study. For example, if people are asked to rate different cold drinks (say Limca, Nova-cola, and Gold Spot and so on) according to preference, a factor analysis may reveal some salient characteristics of cold drinks that underline the relative preferences.

(iv) The technique may be used in the context of empirical clustering of products, media or people i.e. providing a classification scheme when data scored on various rating scales have to be grouped together.

LIMITATION

One should also be aware of several limitations of factor analysis. Important ones are as follows:

(i) Factor analysis, like all multivariate techniques, involved laborious computations involving heavy cost burden.

(ii) The single factor analysis are considered generally less reliable and dependable for very often a factor analysis starts with a set of imperfect data. "the factors are nothing but blurred averages, difficult to be identified". To overcome this difficulty, it has been realized that analysis should at least be done twice. If we get more or less similar results from all rounds of analyses, our confidence concerning such results increases.

iii) Factor analysis is a complicated decision tool that can be used only when one has thorough knowledge and enough experience of handling this tool. Even then, at times it may not work well and may even disappoint the user.

To conclude, we can state that in spite of all the said limitations "When it works well, factor analysis help the investigator makes sense of large bodies of interwined data. When it works unusually well, it also points out some interesting relationships that might not have been obvious from examination of the input data alone".



CONCLUSION

Thus Factor analysis is an interdependence technique. The complete sets of interdependent relationships are examined. There is no specification of dependent variables, independent variables, or causality. Factor analysis assumes that all the rating data on different attributes can be reduced down to a few important dimensions. This reduction is possible because the attributes are related. The rating given to any one attribute is partially the result of the influence of other attributes.