Chapter 21

Multidimensional Scaling and Conjoint Analysis

True/False Questions

1. The conjoint analysis procedure is based on trade-offs respondents make when evaluating alternatives.(True, easy, page 611)

2. The number of brands or stimuli selected for use in MDS analysis and the specific brands included does not affect the nature of the resulting dimensions and configurations. (False, moderate, page 612)

3. The choice of the number and specific brands or stimuli to be included in the MDS analysis should be based on the statement of the marketing research problem, theory, and the judgment of the researcher.(True, easy, page 613)

4. Preference data may be direct or derived.(False, moderate, page 613)

5. Direct approaches to collecting perception data are attribute-based approaches.(False moderate, page 613)

6. Derived approaches to collecting perception data require respondents to rate the brands or stimuli on the identified attributes using semantic differential scales or Likert scales. (True, moderate, page 613)

7. The direct approaches to collecting perception data are used more frequently than the attribute-based approaches.(True, moderate, page 614)

8. Preference data order the brands or stimuli in terms of respondents’ preference for some property.(True, moderate, page 614)

9. The configuration derived from preference data is very similar to that obtained from similarity data.(False, difficult, page 615)

10. Non-metric MDS procedures assume that the input data are ordinal, but they result in metric output.(True, difficult, page 615)

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11. The metric MDS procedures assume that input data are metric and the output is also metric. (True, easy, page 615)

12. The metric and non-metric MDS methods often produce vastly different results.(False, difficult, page 615)

13. Spatial maps are computed in such a way that the fit increases as the number of dimensions decreases.(False, difficult, page 615)

14. The objective in MDS is to obtain a spatial map that best fits the input data in the smallest number of dimensions.(True, easy, page 615)

15. Each dimension determined in MDS represents only one attribute. (False, moderate, page 617)

16. MDS solutions are subject to substantial random variability.(True, moderate, page 617)

17. Stress values indicate the proportion of variance of the optimally scaled data that is not accounted for by the MDS model.(True, moderate, page 617)

18. An assumption of MDS is that the similarity of stimulus A to B is the same as the similarity of stimulus B to A.(True, moderate, page 618)

19. In order to perform internal analysis of preferences, both preference and perception data must be obtained. (False, difficult, page 619)

20. External analysis of preferences is preferred in most situations.(True, moderate, page 619)

21. Quantitative data can be mapped using correspondence analysis. (False, moderate, page 621)

22. Results in correspondence analysis are interpreted in terms of proximities among rows and columns. (True, moderate, page 621)

23. Correspondence analysis requires more effort on the part of the respondent than other MDS techniques.(False, moderate, page 621)

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24. Correspondence analysis data is binary or categorical.(True, moderate, page 621)

25. If the attribute-based approaches are used to obtain input data, spatial maps can also be obtained by using factor or discriminant analysis.(True, moderate, page 621)

26. To develop spatial maps by means of discriminant analysis, the dependent variable is the brand rated and the independent variables are the attribute ratings.(True, moderate, page 621)

27. When conducting conjoint analysis, the attributes selected should be salient in influencing consumer preference and choice. (True, easy, page 623)

28. When constructing conjoint analysis stimuli, it is necessary to evaluate all possible combinations of levels of the attributes.(False, moderate, page 624)

29. The full-profile approach to conducting conjoint analysis stimuli is more commonly used than the pairwise approach.(True, moderate, page 625)

30. For metric conjoint analysis input data, the respondents are typically required to provide rank order evaluations.(False, difficult, page 625)

31. With the full-profile approach to constructing conjoint analysis stimuli, respondents rank all the stimulus profiles.(True, difficult, page 625)

32. For metric conjoint analysis input data, the respondents provide ratings. (True, difficult, page 625)

33. In conjoint analysis, the dependent variable is usually preference or intention to buy.(True, difficult, page 625)

34. In conjoint analysis, the importance of an attribute, Ii, is defined in terms of the range of the part-worths, αij, across the levels of that attribute Ii = {max(αij) - min(αij)}, for each i.(True, moderate, page 627)

38. In conjoint analysis, the attribute's importance is normalized to ascertain its importance relative to other attributes, Wi. (True, difficult, page 627)

39. For interpreting conjoint analysis, it is helpful to plot the part-worth functions.(True, difficult, page 629)

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40. If individual-respondent level analysis has been conducted, the estimation sample can be split in several ways to assess the stability of conjoint analysis solutions.(False, difficult, page 630)

41. Conjoint analysis assumes that the important attributes of a product can be identified.(True, easy, page 630)

42. Conjoint analysis assumes that consumers evaluate the choice alternatives in terms of the important attributes and make trade-offs. (True, easy, page 630)

Multiple Choice Questions

43. _____ is a class of procedures for representing perceptions and preferences of respondents spatially by means of a visual display.a. Conjoint analysisb. Correspondence analysisc. Hybrid conjoint analysisd. Multidimensional scaling (MDS)(d, moderate, page 611)

44. The derivation and use of _____ lie at the heart of multidimensional scaling.a. perceptual mapsb. pair-wise tablesc. part-worth functionsd. contrasts(a, moderate, page 611)

45. MDS could be used for all of the marketing applications below except:a. Market segmentation - position brands and consumers in the same space and thus

identify groups of consumers with relatively homogeneous perceptions.b. Assessing advertising effectiveness-spatial maps can be used to determine

whether advertising has been successful in achieving the desired brand positioning.

c. Consumer intention - how do consumer’s intentions to buy the brand vary with different price levels?

d. Channel decisions - judgments on compatibility of brands with different retail outlets could lead to spatial maps useful for making channel decisions.

(c, moderate, page 611)

46. _____ is a lack of fit measure; higher values indicate poorer fits.a. Attribute levelsb. Stress c. R-squared. Relative importance weights(b, moderate, pages 612)

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47. _____ is a squared correlation index that indicates the proportion of variance of the optimally scaled data that can be accounted for by the MDS procedure. This is a goodness-of-fit measure.a. Attribute levelsb. Stress c. R-squared. Relative importance weights(c, easy, page 612)

48. In MDS, at minimum, _____ brands or stimuli should be included so as to obtain a well-defined spatial map. Including more than _____ brands is likely to be cumbersome and may result in respondent fatigue.a. 6; 20b. 6; 25c. 8; 20d. 8; 25(d, moderate, page 612)

49. _____ requires that the researcher specify the purpose for which the MDS results would be used and select the brands or other stimuli to be included in the analysis.a. Formulating the problemb. Obtaining input datac. Selecting an MDS procedured. Deciding on the number of dimensions(a, easy, page 612)

50. In _____ approaches to collecting perception data, the respondents are asked to use their own criteria to judge how similar or dissimilar the various brands or stimuli are. a. direct b. preferencec. derivedd. Likert(a, moderate, page 613)

51. In which approach to collecting perception data are respondents often required to rate all possible pairs of brands or stimuli in terms of similarity on a Likert scale?a. direct b. preferencec. derivedd. Likert(a, moderate, page 613)

52. Which is a disadvantage of the direct approach to collecting perception data? a. The criteria are influenced by the brands or stimuli being evaluated.b. The researcher must identify all the salient attributes.c. The spatial map obtained depends upon the attributes identified.d. Both b and d are disadvantages.(a, moderate, page 614)

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53. Which is a disadvantage of the derived approach to collecting perception data?a. The criteria are influenced by the brands or stimuli being evaluated.b. The researcher must identify all the salient attributes.c. It may be difficult to determine before analysis if and how the individual

respondents’ judgments should be combined.d. It may be difficult to label the dimensions of the spatial map.(b, moderate, page 614)

54. Which is an advantage of the direct approach to collecting perception data?a. It is easier to label the dimensions.b. It is easy to identify respondents with homogeneous perceptions.c. The researcher does not have to identify a set of salient attributes.d. The respondents can be clustered based on the attribute ratings.(c, moderate, page 614)

55. Which is an advantage of the derived approach to collecting perception data?a. Respondents make similarity judgments using their own criteria, as they would

under normal circumstances.b. It is easy to identify respondents with homogeneous perceptions.c. The researcher does not have to identify a set of salient attributes.d. Both a and c are advantages.(b, moderate, page 614)

56. _____ data order the brands or stimuli in terms of respondents’ preferences for some property.a. Direct b. Preferencec. Derivedd. Likert(b, moderate, page 614)

57. Which of the ways below is not a way in which preference data might be obtained?a. asking respondents to rank brands from the most preferred to the least preferred b. asking respondents to rate all possible pairs of brands in terms of similarity on a

Likert scale c. asking respondents to make paired comparisons and indicate which brand in a pair

they preferd. asking respondents for preference ratings for the various brands (b, difficult, page 614)

58. Which of the following is not a factor influencing the MDS selection procedure? a. whether some of the original values will be used in subsequent analysisb. whether perception or preference data are being scaled, or whether the analysis

requires both kinds of datac. the nature of the input datad. whether the MDS analysis will be conducted at the individual respondent level or

at an aggregate level(a, moderate, page 614)

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59. Which guideline for deciding on the number of MDS dimensions relies on theory or past research to suggest the number of dimensions?a. a priori knowledgeb. interpretability of the spatial mapc. ease of used. elbow criterion (a, moderate, page 615)

60. Which guideline for deciding on the number of MDS dimensions warns that it is difficult to interpret configurations or maps derived in more than three dimensions? a. a priori knowledgeb. interpretability of the spatial mapc. ease of used. elbow criterion (b, difficult, page 615)

61. Which guideline for deciding on the number of MDS dimensions suggests plotting stress versus dimensionality? a. a priori knowledgeb. interpretability of the spatial mapc. ease of used. elbow criterion (d, moderate, page 615)

62. Which guideline for deciding on the number of MDS dimensions suggests it is easier to work with two-dimensional maps or configurations than with those involving more dimensions?a. a priori knowledgeb. interpretability of the spatial mapc. ease of used. elbow criterion (c, difficult, page 615)

63. Various ways to label dimensions obtained in MDS were mentioned in the text. Which of the ways below was not mentioned in your text? a. axes may be labeled for the attributes with which they are most closely alignedb. label based on the criteria respondents used in making their evaluationsc. respondents can be shown their maps and asked to label the dimensions by

inspecting the configurationsd. none of the above(d, moderate, page 617)

64. Which of the following is a way to interpret the configuration or spatial map? a. examine dimension centroidsb. profile dimensions in terms of variables that were not used in the MDS procedurec. examine variables that load high on a factord. examine the coordinates and relative positions of the brands(d, difficult, page 617)

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65. Values of .60 or better are considered acceptable values of _____, the index of fit. a. attribute levelsb. stress c. R-squared. relative importance weights(c, difficult, page 617)

66. Which of the Kruskal’s stress formula 1 values below represent a perfect fit of the MDS model?a. 20 b. 10c. 5d. 0(d, difficult, page 618)

67. Which of the following is not a way to assess reliability and validity of the MDS solution?a. Collect input data at two different points in time and then determine test-retest

reliability.b. Selectively eliminate stimuli from the input data and then determine the solution

from the remaining stimuli. c. Add a random error term to the input data, subject the resulting data to MDS

analysis, and compare the solutions.d. All of the above are ways to assess reliability and validity.(d, difficult, page 618)

68. In MDS, when a spatial map is obtained, it is assumed that interpoint distances are _____ scaled and that the axes of the map are multidimensional _____ scaled. a. interval; intervalb. ratio; intervalc. ordinal; intervald. interval; ratio(b, difficult, page 618)

69. _____ is a method of configuring a spatial map such that the spatial map represents both brands or stimuli and respondent points or vectors and is derived solely from the preference data.a. Metric analysis of preferencesb. Correspondence analysis c. Internal analysis of preferencesd. External analysis of preferences(c, difficult, page 619)

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70. _____ is a method of configuring a spatial map, such that the ideal points or vectors based on preference data are fitted in a spatial map derived from perception data.a. Metric analysis of preferencesb. Correspondence analysisc. Internal analysis of preferencesd. External analysis of preferences(d, difficult, page 619)

71. _____ is an MDS technique for scaling qualitative data that scales the rows and columns of the input contingency table in corresponding units so that each can be displayed in the same low-dimensional space.a. Metric analysis of preferencesb. Correspondence analysisc. Internal analysis of preferencesd. External analysis of preferences(b, difficult, page 621)

72. Which statement is true about correspondence analysis?a. The interpretation of results is similar to that in principal components analysis.b. An advantage over other MDS techniques is that it reduces the data collection

demands put on the respondents because only binary or categorical data are obtained.

c. A disadvantage is that between-set distances cannot be meaningfully interpreted. d. All of the statements are true.(d, difficult, page 621)

73. Which statement is true about using factor analysis to create spatial maps?a. Input data should be obtained via attribute-based approaches to obtaining

perception data.b. Spatial maps are obtained by plotting brand scores on the factors. c. Discriminant weights can be used to label the dimensions.d. Both a and b are correct. (d, moderate, page 621)

74. Which statement is true about using discriminant analysis to create spatial maps?a. Input data should be obtained via attribute-based approaches to obtaining

perception data.b. Spatial maps are obtained by plotting brand scores on the factors. c. Discriminant weights can be used to label the dimensions.d. Both a and c are true. (d, moderate, page 621)

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75. _____ is a technique that attempts to determine the relative importance consumers attach to salient attributes and the utilities they attach to the levels of attributes.a. Internal analysis of preferences b. External analysis of preferences c. Conjoint analysisd. Correspondence analysis(c, difficult, page 621)

76. Which of the following statements is not true concerning conjoint analysis?a. The underlying assumption is that any set of stimuli, such as products, brands, or

stores, is evaluated as a bundle of attributes. b. Conjoint analysis relies on respondent’s subjective evaluations. c. Conjoint analysis seeks to develop the part-worth or utility functions describing

the utility consumers attach to the levels of each attribute.d. The stimuli in conjoint analysis are products or brands.(d, moderate, page 622)

77. Conjoint analysis could be used for all of the marketing applications below except:a. determining the relative importance of attributes in the consumer choice processb. estimating market share of brands that differ in attribute levelsc. used as a general data reduction toold. determining the composition of the most preferred brand(c, difficult, page 622)

78. When conducting conjoint analysis, in _____, the researcher must identify the attributes and attribute levels to be used in constructing stimuli.

a. formulating the problemb. constructing the stimulic. deciding on the form of input datad. selecting a conjoint analysis procedure(a, moderate, page 623)

79. Which statement is not true about formulating the conjoint analysis problem? a. Attributes selected should be salient in influencing consumer preference.b. Once the salient attributes have been identified, their appropriate level should be

evaluated.c. The set of variables selected should describe the similarity between objects in

terms that are relevant to the marketing research problem. d. The researcher should take into account the attribute levels prevalent in the

marketplace and the objectives of the study.(c, moderate, page 623)

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80. In (the) _____ for constructing conjoint analysis stimuli, respondents evaluate two attributes at a time until all the possible pairs of attributes have been evaluated.a. full-profile approachb. pair-wise approachc. two-factor evaluationsd. both b and c(d, moderate, page 624)

81. When constructing conjoint analysis, full or complete profiles of brands are constructed for all the attributes in (the) _____.a. full-profile approachb. pair-wise approachc. two-factor evaluationsd. both b and c(a, moderate, page 625)

82. Which statement is not true about the pair-wise approach to constructing conjoint analysis stimuli?a. It is possible to reduce the number of paired comparisons by using cyclical

designs.b. The number of stimulus profiles can be greatly reduced by means of fractional

factorial designs.c. The advantage of pair-wise is that it is easier for the respondents to provide

judgments on the paired comparisons. d. The disadvantage of pair-wise is that it requires more evaluations than the full-

profile approach.(b, difficult, page 625)

83. The basic conjoint analysis model expressing the fundamental relationship between attributes and utility in conjoint analysis is shown below:

U(X)=

What does αij represent?a. 1 if the jth level of the ith attribute is present, or 0 otherwise.b. the part-worth contribution or utility associated with jth level (j, j=1, 2, …ki) of

the ith attribute (i, i=1, 2, …m)c. number of attributesd. number of levels of attribute i(b, moderate, page 626)

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84. The basic conjoint analysis model expressing the fundamental relationship between attributes and utility in conjoint analysis is shown below:

U(X)=

What does xij represent?a. 1 if the jth level of the ith attribute is present, or 0 otherwise.b. the part-worth contribution or utility associated with jth level (j, j=1, 2, …ki) of

the ith attribute (i, i=1, 2, …m)c. number of attributesd. number of levels of attribute i(a, moderate, page 626)

85. The basic conjoint analysis model expressing the fundamental relationship between attributes and utility in conjoint analysis is shown below:

U(X)=

What does ki represent?a. 1 if the jth level of the ith attribute is present, or 0 otherwise.b. the part-worth contribution or utility associated with jth level (j, j=1, 2, …ki) of

the ith attribute (i, i=1, 2, …m)c. number of attributesd. number of levels of attribute i(d, moderate, page 626)

86. The basic conjoint analysis model expressing the fundamental relationship between attributes and utility in conjoint analysis is shown below:

U(X)=

What does m represent?a. 1 if the jth level of the ith attribute is present, or 0 otherwiseb. the part-worth contribution or utility associated with jth level (j, j=1, 2, …ki) of

the ith attribute (i, i=1, 2, …m)c. number of attributesd. number of levels of attribute i(c, moderate, page 626)

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87. Decisions related to selecting the conjoint analysis procedure include all of the following except:a. whether perception or preference data are being scaledb. whether to average the data at the individual-respondent level or the aggregate

levelc. which grouping procedure to used. which model for estimating parameters should be specified(a, difficult, page 627)

88. Which of the following is not one of the procedures for assessing the reliability and validity of conjoint analysis results?a. The goodness of fit of the estimated model (R2) should be evaluated. b. Stress values or badness of fit measures should be evaluated. Stress values vary

with the type of conjoint analysis procedure and the data being analyzed. c. Test-retest reliability can be assessed by obtaining a few replicated judgments and

correlating them.d. Internal validity can be determined by correlating predicted evaluations with those

obtained from the respondents.(b, difficult, page 629)

89. _____ is a form of conjoint analysis that can simplify the data collection task and estimate selected interactions as well as all main effects. a. Conjoint analysisb. Correspondence analysisc. Hybrid conjoint analysisd. Multidimensional scaling (MDS)(c, easy, page 632)

Essay Questions

90. What are the steps involved in conducting multidimensional scaling?

Answer formulate the problem obtain input data select an MDS procedure decide on the number of dimensions label the dimensions and interpret the configuration assess reliability and validity

(moderate, page 612)

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91. What are the advantages and disadvantages of the direct and derived approaches to obtaining perception data for multidimensional scaling?

AnswerDirect approaches have the advantage that the researcher does not have to identify a set of salient attributes. Respondents make similarity judgments using their own criteria, as they would under normal circumstances. The disadvantages are that the criteria are influenced by the brands or stimuli being evaluated. If the various brands of automobiles being evaluated are in the same price range, then price will not emerge as an important factor. It may be difficult to determine before analysis if and how the individual respondents’ judgments should be combined. Furthermore, it may be difficult to label the dimensions of the spatial map. The advantage of the attribute-based approach is that it is easy to identify respondents with homogeneous perceptions. The respondents can be clustered based on the attribute ratings. It is also easier to label the dimensions. A disadvantage is that the researcher must identify all the salient attributes, a difficult task. The spatial map obtained depends upon the attributes identified. (difficult, page 614)

92. Which approach is best to use to obtain perception data – the direct approach or the derived approach?

AnswerThe direct approaches are more frequently used than the attribute-based approaches. However, it may be best to use both these approaches in a complementary way. Direct similarity judgments may be used for obtaining the spatial map, and attribute ratings may be used as an aid to interpreting the dimensions of the perceptual map. (difficult, page 614)

93. What are the disadvantages of internal analysis of preferences?

AnswerIn internal analysis, the differences in perceptions are confounded with differences in preferences. It is possible that the nature and relative importance of dimensions may vary between the perceptual space and the preference space. Two brands may be perceived to be similar (located close to each other in the perceptual space) yet, one brand may be distinctly preferred over the other (i.e., the brands may be located apart in the preference space). These situations cannot be accounted for in internal analysis. In addition, internal analysis procedures are beset with computational difficulties.(moderate, page 619)

94. Contrast conjoint analysis with MDS.

AnswerLike multidimensional scaling, conjoint analysis relies on respondents’ subjective evaluations. However, in MDS, the stimuli are products or brands. In conjoint analysis, the stimuli are combinations of attribute levels determined by the researcher. The goal in MDS is to develop a spatial map depicting the stimuli in a

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multidimensional perceptual or preference space. Conjoint analysis, on the other hand, seeks to develop the part-worth or utility functions describing the utility consumers attach to the levels of each attribute. The two techniques are complementary.(moderate, page 622)

95. What are the limitations of conjoint analysis?

AnswerIn situations where image or brand name is important, consumers may not evaluate the brands or alternatives in terms of attributes. Even if consumers consider product attributes, the trade-off model may not be a good representation of the choice process. Another limitation is that data collection may be complex, particularly if a large number of attributes are involved and the model must be estimated at the individual level.(moderate, page 632)

96. What are the two main purposes for which hybrid conjoint analysis models were developed?

AnswerHybrid models have been developed to serve two main purposes: (1) simplify the data-collection task by imposing less of a burden on each respondent, and (2) permit the estimation of selected interactions (at the subgroup level) as well as all main (or simple) effects at the individual level.(moderate, page 632)

97. How does hybrid conjoint analysis simplify the data collection task?

AnswerIn the hybrid approach, the respondents evaluate a limited number, generally no more than nine, conjoint stimuli, such as full profiles. These profiles are drawn from a large master design, and different respondents evaluate different sets of profiles, so that over a group of respondents, all the profiles of interest are evaluated. In addition, respondents directly evaluate the relative importance of each attribute and desirability of the levels of each attribute. Combining the direct evaluations with those derived from the evaluations of the conjoint stimuli, it is possible to estimate a model at the aggregate level and still retain some individual differences.(difficult, pages 632-633)

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