The authors examine the robustness of MDS configurations when incomplete rather than complete input data are used. Using two empirical studies, they show that robustness varies as the amount of incomplete data increases and that random methods of data deletion perform as well as cyclic designs. These findings provide empirical support for earlier Monte Carlo literature on the topic. The authors also show that individual characteristics of respondents, namely cognitive integration and imagery, influence the quality of configurations obtained with incomplete data.
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References
1.
AndersonJohn R. (1978), “Arguments Concerning Representations for Mental Imagery,”Psychological Review, 85(July), 249–77.
2.
AndersonJohn R. (1979), “Further Arguments Concerning Representations for Mental Imagery: A Response to Hayes-Roth and Pylyshyn,”Psychological Review, 86(July), 395–406.
3.
BergerGorian H., and GaunitzSamuel C. B. (1979), “Self-Rated Imagery and Encoding Strategies in Visual Memory,”British Journal of Psychology, 70(February), 21–4.
4.
ClatworthyWillard H. (1973), Tables of Two-Associate Class Partially Balanced Designs.Washington, DC: National Bureau of Standards.
5.
CranoWilliam D., and SchroderHarold M. (1967), “Complexity of Attitude Structure and Processes of Conflict Resolution,”Journal of Personality and Social Psychology, 5(January), 110–14.
6.
DriverMichael J., and MockThedore J. (1975), “Human Information Processing, Decision Style Theory, and Accounting Information Systems,”Accounting Review (July), 490–508.
7.
ErnestCarole H. (1980), “Imagery Ability and the Identification of Fragmented Pictures and Words,”Acta Psychologica, 44(January), 51–7.
8.
GoldsteinKenneth M., and BlackmanSheldon (1978), Cognitive Style: Five Approaches and Relevant Research.New York: John Wiley & Sons, Inc.
9.
GraefJed, and SpenceIan (1979), “Using Distance Information in the Design of Large Multidimensional Scaling Experiments,”Psychological Bulletin, 86(January), 60–6.
10.
GreenPaul E. (1975), “On the Robustness of Multidimensional Scaling Techniques,”Journal of Marketing Research, 12(February), 73–81.
11.
HenryW. A. (1980), “The Effect of Information Processing Ability on Processing Accuracy,”Journal of Consumer Research, 1(June), 42–8.
12.
IssacPaul D. (1982), “Considerations in the Selection of Stimulus Pairs for Data Collection in Multidimension Scaling,” in Proximity and Preference: Problems in the Multidimensional Analysis of Large Data Sets, GolledgeR. G., and RaynerJ. N., eds. Minneapolis: University of Minnesota Press, 80–9.
13.
IssacPaul D., and PoorDavid S. (1974), “On the Determination of Appropriate Dimensionality in Data with Error,”Psychometrika, 39(March), 91–109.
14.
KierasDavid (1978), “Beyond Pictures and Words: Alternative Information-Processing Models for Imagery Effects in Verbal Memory,”Psychological Bulletin, 85(May), 532–54.
15.
KosslynStephen M. (1980), Image and Mind.Cambridge, MA: Harvard University Press.
16.
KruskalJoseph B., and WishMyron (1978), Multidimensional Scaling.Beverly Hills, CA: Sage Publications, Inc.
17.
LutzKathy A., and LutzRichard J. (1978), “Imagery-Eliciting Strategies: Review and Implications of Research,” in Advances in Consumer Research, Vol. 5., Keith HuntH., ed. Ann Arbor, MI: Association for Consumer Research, 611–20.
18.
MacCallumRobert C. (1978), “Recovery of Structure in Incomplete Data by ALSCAL,”Psychometrika, 44(March), 69–74.
19.
MacCallumRobert C., and CorneliusEdwin T. (1977), “A Monte Carlo Investigation of Recovery of Structure by ALSCAL,”Psychometrika, 42(September), 401–28.
20.
MalhotraNaresh K. (1987), “Validity and Structural Reliability of Multidimensional Scaling,”Journal of Marketing Research, 24(May), 164–73.
21.
MarksDavid F. (1973), “Visual Imagery Differences in the Recall of Pictures,”British Journal of Psychology, 64(February), 17–24.
22.
MarksDavid F. (1983), “Mental Imagery and Consciousness: A Theoretical Review,” in Imagery: Current Theory, Research and Application, SheikhAnees A., ed. New York: John Wiley & Sons, Inc., 96–130.
23.
McKelvieStuart J., and DemersElizabeth G. (1979), “Individual Differences in Reported Visual Imagery and Memory Performance,”British Journal of Psychology, 70(February), 51–7.
24.
MetzlerJacqueline, and ShepardRoger N. (1974), “Transformational Studies of the Internal Representation of Three-Dimensional Objects,” in Theories in Cognitive Psychology: The Loyola Symposium, SosloRobert L., ed. New York: John Wiley & Sons, Inc., 147–201.
25.
MooreWilliam L., and LehmannDonald R. (1982), “Effects of Usage and Name on Perceptions of New Products,”Marketing Science, 1(Fall), 41, 349–73.
26.
PipkinJohn S. (1982), “Some Remarks on Multidimensional Scaling in Geography,” in Proximity and Preference: Problems in Multidimensional Analysis of Large Data Sets, GolledgeR. G., and RaynerJ. N., eds. Minneapolis: University of Minnesota Press, 47–79.
27.
RichardsonJohn T. E. (1980), Mental Imagery and Human Memory.London: Macmillan Publishing Co., Inc.
28.
SchiffmanSusan C., and Lance ReynoldsM., and YoungForrest W. (1981), Introduction to Multidimensional Scaling.New York: Academic Press, Inc.
29.
SchroderHarold M., DriverMichael J., and StreufertSigfried (1967), Human Information Processing.New York: Holt, Rinehart and Winston.
30.
ScottW. A., and OsgoodD. W., and PetersonC. (1979), Cognitive Structure: Theory and Measurement of Individual Differences.Washington, DC: V. H. Winston and Sons.
31.
SheehanPeter W., and AshtonR., and WhiteK. (1983), “Assessment of Mental Imagery,” in Imagery: Current Theory, Research and Application, SheikhAnees A., ed. New York: John Wiley & Sons, Inc., 189–221.
32.
ShepardRoger N. (1975), “Form, Formation and Transformation of Internal Representations,” in Information Processing and Cognition: The Loyola Symposium.Hillsdale, NJ: Lawrence Erlbaum Associates.
33.
ShepardRoger N. (1978), “The Mental Image,”American Psychologist, 33(February), 125–37.
34.
ShepardRoger N., and PodgornyP. (1978), “Cognitive Processes that Resemble Perceptual Processes,” in Handbook of Learning and Cognitive Processes, EstesWilliam K., ed. Hillsdale, NJ: Lawrence Erlbaum Associates.
35.
SpectorAron N., and RivizzignoVictoria L. (1982), “Sampling Designs and Recovering Cognitive Representations of an Urban Area,” in Proximity and Preference: Problems in the Multidimensional Analysis of Large Data Sets, GolledgeR. G., and RaynerJ. N., eds. Minneapolis: University of Minnesota Press, 47–79.
36.
SpenceIan (1982), “Incomplete Experimental Designs for Multidimensional Scaling,” in Proximity and Preference: Problems in the Multidimensional Analysis of Large Data Sets, GolledgeR. G., and RaynerJ. N., eds. Minneapolis: University of Minnesota Press, 29–46.
37.
SpenceIan (1983), “Monté Carlo Simulation Studies,”Applied Psychological Measurement, 7(Fall), 405–26.
38.
SpenceIan, and DomoneyDennis W. (1974), “Single Subject Incomplete Designs for Nonmetric Multidimensional Scaling,”Psychometrika, 39(December), 469–90.
39.
SpenceIan, and GraefJed (1974), “The Determination of Underlying Dimensionality of an Empirically Obtained Matrix of Proximities,”Multivariate Behavioral Research, 9(July), 331–42.
40.
StreufertSigfried, and DriverMichael J. (1967), “Impression Formation as a Measure of the Complexity of Conceptual Structure,”Educational and Psychological Measurement, 27(Winter), 1025–39.
41.
StreufertSigfried, and StreufertSusan C. (1978), Behavior in the Complex Environment.New York: John Wiley & Sons, Inc.
42.
SummersJohn O., and MacKayDavid B. (1976), “On the Validity and Reliability of Direct Similarity Judgments,”Journal of Marketing Research, 13(August), 289–95.
43.
TakaneYoshio, YoungForrest W., and de LeeuwJan (1977), “Nonmetric Individual Differences Multidimensional Scaling: An Alternative Least Squares Method with Optional Scaling Features,”Psychometrika, 42(March), 7–67.
44.
YoungForrest W. (1970), “Nonmetric Multidimensional Scaling: Recovery of Metric Information,”Psychometrika, 35(December), 455–73.
45.
YoungForrest W., and CliffNorman (1972), “Interactive Scaling with Individual Subjects,”Psychometrika, 37(December), 385–415.
