1. MULTIVARIATE ANALYSIS

2. Multivariate analysis is the analysis of the simultaneous relationships among three or more phenomena. In a multivariate analysis, the focus shifts from paired relationships to the more complex simultaneous relationships among phenomena. Multivariate analysis is classified into two broad categories: Functional methods and Structural methods.

3. 1. Functional methods The functional methods are also called the dependence methods. With the help of such methods, the marketing researcher can develop predictive models which can be used for forecasting. Some of the important functional multivariate methods are multiple regression analysis, discriminant analysis, multivariate analysis of variance and canonical analysis.

4. 2. Structural methods The structural methods, which are also called the interdependence methods, are essentially descriptive and are not useful for predictive purposes. They are helpful; in reducing large and complex data into meaningful groups and in bringing out relationships which are not otherwise apparent. Some of the structural multivariate methods are factor analysis, cluster analysis, multi-dimensional scaling and conjoint analysis.

5. DISCRIMINANT ANALYSIS A discriminant analysis enables the researcher to classify persons or objects into two or more categories. For example, consumers may be classified as heavy and light users. In many cases the classification will be dichotomous such as users and non-users, high and low and so on. In discriminant analysis, a scoring system is used on the basis of which an individual or object is assigned a score. This in turn forms the basis for classifying an individual in the most likely class or category.

6. DISCRIMINANT ANALYSIS Suppose an individual is 25 years of age, earns an annual income of Rs.60000 and has undergone formal education for a period of 17 years. Each of these three variables is given a weight, indicating its relative importance. Symbolically, Y = b1 + b2(60000) + b3(17). Where Y is a dependent variable.

7. DISCRIMINANT ANALYSIS A certain limit is fixed for the value of Y below which all values will be classified in Group I and all the others in Group II. The values of b1, b2 and b3 indicate their importance. One major advantage of linear discriminant analysis is that it enables the researcher to know by a simple device, whether an individual is likely to belong to one or the other category on the basis of his overall score.

8. FACTOR ANALYSIS The factor analysis was first used by Charles Spearman, Psychologists use it as a technique of indirect measurement. When they are interested to test human personality and intelligence, a set of questions is developed for this purpose. They believe that a person gives this set of questions and tests would respond on the basis of some structure that exists in his mind. Thus, his responses would form a certain pattern. This approach is based on the assumption that the underlying structure in answering the questions would be the same in the case of different respondents.

9. FACTOR ANALYSIS In regression analysis, the problem is to predict the value of a dependent variable on the basis of one or more independent variables. Unlike the regression analysis, factor analysis is not based on the usual distinction between dependent and independent variables, instead it rather considers all the variables simultaneously. There are 2 objects of factor analysis. First, it simplifies the data by reducing a large number of variables to a set of a small number of variables. Secondly, it analyses the interdependence of interrelationships among a total set of variables.

10. Example Mukherjee carried out factor analysis in order to identify major factors for determining consumer’s evaluation of a brand of coffee. He selected on a random basis 94 consumers each of whom was given up a cup of coffee. The test subjects were not told which brand of coffee they were given. After they had drunk the coffee, they were asked to rate it on 14 semantic- differential scales. The 14 attributes which were investigated are:

11. 14 Attributes 1.Pleasant flavour – Unpleasant flavour 2.Stagnant, muggy taste – Sparkling, refreshing taste 3.Mellow taste – Bitter taste 4.Cheap taste – Expensive taste 5.Comforting, harmonious – Irritating, discordant 6.Smooth, friendly taste – Rough, hostile taste 7.Dead, lifeless, dull taste - Alive, lively, peppy taste 8.Tastes artificial – Tastes like real coffee 9.Deep distinct flavour – Shallow indistinct flavour 10.Tastes warmed over – Tastes just brewed 11.Hearty, full bodied, full flavour – Warm, thin empty flavour 12.Pure, clear taste – Muddy, swampy taste 13.Raw taste – Stale taste 14.Overall performance: Excellent quality – Very poor quality

12. Example A factor analysis of the ratings given by the 94 consumers indicated that four factors could summarise the 14 attributes. These factors were 1.Comforting quality 2. Heartiness 3. Genuineness 4. Freshness It may be noted that to identify the factors these terms were chosen by the researcher. Another researcher may prefer to use somewhat different terms.

13. Attributes represented by each of the four factors FACTOR ATTRIBUTES A. Comforting quality 1. Pleasant flavour 3. Mellow taste 5. Comforting taste 12. Pure, clear taste B. Heartiness 9. Deep, distinct flavour 11. Hearty, full bodied, full flavour C. Genuineness 2. Sparkling taste 4. Expensive taste 6. Smooth, friendly taste 7. Alive, lively, peppy taste 8. Tastes like real coffee 14. Overall performance D. Freshness 10. Tastes just brewed 13. Raw taste

14. Limitations Sometimes, more relevant factors may be left out. Factor analysis is a complicated tool and should be used by the researcher only when he has a good understanding of the technique. An exercise in factor analysis involving a large number of variables, say 50, is much bothersome and costly. Its utility depends to a large extent on the judgment of the researcher.

15. CLUSTER ANALYSIS Cluster analysis is used to classify persons or objects into a small number of mutually exclusive and exhaustive groups. There should be high internal (within-cluster) homogeneity and high external (between-cluster) heterogeneity. In marketing research, cluster analysis has been increasingly used, because of its utility in resolving the problem of classifying consumers, products, etc.

16. Example The type of vacations taken by 15 individuals – A to O. A two dimensional perceptual map has been drawn on the basis of data relating to i)Number of vacation days (y-axis) and ii)The expenditure on vacations during a given year (x-axis). It will be seen that there are three distinct clusters. The first cluster comprising five individuals C, F, H, L and M shows that although these individuals take too many vacations they do not spend much on their vacations.

17. Example.C.M.H.F.L. O.N..K.G.D.I.B.A.J.E Expenditure on vacations (Rupees) No.of vacation days

18. Example The second cluster comprising six individuals D, G, I, K, N and O shows that they take vacations moderately and also spend moderately – neither too much nor too less. Finally, the third cluster comprising four individuals A, B, E and J shows that they have relatively few vacation days but spend substantially more on their vacations. On the basis of this perceptual map, the utility of classifying individuals into clusters becomes apparent. It will be seen that the points included in a cluster are close to each other and the points falling in two or more clusters are at a good distance from each other. This is the essence of cluster analysis i.e., to classify individuals or objects on the basis of their similarity or distance from each other.

19. Uses of Cluster analysis in marketing One of the important uses of cluster analysis in marketing is market segmentation. Marketing managers are often required to identify similar segments so that marketing programmes can be formulated to meet special requirements of each market segment. The main task involved in segmentation is to classify people, materials, etc. into groups based on certain common characteristics.

20. Limitations Cluster analysis lacks standard statistical tests. Different people may use different clusters from the same set of data.

21. MULTIDIMENSIONAL SCALING Consumers generally prefer a particular brand of a product not on the basis of one attribute but on a number of attributes. Multidimensional scaling (MDS) is a data reduction technique. It enables us to represent the proximities between objects spatially as in a map. The term proximities means any set of numbers that express the amount of similarity or difference between pairs of objects. The term objects refer to things or events. The main purpose of MDS is to map the objects in a multidimensional space such that their relative positions in the space show the degree of perceived proximity or similarity among them.

22. MDS MDS involves two aspects. First, it helps in the identification of attributes on the basis of which consumers perceive or evaluate products or brands. Second, it enables the positioning of different products or brands on the basis of these attributes. It helps generate a perceptual map, indicating the location of the brands on the basis of attributes.

23. Approaches to MDS – Attribute based Example Let us assume that only two dimensions or attributes are involved in this example which pertains to the preferences of students of the MBA courses offered by some universities. The dimensions are: 1. Prestigious course 2.Quantitative content

24. Example.I.B.A.C.F.J.E.D.H.G Less Prestigious More Prestigious Less Quantitative More Quantitative

25. Attribute based Example The points indicated by letters A to J show a student’s comparison in the MBA programmes in ten different universities. The vertical dimension indicates the relative quantitative content of the MBA course while the horizontal dimension shows the relative prestige of the course. It will be seen from this perceptual map that points which are close to each other show similarity in the student’s perception.

26. Limitations The selection of various attributes or dimensions which are regarded important to respondents is subjective. It becomes extremely difficult to interpret the results of MDS. It is particularly suited for product life cycle analysis, market segmentation, vendor evaluation, measuring advertising effectiveness and test marketing. The researcher must have a good understanding of MDS before he decides to use it.

27. CONJOINT ANALYSIS Conjoint analysis is concerned with the measurement of the joint effect of two or more attributes that are important from the view point of the consumer. In a situation where a company would like to know the most desirable attributes or their combinations for a new product or service, the use of conjoint analysis will be most appropriate. For example, an Airlines corporation would like to know which is the most desirable combination of attributes to a frequent traveller – punctuality in the operation of flights or the quality of food served on the flight.

28. Conjoint Analysis The use of conjoint analysis involves three steps: i)Identification of the relevant product or service attributes ii)Collection of data and iii)Estimation of part – worth utility function. In order to identify product attributes, several approaches are available to the researcher. He may interview a number of consumers directly. Alternatively, focus group interviews with consumers may be held. Another option is to ascertain the attributes from knowledge persons such as the product manger, retailers, etc.

29. Conjoint Analysis As regards the collection of data, the ‘trade-off’ approach or the ‘full profile’ approach may be used. The first approach involves the consideration of only two attributes at a time by the respondents. In contrast, the full profile approach involves the consideration of all the attributes at the same time. The respondents are asked to rank all the alternatives. As regards the estimation of part-worthy utility values, the researcher may use one of the several methods that are available. These are: regression methods, mathematical programming methods and econometric methods.

30. Conjoint Analysis Although in recent years research based on conjoint analysis has been done, it is still not used frequently as other multivariate techniques. This is partly on the fact that relatively few organisations or people are fully conversant with this technique.