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Proximity and Preference

Proximity and Preference: Problems in the Multidimensional Analysis of Large Data Sets

Reginald G. Golledge
John N. Rayner
Copyright Date: 1982
Edition: NED - New edition
Pages: 356
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  • Book Info
    Proximity and Preference
    Book Description:

    Proximity and Preference was first published in 1982. How does one design experiments for collecting large volumes of data such as those needed for marketing surveys, studies of travel patterns, and public opinion polls? This is a common problem for social and behavioral scientists. The papers in this collection address the problems of working with large data sets primarily from the perspectives of geography and psychology, two fields that share a common quantitative research methodology. After an introductory paper on substantive and methodological aspects of the interface between geography and psychology, the book is divided into three sections, experimental design and measurement problems, preference functions and choice behavior, and special problems of analyzing large data sets with multidimensional methods. Each paper is directed toward some fundamental problem such as those relating to experimental design, data reliability, and the selection of analytical methods which are appropriate for data sets of various sizes, completeness, and reliability.

    eISBN: 978-0-8166-6263-0
    Subjects: Statistics

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-viii)
  3. Preface
    (pp. ix-xviii)
    Reginald G. Golledge and John N. Rayner
  4. Introduction — Substantive and Methodological Aspects of the Interface between Geography and Psychology
    (pp. xix-xl)
    Reginald G. Golledge

    The last two decades have seen an increase in the number of cross-disciplinary interactions in the social and behavioral sciences. This is part of the breakdown of strict boundaries between the disciplines and reflects a desire to gain an increased understanding of both human and physical phenomena and the relationships between them. Although there have been ongoing casual flirtations between geography and psychology for the better part of this century—particularly with respect to the use of maps and the understanding of space and spatial orientation—there was, prior to 1960, no clearly identified strong link between the two subjects...

  5. Part 1. Experimental Design and Measurement Problems

    • Chapter 1.1 Surveying Multidimensional Measurement
      (pp. 3-9)
      W. R. Tobler

      The largest multidimensional data set encountered in the history of geography was in the exploration of the world. One of the problems was to establish the geometric relation of all places to each other. This was to be done in a two-dimensional space of poorly known size and shape. This two-dimensional space, of course, contains an infinity of places, so some choice had to be made to determine which relations should be the first to be established. A sampling framework was required. Smaller-scale surveying is known to have been practiced in ancient Egypt, China, and Rome, but the earliest systematic...

    • Chapter 1.2 Interactively Ordering the Similarities among a Large Set of Stimuli
      (pp. 10-28)
      Forrest W. Young, Cynthia H. Null, Warren S. Sarle and Donna L. Hoffman

      When using a multidimensional scaling procedure, most researchers collect data by having subjects rate the similarity of all possible pairs of stimuli. When the number of stimuli is large (say 25), the number of pairs is very large (300), and the task is extremely arduous. Since using a large number of stimuli is often desirable and is necessary if one expects a solution with more than three dimensions [10], some way of limiting the size of the task is of great interest.

      Many researchers have avoided the large number of pairs required by a large number of stimuli by using...

    • Chapter 1.3 Incomplete Experimental Designs for Multidimensional Scaling
      (pp. 29-46)
      Ian Spence

      The major problem that faces a researcher who desires to use multidimensional scaling procedures with large numbers of stimulus objects is the difficulty, or undesirability, of presenting a subject with all possible pairs of the stimuli. This number rises almost as the square of the number of objects; for example, with 10 or 20 stimuli the subject has to judge 45 or 190 pairs, respectively, whereas with 40 or 50 stimuli the number of judgments required rises to 780 or 1225. Clearly, there comes a point when the patience of even the most highly motivated subject is exhausted, not to...

    • Chapter 1.4 Sampling Designs and Recovering Cognitive Representations of an Urban Area
      (pp. 47-79)
      Aron N. Spector and Victoria L. Rivizzigno

      The general aim of this paper is to examine multidimensional scaling as a means of recovering information concerning how people cognize the relative locations of places in the urban environment. This examination leads to a more specific aim of determining how best to collect and analyze large sets of scaling data.

      An experiment to uncover cognitive information about an urban environment focused on Columbus, Ohio, where individuals were asked to evaluate the relative spatial separation of a sample of locations drawn from the Columbus metropolitan area. These distance judgments were then subjected to multidimensional scaling analysis.

      In this analysis, only...

    • Chapter 1.5 Considerations in the Selection of Stimulus Pairs for Data Collection in Multidimensional Scaling
      (pp. 80-89)
      Paul D. Isaac

      A recurrent problem in data collection for multidimensional scaling is the rapid increase in the number of distances${({_{2}^{n}})}$as the number of stimuli (n) is increased. For designs involving direct judgment of similarity, the solution seems to be to reduce the number of pairs actually judged. Two approaches previously taken have been the use of interactive scaling [10], which involves on-line participation of a subject with rational selection of pairs based on previous responses, and the use of cyclic designs to delete pairs a priori [6]. Neither of these approaches is altogether satisfactory — interactive scaling because of the...

    • Chapter 1.6 The Interface between the Types of Regression and Methods of Collecting Proximity Data
      (pp. 90-115a)
      Phipps Arabie and Sigfrid D. Soli

      The advent of nonmetric multidimensional scaling as it appeared to researchers in the area [31, 32, 36], consisted of two major leaps forward: (1) the input data were only viewed as being measured on an ordinal scale when Kruskal’s [17] monotone regression was substituted for earlier methods that made heavier demands of the data, and (2) the cumbersome method of complete triads [38] was no longer the only truly respectable procedure for collecting the proximities matrix. In fact, any consistent method that yielded a partial ordering of all the interstimulus proximities, or a major subset thereof, became admissible.

      Thus, the...

  6. Part 2. Preference Functions and Choice Behavior

    • Chapter 2.1 Data Theory and Problems of Analysis
      (pp. 116-130)
      Lawrence Hubert

      There is at least one distinct advantage to writing the first paper in a section devoted to a topic as broad as “preference functions and choice behavior” Compared to the more difficult task of providing the final summary and critique, an introductory statement for such an extensive subject allows a great degree of latitude in what can be emphasized. Granted, an overview that relates to the other papers in an integral manner is still expected, but a truly comprehensive analysis is not. This presentation takes full advantage of this sanction. I will limit myself to making a brief introduction to...

    • Chapter 2.2 Recovering the Parameters of a Decision Model from Simulated Spatial Choice Data
      (pp. 131-143)
      James A. Kohler and Gerard Rushton

      Geographers have long been interested in how people choose a place for a particular purpose from among the many places available. Early modeling efforts had as their goal the replication of observed flows. These models were various forms of the gravity model and most often were transformed into linear regression models for solution by least squares methods. Correlation coefficients were generally regarded as adequate measures of goodness of fit, and the regression coefficients were interpreted causally as reflecting the degree of importance of the variable in question. Thus, large coefficients on the variable distance were interpreted to mean that distance...

    • Chapter 2.3 A Revealed Preference Analysis of Intraurban Migration Choices
      (pp. 144-168)
      W. A. V. Clark

      Although Rushton’s [16] methodology for the analysis of spatial choices was published some time ago, there has been only limited application of the methodology in geography. Recently, there have been attempts to compare the spatial preference scaling model with a utility theory approach [19] and to extend it “by improving its mathematical and conceptual base” [7] and in particular to enlarge the number of locational types that might be considered in the model. Nevertheless, the empirical applications of the model have been only to consumer behavior [7, 16, 17], and its validity for investigating other choice situations has not been...

    • Chapter 2.4 Data Problems and the Application of Conjoint Measurement to Recurrent Urban Travel
      (pp. 169-190)
      Patricia K. Burnett

      Over the past few years, some interest has been shown in the decomposition of space preference functions [20, 21, 25, 27]. It is desirable to recover the part-worths of different attributes of spatial alternatives in the choice process. One rationale for this interest is that it is necessary for practical purposes to predict the degree to which an attribute must be altered in order to achieve a desired spatial choice effect. It is necessary, for example, to be able to predict the spatial choice effects of a deliberate alteration of the attributes of shopping destinations, such as price, quality of...

    • Chapter 2.5 Applications of Functional Measurement to Problems in Spatial Decision Making
      (pp. 191-213a)
      Jordan J. Louviere

      Many problems of interest to geographers, planners, and other spatial scientists can be viewed as problems in human decision making, judgment, evaluation, or choice. Many such judgments are of direct interest in that they involve a judgment or decision to move, to travel, to locate, et cetera. Others are of indirect interest in that they are not concerned directly with spatial behavior but may have consequences for spatial behavior. An example of the latter is a planner’s evaluation of zoning requests for land-use classification changes by a planning commission.

      This paper deals with a particular theory of how individuals make...

  7. Part 3. Special Problems

    • Chapter 3.1 Some Remarks on Multidimensional Scaling in Geography
      (pp. 214-232)
      John S. Pipkin

      The papers in this section on special problems fall neatly into two groups, a symmetry that I will disturb with some disjointed observations on the explanatory role of MDS configurations and on a class of alternative representational models appropriate mainly in geographic applications.

      Considering the diversity of perspectives on MDS techniques that has emerged in the social sciences and in marketing, the papers by Deutscher and Green are remarkably similar in outlook. They address the problems of data reliability associated with large stimulus sets. Deutscher’s concerns encompass the merits of alternative data collection procedures for stimuli too numerous for exhaustive...

    • Chapter 3.2 Comparing Objective and Cognitive Representations of Environmental Cues
      (pp. 233-266)
      Reginald G. Golledge, John N. Rayner and Victoria L. Rivizzigno

      A survey of recent literature [23] indicates the existence of a considerable quantity of empirical evidence related to cognitions of different urban environments. Various investigations have pointed to the existence of point, areal, and linear components of cognitive representations of cities [1, 4, 7, 8, 20]. Since this research area is still in its infancy, however, considerable difficulties have arisen: first, concerning the extracting of information from individuals so as to develop cognitive representations; second, concerning attempts at incorporating the information thus extracted into maps or models of the representations. Some of these difficulties can be attributed to a lack...

    • Chapter 3.3 Recovering the Dimensions through Multidimensional Scaling — Remarks on Two Problems
      (pp. 267-271)
      B. Marchand

      I have used multidimensional scaling at different times to recover the geometric configuration of elements in a mental space and to compare it to an objective configuration of these elements [4]. In the process, I have run into two difficult problems, which I would like to discuss here. The problems concern the imposition of structure in the data-gathering stage and the fractional dimensionality situation.

      Experimenter intrusion into data-gathering situations is all too common in geography. Many researchers fail to recognize that task-related structure can be imposed both by the direct intervention of the experimenter and by the procedures he or...

    • Chapter 3.4 Issues in Data Collection and Reliability in Marketing Multidimensional Scaling Studies — Implications for Large Stimulus Sets
      (pp. 272-288)
      Terry Deutscher

      Academicians and practitioners in the field of marketing have been quick to capitalize on the advances that psychometricians have made in the area of multidimensional scaling. In fact, it would not be presumptuous to claim that the fields of marketing and geography are probably the two that have made the greatest practical use of the techniques.

      MDS applications in marketing are described in books by Green and Carmone [13] and Green and Rao [14], as well as in the journal literature in the field, most notably theJournal of Marketing Research. The techniques have been used for innumerable purposes ranging...

    • Chapter 3.5 Suggestions for Identifying Sources of Unreliability in Multidimensional Scaling Analyses
      (pp. 289-304)
      Rex S. Green

      A relatively unsettled issue for real-world applications of multidimensional scaling (MDS) techniques is the estimation of the reliability, or repeatability, of the estimated scale values (i.e., the dimension loadings, parameter estimates, and recovered distances) that are synonymous with the spatial coordinates, et cetera. Ideally, it would be helpful to have estimates of the reliability of: each point location, which Best, Young, and Hall [1] refer to as “wobble”; each defined scale or direction in the space that is interpreted; and the MDS solution ofpdimensions. Since the issue of reliability of measurement relates to the way in which the...

  8. Index
    (pp. 305-310)
  9. Back Matter
    (pp. 311-311)