All Minds Factored!!

Factor Analysis was the topic of discussion in the class today. Factor analysis is a process of reducing the number of variables that impact the decision making process of a manager by dividing them into a certain number of factors on the basis of some common features. Factor analysis was explained to us in the class with a simple, yet clear example by Sir. Let us take an example of a premium high-end car. The number of units sold by the manufacturer would depend on several factors like the price of the car, the price of the competitor’s offering, the resale value of the car, the after sales service, availability of components, number of service outlets in the country, etc. These components can be divided into two major parts: The Price and the Service. These two components are called as factors.

Factor analysis can be used to serve the following purposes:

1. The number of variables for further research can be reduced, thus improving drastically the efficiency and the quality of the analysis of the research.

2. When the amount of data available is very large and difficult to comprehend, factor analysis can be used for qualitative and quantitative analysis.

3. Factor analysis can also be used to check whether a particular variable is contributing to the factor, and hence to check the hypothesis of dependency of the research on a particular quality.

Factor analysis has its applications in various fields like Economics (To reduce the large number of factors impacting the economy of a country into small, important factors), Psychology (Crucial factors concerning the behaviour of an individual can be classified unto a common head to reduce the complexity of analysis), Science (Various attributes may be used for the analysis of a particular experiment, which may refer to a single quality), Marketing, etc. But the focus is to analyse the impact of factor analysis on the world of marketing.

1. The pricing decision of a product may be dependent on various factors like cost of manufacturing, Pricing of the major players, Inflation expected in the future, Ease of Availability of the raw materials in the future, Capability of altering the price of the product in the near future, Demand of the product, etc. But, to ease the decision making process, these factors can be divided into heads such as economic factors, cost, Competitor’s analysis, etc. Hence, Factor analysis can be used to make important strategic decisions like pricing.

2. With the help of analysis of various variables unto the formation of the components, the differentiator for a product from that of the competitor can be identified. That analysis may help in establishing the positioning of the company in the minds of the consumers. For example, if a car has the best fuel efficiency in its segment, the entire positioning of the car can be done on the basis of that attribute.

3. It can also be used in Market research. Market research results would contain a lot of data that is irrelevant if analysed on individual basis. Hence, factors can be formed from the variables to understand the results more clearly. Taking the example of a consumer satisfaction survey, the variables can be divided into satisfaction with the quality, service, price, etc.

4. Factor analysis can be used to form perceptual maps, which can be used for effective segmentation of the consumer groups as well.

Author: Malhar Shah

Group: Marketing - Group 4

Factor Anlaysis – What & Why?

Selecting Variables/Items for the Analysis. Ideally the researcher will select items which are reliable and will have good communalities. Include enough variables so that each common factor will be represented by at least three or four variables.

Selecting Subjects for the Analysis. Don't make the mistake of sampling from a population of subjects for which there is little variance in the factors you wish to estimate. You might even want to sample in such a way that your subjects will vary exceptionally much with respect to the factors you wish to estimate but little on other attributes.

Principal Components Analysis or Factor Analysis? If your purpose is to reduce the information in many variables into a set of weighted linear combinations of those variables, use Principal Components Analysis (PCA), which does not differentiate between common and unique variance. If your purpose is to identify the latent variables which are contributing to the common variance in a set of measured variables, use Factor Analysis (FA), which will attempt to exclude unique variance from the analysis.

Exploratory or Confirmatory Factor Analysis? If you wish to restrict the number of factors extracted to a particular number and specify particular patterns of relationship between measured variables and common factors, and this is done a priori (before seeing the data), then the confirmatory procedure is for you. If you have no such well specified a priori restrictions, then use the exploratory procedure.

Which Factor Extraction Procedure? Maximum Likelihood (ML) extraction allows computation of assorted indices of goodness-of-fit (of data to the model) and the testing of the significance of loadings and correlations between factors, but requires the assumption of multivariate normality. Principal Factors (PF) methods have no distributional assumptions. It is suggested to go with ML extraction that one first examine the distributions of the measured variables for normality. Unless there are severe problems ( |skew| > 2, kurtosis > 7), they say go with ML. If there are severe problems, consider trying to correct the problems (by transforming variables, for example) rather than using PF methods.

How Many Factors to Extract? Prefer overfactoring (too many factors) to underfactoring (too few factors). Overfactoring is likely to lead to a solution where the major factors are well estimated by the obtained loadings but where there are also additional poorly defined factors (with few, if any, variables loading well on them). Underfactoring is likely to lead to factors that are poorly estimated (poor correspondence between the structure of the true factors and that of the estimated factors), a more serious problem.

The authors spoke kindly of "parallel analysis," in which the obtained eigenvalues are compared to those one would expect to obtain from random data. If the first m eigenvalues are those which have values greater than what would be expected from random data, then one adopts a solution with m factors. Regretfully, this method is not available in the major statistical programs.

The goodness-of-fit statistics available from ML factor analysis may be helpful in determining the number of factors to retain. The analyst first decides how many factors, at most, e would be willing to retain. Then e fits models with 0, 1, 2, 3, ... up to that number of factors and compares them with respect to goodness-of-fit.

The authors also note that "a model that fails to produce a rotated solution that is interpretable and theoretically sensible has little value." This sounds like what I call the "meaningfulness criterion." I typically examine, in addition to the solution with what seems at first to have the correct number of factors, solutions with one or two more or fewer factors. I then adopt the solution which makes the most sense to me.

What Type of Rotation? The authors make a strong argument in favor of oblique rotations rather than orthogonal solutions. They note that dimensions of interest to psychologists are not often dimensions we would expect to be orthogonal. If the latent variables are, in fact, correlated, then an oblique rotation will produce a better estimate of the true factors and a better simple structure than will an orthogonal rotation -- and if the oblique rotation indicates that the factors have close to zero correlations between one another, then the analyst can go ahead and conduct an orthogonal rotation (which should then give about the same solution as the oblique rotation).

What Do Researchers Actually Do? Based on articles published between 1991 and 1995 in the Journal of Personality and Social Psychology and the Journal of Applied Psychology, about half use a PCA, despite the fact that the primary goal was to identify latent variables, in which case FA should have been employed. They do often report the reliabilities of their variables, but not the communalities (which are more informative). Frequently they do not explain the method they used to decide how many factors to retain, and when they do report the method it is most likely to be the eigenvalue-greater-than-one method They use varimax rotation. When asked to provide a copy of their data so that Fabrigar et al. could determine if a better solution would be obtained by making decisions other than those made by the researchers, most researchers failed to provide the data. For those that did provide the data, Fabrigar et al. found that an oblique rotation often produced a slightly better simple structure than did a varimax rotation, but the pattern of loadings was almost always the same with varimax as with oblique rotation.

Why do Researchers Make These Decisions? That is, why do they elect to do a PCA, retain as many factors as have eigenvalues greater than 1, and use varimax rotation? Well, maybe it is just because these are the defaults for factor analysis in SPSS. You know, one does not have to understand anything about factor analysis to be able to point and click.

Reference: http://core.ecu.edu/psyc/wuenschk/stathelp/efa.htm

Author: Ankit Gupta (13066)

Marketing Group 1

To analyse or not to analyse

The class session held today was rather entertaining. A simple flight trip was analyzed on the basis of various factors such as comfort, stoppage and price. I was to discover that I wasn't price conscious much but more distance and comfort conscious and a utility could be obtained such that the preferences of an individual could be ascertained.

.A scatter plot tends to represent data between two variables in the form of scattered dots, and where the dots would be crowded, the confluence of data there would be higher. Getting back to factor analysis, it has been found to be rather useful in dealing with large quantities of data.

A wide range of applications from psychometry to operations as well as statistical data analysis in voters preferences for a particular attribute in a candidate were found.

A scree plot essentially plots the components on the X axis and the eigen values of the cluster on the Y axis. The curve ranges from a bit abrupt to smooth . A good scree plot is one in which it drops each and every moment as one moves from the left to the right.

Card List

	Card ID	brand	Spd	Looks	RV	Miles	Pri	SFTY
1	1	Toyota	Fast	Equal	High	High	Cheap	High
2	2	Honda	Fast	Less	Low	Moderate	Expensive	High
3	3	Maruti	Very Fast	More	Moderate	Low	Cheap	High
4	4	Audi	Slow	Less	Moderate	High	Expensive	Moderate
5	5	BMW	Slow	Equal	High	Low	Affordable	Low
6	6	Mercedes	Fast	Equal	Moderate	Moderate	Affordable	Moderate
7	7	Tata	Fast	More	High	Low	Expensive	Moderate
8	8	Mercedes	Fast	More	Moderate	High	Cheap	Low
9	9	Mercedes	Slow	Less	High	Low	Expensive	High
10	10	Mercedes	Very Fast	More	High	High	Expensive	High
11	11	BMW	Fast	More	Low	High	Expensive	High
12	12	Mercedes	Medium	Less	Low	Low	Cheap	Low
13	13	Maruti	Fast	Less	High	High	Expensive	Low
14	14	BMW	Very Fast	Less	High	Moderate	Cheap	Moderate
15	15	Audi	Very Fast	Equal	Low	High	Expensive	Low
16	16	Audi	Fast	More	High	Low	Affordable	High
17	17	Honda	Slow	More	High	High	Cheap	Moderate
18	18	Audi	Medium	More	High	Moderate	Cheap	High
19	19	BMW	Medium	More	Moderate	High	Expensive	High
20	20	Tata	Very Fast	Less	Moderate	High	Affordable	High
21	21	Honda	Very Fast	More	High	High	Affordable	Low
22	22	Honda	Medium	Equal	Moderate	Low	Expensive	High
23	23	Tata	Medium	More	High	Moderate	Expensive	Low
24	24	Toyota	Slow	More	Moderate	Moderate	Expensive	Low
25	25	Maruti	Medium	Equal	High	High	Expensive	Moderate
26	26	Tata	Slow	Equal	Low	High	Cheap	High
27	27	Toyota	Medium	Less	High	High	Affordable	High
28	28	Mercedes	Slow	More	High	High	Expensive	High
29	29	Maruti	Slow	More	Low	Moderate	Affordable	High
30	30	Toyota	Very Fast	More	Low	Low	Expensive	Moderate
31	31	Mercedes	Medium	More	Low	High	Affordable	Moderate
32	32	Mercedes	Very Fast	Equal	High	Moderate	Expensive	High

I decided to use factor analysis to decide which car I would be interested in. And it turned out that I was more brand and looks conscious rather than price and mileage conscious .The above would be the orthogonal design that resulted from the factors I had chosen.

MAC LOBO

FINANCE - GROUP 1