1. Factor Analysis for Data Reduction

2. Introduction 1. Factor Analysis is a set of techniques used for understanding variables by grouping them into “factors” consisting of similar variables 2. It can also be used to confirm whether a hypothesized set of variables groups into a factor or not 3. It is most useful when a large number of variables needs to be reduced to a smaller set of “factors” that contain most of the variance of the original variables 4. Generally, Factor Analysis is done in two stages, called Extraction of Factors and Rotation of the Solution obtained in stage 5. Factor Analysis is best performed with interval or ratio-scaled variables Slide 1

3. Application Areas/Example 1. In marketing research, a common application area of Factor Analysis is to understand underlying motives of consumers who buy a product category or a brand 2. The worked out example in the chapter will help clarify the use of Factor Analysis in Marketing Research 3. In this example, we assume that a two wheeler manufacturer is interested in determining which variables his potential customers think about when they consider his product 4. Let us assume that twenty two-wheeler owners were surveyed by this manufacturer (or by a marketing research company on his behalf). They were asked to indicate on a seven point scale (1=Completely Agree, 7=Completely Disagree), their agreement or disagreement with a set of ten statements relating to their perceptions and some attributes of the two-wheelers. 5. The objective of doing Factor Analysis is to find underlying "factors" which would be fewer than 10 in number, but would be linear combinations of some of the original 10 variables Slide 2

4. The research design for data collection can be stated as follows- Twenty 2-wheeler users were surveyed about their perceptions and image attributes of the vehicles they owned. Ten questions were asked to each of them, all answered on a scale of 1 to 7 (1= completely agree, 7= completely disagree). 1. I use a 2-wheeler because it is affordable. 2. It gives me a sense of freedom to own a 2-wheeler. 3. Low maintenance cost makes a 2-wheeler very economical in the long run. 4. A 2-wheeler is essentially a man’s vehicle. 5. I feel very powerful when I am on my 2-wheeler. 6. Some of my friends who don’t have their own vehicle are jealous of me. 7. I feel good whenever I see the ad for 2-wheeler on T.V., in a magazine or on a hoarding. 8. My vehicle gives me a comfortable ride. 9. I think 2-wheelers are a safe way to travel. 10. Three people should be legally allowed to travel on a 2-wheeler. Slide 3

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12. 1. Now we will attempt to interpret factor 2. We look in fig 4, down the column for Factor 2, and find that variables 8 and 9 have high loadings of 0.85203 and 0.87772, respectively. This indicates that factor 2 is a combination of these two variables. 2. But if we look at fig. 2, the unrotated factor matrix, a slightly different picture emerges. Here, variable 3 also has a high loading on factor 2, along with variables 8 and 9. It is left to the researcher which interpretation he wants to use, as there are no hard and fast rules. Assuming we decide to use all three variables, the related statements are “low maintenance”, “comfort” and “safety” (from statements 3, 8 and 9). We may combine these variables into a factor called “utility” or “functional features” or any other similar word or phrase which captures the essence of these three statements / variables. Slide 8

13. 3. For interpreting Factor 3, we look at the column labelled factor 3 in fig. 4 and find that variables 1 and 10 are loaded high on factor 3. According to the unrotated factor matrix of fig. 2, only variable 10 loads high on factor 3. Supposing we stick to fig. 4, then the combination of “affordability’ and “cost saving by 3 people legally riding on a 2-wheeler” give the impression that factor 3 could be “economy” or “low cost”. 4. We have now completed interpretation of the 3 factors with eigen values of 1 or more. We will now look at some additional issues which may be of importance in using factor analysis. Slide 8 contd...

14. Slide 9 Additional Issues in Interpreting Solutions 1. We must guard against the possibility that a variable may load highly on more than one factors. Strictly speaking, a variable should load close to 1.00 on one and only one factor, and load close to 0 on the other factors. If this is not the case, it indicates that either the sample of respondents have more than one opinion about the variable, or that the question/ variable may be unclear in its phrasing. 2. The other issue important in practical use of factor analysis is the answer to the question ‘what should be considered a high loading and what is not a high loading?” Here, unfortunately, there is no clear-cut guideline, and many a time, we must look at relative values in the factor matrix. Sometimes, 0.7 may be treated as a high value, while sometimes 0.9 could be the cutoff for high values.

15. Slide 9…contd… Additional Issues (Contd.) 1. The proportion of variance in any one of the original variables which is captured by the extracted factors is known as Communality. For example, fig. 3 tells us that after 3 factors were extracted and retained, the communality is 0.72243 for variable 1, 0.45214 for variable 2 and so on (from the column labelled communality in fig. 3). This means that 0.72243 or 72.24 percent of the variance (information content) of variable 1 is being captured by our 3 extracted factors together. Variable 2 exhibits a low communality value of 0.45214. This implies that only 45.214 percent of the variance in variable 2 is captured by our extracted factors. This may also partially explain why variable 2 is not appearing in our final interpretation of the factors (in the earlier section). It is possible that variable 2 is an independent variable which is not combining well with any other variable, and therefore should be further investigated separately. “Freedom” could be a different concept in the minds of our target audience. 2. As a final comment, it is again the author’s recommendation that we use the rotated factor matrix (rather than unrotated factor matrix) for interpreting factors, particularly when we use the principal components method for extraction of factors in stage 1.