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Multidimensional scaling and tourism research
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MULTIDIMENSIONAL SCALING AND TOURISM RESEARCH Mark F e n t o n Curtin University of Technology, Australia P h i l i p Pearce James Cook Univ. of North Queensland, Australia
Abstract: Multidimensional scaling (MDS) is a tbrm of analysis which permits the relationships a m o n g a set of elements to be represented as interelement distances in spaces. It is suitable for data collected according to a n u m b e r of difti~rent formats. This article describes a n u m b e r of the tormal and technical features of M D S analysis and its variants. The main purpose of M D S approaches lie in their capacity to explore the structure underlying a set of judgements. Existing and potential uses of the multidimensional scaling procedure in tourist studies are discussed. It is concluded that the multidimensional scaling approach can provide more than a complex technique tot simplifying data sets. It is also argued that the technique can be used to test hypotheses and conceptual arguments in the tourist literature. K e y w o r d s : multidimensional scaling, tourism research.
R~sumd: Fanalyse 5 l'~chelle muhidimensionnelle ct la recherche en tourisme. I2analyse 5 l'dchelle multidimensionnelle ( E M D ) est une mdthode d'analyse qui permet que les rapports entre les ~l~mcnts d'un ensemble soient reprdsent~s comme des distances entre dldments dans l'espace. Cette m6thode convient h des donndes qu'on a recueillies par plusieurs moyens difli~rents. Le present article ddcrit quelques-uncs des caract6ristiques formelIes et techniques de l'analyse E M D et de ses variantes. Le but principal des approches E M D se trouve dans leur capacitd d'explorer la structure qui est 5 la base d'un ensemble de jugements. On discute des usages actuels et ~ventuels du procddd de l'analyse ~l l'6chelle multidimensionnelle dans l'dtude du tourisme. On conclut que l'approche de l'dchelle muhidimensionnelle peut offrir plus qu'une technique con> plexe pour simplifier des ensembles de donn~es. O n soutient aussi qu'il est possible d'utiliser cette technique pour v6rifier des hypoth}ses et des arguments conceptuels dans les oeuvres de recherche touristique. M o t s clef: analyse 5 l'dchelle muhidimensionnelle, recherche en tourisme.
INTRODUCTION Imagine that a map of Australia lies across a desk. Recorded in kilometers are the distances among all major cities in Australia, resulting in a triangular data set which represents all the intercity distances. M a r k F e n t o n is a lecturer in psychology at the Curtin University of Technology (Bentley WA 6102, Australia). His research interests include environmental perception and computer ergonomics. P h i l i p Pearce is a senior lecturer in psychology at J a m e s Cook University. He has spent ten years conducting research into social psychological aspects of tourists. 236
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With this data set of all intercity distances, it would be possible to construct, on the basis of these distances, a map showing the location of each of these cities. Now this could take some time since each city would have to be positioned on the map in such a way that the map of distances represent the data matrix o'f distances among cities. Rather than developing the map by hand, the data could be subjected to a multidimensional scaling analysis (MDS), the result of which would be a map of Australian cities, where the mapped intercity distances would be identical to the matrix. Multidimensional scaling began primarily as a variant of factor analysis within the field of psychophysics in the late 1930s (Eckart and Young 1936; Richardson 1938; Young and Householder 1938). Later, through the papers of Shepard (1962, 1972), Kruskal (1964), and Carroll and Chang (1970), it was expanded into a broad family of scaling techniques. While it was initially developed within the area of psychology, it has been usefully applied to a number of areas outside the general scope of psychology, including marketing (Green and Carmone 1972), political science (Easterling 1984), and archaeology (Hodson, Kendall, and Tautu 1971). The twofold aim of MDS is to reduce data so as to make them more manageable and meaningful, and at the same time to identify whether there is any inherent underlying structure within the data. Both aims of MDS are related, as the recovery of underlying structure usually means the reduction of the entire data set to a manageable and limited number of dimensions, clusters, or groupings. Multidimensional scaling has many elements in common with factor analysis, but it differs from it in three important respects. First, while factor analysis, like MDS, attempts to identify the inherent structure within data, factor analysis requires that the variables to be analyzed must be measured on at least an interval scale. MDS does not necessarily require this assumption as it determines inherent structure on the ordered relations existing among elements. Second, an MDS solution is usually easier to interpret than a factor analysis solution, as the MDS model is based on the distance between points in a multidimensional space. In factor analysis, the model which is generated is based on the angles between vectors. A third important difference between MDS and factor analysis, which is related to the interpretation of the final configuration, is that the researcher using MDS usually finds relatively fewer dimensions than would occur if the data were analyzed through factor analysis. As Shepard (1972:3) has noted "the high dimensionality characteristic of factor-analytic results is in part a consequence of the rigid assumptions of linearity upon which the standard factoranalytic methods have been based", and, as such, one would expect a solution of lower dimensionality when the assumptions of linearity are removed. The data on which the MDS analysis is based consist of a series of "proximities" which indicate the degree of similarity or dissimilarity among elements within a defined set. The proximity measures may be either "direct" or "derived" measures of proximity. If the measures are direct, then the subject has usually provided a direct estimate of the degree of (dis)similarity between any pair of elements, either through a rating or
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classification task. Derived proximities, on the other hand, usually consist of some m e a s u r e of association a m o n g elements within a set which are not m a d e directly by a subject. MEASURES OF PROXIMITY
Oirec! Measures of ProxbniO, O n e of the most c o m m o n measures of direct p r o x i m i t y is paired comparisons. T h r o u g h pairwise j u d g m e n t s , the subject indicates the degree to which two elements are similar or dil'l~rent. In this task, a bipolar rating scale of which the endpoints are a n c h o r e d with the verbal labels o f " v e r y similar" and "very different" is used to record the judgment. While the use of the rating scale is the most c o m m o n tbrm of eliciting direct measures of p r o x i m i t y from subjects, Schiffrnan, Reynolds and Young (1981) have suggested that it is sometimes a difticuh and somewhat a m b i g u o u s task to p e r f o r m in terms of assigning a specific m e a n i n g to the n u m e r i c points on the scale. For this reason, Schiffman et al. (1981) have suggested that rather than m a k i n g j u d g ments of similarity with reference to a n u m e r i c scale, a less a m b i g u o u s and m o r e effective p r o c e d u r e is to have subjects simply place a mark on a line of which the e n d p o i n t s of the line arc a n c h o r e d with the verbal labels "exact same" and "most different." T h e length of the line is then m e a s u r e d in millimeters from the verbal label up to and including the mark, and as such rcpresents a direct m e a s u r e of proxiinity between elements. A second m e t h o d o f u b t a i n i n g direct measures of p r o x i m i t y is to have sutzjccts sort a large pool of elements into a n u m b e r of smaller groups which are perceived as being alike on some attribute of interest. T h e n u m b e r of groupings can be p r e d e t e r m i n e d by the researcher or determ i n e d d u r i n g the sorting by the subject. After completion, a inatrix is constructed of b i n a r y values representing the degrce of similarity between elements, where a 1 might indicate that the elements were sorted into the same group with a 0 indicating that the elements were sorted into different groups. A third m e t h o d of o b t a i n i n g some index of similarity a m o n g elements is to have subjects rank o r d e r the elements on a particular attribute. Alternatively, elements may be r a n k - o r d e r e d in terms of how similar they arc to a predefined standard. T h e completed m a t r i x represents a rectangular matrix of elements by attributes, or elements by standards, where the values in the body of the m a t r i x represent the r a n k i n g of the element in relation to the attribute or standard. While there are a n u m b e r of other variants of the three p r o c e d u r e s for o b t a i n i n g direct measures of p r o x i m i t y (see C o x o n 1982, C h a p . 10), the rating, grouping, and ranking p r o c e d u r e s are the most cominon within the behavioral sciences literature. Examples of obtaining direct proximities t h r o u g h the use of rating scales include research on the perception of natural settings (Fenton 1985) and the perception of nations (Wish 1971), while examples of the use of g r o u p i n g p r o c e d u r e s include the perception of tourist highways (Pearee and P r o m n i t z 1984),
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urban settings (Nassar 1980), and music (Halpern 1984). The ranking procedure is not as common as either the rating or grouping methods, but has been used by Harshman and De Sarbo (1984) in the context of marketing research. One important consideration which is often overlooked in planning a study, which uses MDS and is based on direct measures of proximity, is the number of elements that are going to be used and the time required to obtain direct measures of proximity among all elements. For example, if the researcher who decides to use the paired comparisons procedure wishes to know what the underlying dimensions are that subjects use in discriminating among four elements, then in order to form a complete proximity matrix six paired comparisons will have to be completed; with eight elements 28 paired comparisons will be required; with 12 elements 66 comparisons; and with 20 elements 190 comparisons. Clearly, as the number of elements increases, there is a corresponding and rapid increase in the number of paired comparisons required. In addition, Schiffman et al. (1981) indicate that while the time required to complete a paired comparisons task depends upon the type of elements used, paired comparisons among all possible pairs of 20 elements, with no readaption or rest intervals, could take upwards of l :/2 hours. In order to partly reduce the time required to complete a set of paired comparisons, MacCallum (1979:69) has suggested the use of an incomplete data design, where only a certain percentage of the proximity matrix is completed by any one individual. Monte Carlo studies, which have compared analyses based on different percentages of incomplete data, have shown "that very accurate recovery of true distances, stimulus coordinates, and weight vectors could be achieved with as much as 60% missing data as long as sample size was sufficiently large and the level of random error was low."
Indirect Measures of Proximity Indirect measures of proximity usually consist of some index of association, such as a correlational index, as in Pearson's r; a contingency measure, such as Cramer's V or Phi; or a distance measure as usually found in Euclidian, City Block, or Minkowski distances. Given that such indexes of proximity are normally based on aggregated data either across individuals, stimuli, or replications on the variable of interest, then the resulting spatial configuration may simply be an artifact of the process of aggregation. One of the most valuable reference sources for identifying the different types of indirect measures of proximity available is the SPSSx Users Guide (1986). Not only are the measures identified and the defining formulae supplied, but the SPSSx proximities program module will generate selected proximities on the basis of either the rows or columns of a square or rectangular matrix.
How M D S Works MDS consists of a broad family of scaling techniques, where the
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selection of any one p r o c e d u r e is d e p e n d e n t on the type of data to bc analyzed, decisions as to how the data are to be treated d u r i n g the analysis, and which end result is required. As such, the tbllowing discussion applies only to the most c o m m o n e l e m e n t a r y torm of M D S , which will be r e f e r r e d to as classical m u l t i d i m e n s i o n a l scaling ( C M D S ) . M a n y of the other M D S procedures are simply an extension of this basic model. Given a triangular matrix of either derived or direct proximities p r o d u c e d t h r o u g h any of the p r o c e d u r e s previously discussed, the ob.jective of M D S is to take the proximities a m o n g elements and represent them as distances in a space of minimal dimensionality so that the distances a p p r o x i m a t e as best as possible the proximities a m o n g elements. This is accomplished t h r o u g h an iterative cycle and begins with an estimated or r a n d o m starting configuration of" distances a m o n g elements. T h e distances in the starting configuration are then c o m p a r e d to the original p r o x i m i t y values a m o n g elements and a "goodness of fit function computed," which in most M D S procedures is usually identified as "stress." O n c e this function has been c o m p u t e d the starting configuration is adjusted so that it m o r e closely a p p r o x i m a t e s the original proximities. Again this adjusted contiguration is c o m p a r e d to the original p r o x i m i t y values with a goodness of" fit function being computed. This iterative cycle continues until the m a x i m u m n u m b e r of iterations specified by the user has been reached or the i m p r o v e m e n t in fit or stress is less than a critical interval, which leads to the completion of the iterative cycle. T h e process of locating elements in a space, where the distances a m o n g elements c o r r e s p o n d as m u c h as possible to the proximities, may be u n d e r t a k e n in a space of any dimensionality as specified by the user prior to the analysis. Solutions will normally be obtained in a n u m b e r of dimensions, b e g i n n i n g with a one-dimensional solution. As for the m a x i m u m dimensionality for the data set, Kruskal and Wish (1978:34), as a rule of' t h u m b , have indicated that in o r d e r tbr the solution to be statistically stable, the n u m b e r of elements minus one should be greater than four times the proposed dimensionality. O n c e a series of dimensional solutions is o b t a i n e d for a data set, the researcher is then taced with the problem of selecting the most a p p r o p r i a t e dimensionality and i n t e r p r e t i n g the dimensional solution.
Interpreting the M D S Solution It must be e m p h a s i z e d that there is no one index that will identify the correct dimensional representation for the data. Although the goodness of fit function for each configuration m a y partially answer this question, consideration must also be given to the interpretability of the dimensional space. W h e n using stress to identify the a p p r o p r i a t e dimensionality, it is usual to construct a plot showing the relationship between stress levels and dimensional solutions (i.e., Kruskal and Wish 1978, Fig. 16; Schifflnan et al. 1981, Fig. 1.6). W h e n inspecting the plot, the dimensionality after which there is little or no substantial i m p r o v e m e n t in stress is usually selected as the most appropriate dimensional solution.
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In addition to an evaluation of the stress value, careful consideration must be given to the interpretation of the dimensional solution. It may well be that the solution with the optimum stress value is not necessarily the most interpretable and meaningful solution, and solutions in a higher or lower dimensionality may also need to be considered.
Data Theory A n u m b e r of schemes have been developed for classifying the broad range of M D S procedures, the earliest of which was probably that developed by Shepard (1972). However, the most recent non-mathematical overview of MDS, which at the same time attempts a partial taxonomy of M D S models in terms of a general data theory, is that proposed by Schiffman et al. (1981). Th e concepts embedded within the data theory proposed by Schiffman et al. (1981) attempt to link attributes of the data with the model being used to understand the data. As such, three organizing concepts are used to define the data theory proposed: the shape of the data, the n u m b e r of"ways" of the data, and the nature of the M D S model.
Shape or Mode of the Data T h e data for an M D S analysis can be in the form of a rectangular or square matrix. A rectangular data matrix is sometimes also referred to as two-mode data since the proximities within a rectangular matrix emphasize the degree of relationship between two distant sets of elements. For instance, the columns of a rectangular data matrix may represent specific objects, places, or people, while the rows may consist of the rating scales on which the column elements are judged. This is a c o mmo n type of data matrix collected in behavioral science research, and is in fact the type of matrix that is most often analyzed through factor analysis. By contrast, the second data shape com m on to M D S data is the square data matrix which is also sometimes identified as consisting of one mode data. In this matrix, the proximities denote the degree of relatedness among one set of elements, rather than two, as in the case of rectangular data. If the square matrix is symmetrical (i.e., where there is no substantive difference between asking the degree of similarity between element A and B and element B and A), then a special case of the square matrix can be developed known as the triangular or offdiagonal data matrix. Such a triangular data matrix is the most common form of data matrix to be analyzed by MDS. In some circumstances, it may not be possible to assume symmetry in proximity measures. For example, asymmetric proximity measures may be found in interpersonal perception research, where person A may regard himself as similar to person B, but person B may regard himself as very dissimilar to person A. While it is possible to use a specific M D S program to analyze such data ( A L S C A L - - A M D S ) , it is possible under some circumstances to consider the asymmetry as noise, and to average the two proximity measures and form a triangular data matrix. A second alternative in dealing with this situation is to analyze
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the upper and lower triangles of the original square matrix separately and compare the resulting solutions.
The 'q4hy" ~ the Data The way of the data simply represents the dimensionality of the original data matrix to be analyzed. Any data matrix must in the first instance be two-way data representing the columns and rows of either a square or rectangular matrix. Three-way data usually takcs the form of several matrices, where the third way is usually represented by either individual subjects or replications over time. It is possible to go beyond three-way or even three mode data (of. Law, Snyder, Hattie and McDonald 1984 tot a review of such approaches), and there are M D S programs which will analyze such data (i.e., C A N D E C O M P and PARAFAC). However, the procedure is extremely rare. As Coxon (1982:187) indicates, "users are advised to proceed beyond three-way data with considerable caution. T h e y are in largely uncharted territoIt is appropriate when discussing data suitable tot M D S analysis to use both the n u m b e r of modes and n u m b e r of ways to define the original data matrix. For instance, a triangular data matrix of averaged proxiinity measures across subjects which represents the degree of dissimilarity a m o n g a n u m b e r of countries recently visited could be defined as one mode (countries), two-way data. If, on the other hand, one did not average across subjects but wished to include individual subjects' data matrices in the M D S analysis, one would then have two mode (countries, subjects),hrec-way data. Ahcrnatively, the researcher might ask sut~jects to complete a rectangular matrix consisting of ratings given to countries on a n u m b e r of predefined scales. If the researcher does not aggregate across subjects but includes each individual subject's rectangular matrix in the analysis, then there would be three mode (countries, rating scales, subjects), three-way data.
MDS Models There are two broad classes of M D S models that can be defined as either unweighted M D S or weighted M D S . O n l y the first of these two will be reviewed here. T h e most significant difference between the two types of M D S procedures is that weighted M D S specifically examine the variation a m o n g matrices that might occur in three-way data. In this case, and if" individuals are represented by different matrices, then it is possible to examine the weighting given by individuals to the averaged spatial configuration.
~ku,,eighted MDS The most c o m m o n unweighted M D S model is Classical Multidimensional Scaling ( C M D S ) . This model attempts to identify the underlying structure of" one mode two-way data (i.e., proximity data represented in a lower triangular matrix). In this model, the proximi-
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ties, which usually represent the degree of dissimilarity between elements, are represented as distances in a multidimensional space. There are a number of MDS programs which will analyze data of this type including MINISSA from within the MDS(X) set of programs, KYST, P O L Y C O N , M U L T I S C A L E , and A L S C A L . A L S C A L is perhaps tile most appropriate MDS program, as apart from it also being an integral part of the SPSSx statistical package, it has theoretically no limit to the size of the data which can be analyzed, although system memory will ultimately determine this. In addition, A L S C A L has a large number of options available through which the data can be analyzed. For instance, data can be analyzed assuming any level of measurement, as continuous or discrete, and with missing data. Of course, it must be emphasized that while a C M D S program will analyze two-way one mode data, and hopefully produce an interpretable dimensional solution, this may well be that due to some a priori theoretical reason, the researcher is not interested in identifying the underlying dimensional structure, but wishes to know if there is any clustering or grouping of the elements. In this case, rather than a dimensional analysis being most appropriate, a cluster analysis should be used, such as the program C L U S T E R or Q U I C K C L U S T E R from within the SPSSx package, or the clustering algorithm H I C L U S (Johnson 1967) which is available from within the MDS(X) program set. The second type of unweighted MDS is perhaps more appropriately referred to as multidimensional unfolding (MDU), and is used to analyze two-way, two mode data. Data suitable for this type of analysis typically consist of a rectangular data matrix, comprising ratings which have been given to a number of elements on the basis of a series of predefined rating scales. M I N I R S A from within the MDS(X) program series will perform a M D U analysis, but perhaps the most appropriate program is again A L S C A L from the SPSSx package. The M D U analysis produces a multidimensional solution which is very different from that achieved in classical MDS, since one is now identifying a spatial solution which represents the interrelationships between two sets of elements or data modes and not one. Given two sets of elements are represented in the derived spatial configuration, it is often referred to as a joint space solution. For instance, if individuals record their preference for visiting a number of different countries, then a M D U analysis of this two mode data (individuals, countries) would provide a spatial solution where both the individuals and countries were identified in a joint space, with some points in the space representing individuals and some points representing countries. Whenever M D U is used, care should be taken when interpreting the dimensional solutions that emerge as they are notoriously uninterpretable or "degenerate" (Purcell 1984; Schiffman et ah 1981). This instability is a result of the mathematical procedures in transforming joint proximities to joint distances. There are, however, a number of alternatives to the analysis of rectangular, two way two mode data, and since such data matrices are common in behavioral science research, such alternatives are worth
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identifying. First, if a large r e c t a n g u l a r data m a t r i x needed to be analyzed, principal c o m p o n e n t s or factor analysis could be used in preference to M D S , where the factor loadings could be used to interpret one m o d e of the data, while the factor scores could be used to identify the relationship of the second data m o d e to the first. O f course, as mentioned earlier, there are a n u m b e r of drawbacks to the use of factor analysis. T h e second alternative is to p e r f o r m two C M D S analyses on the data matrix. In this case, derived proximities would be obtained for both sets of elements and each derived p r o x i m i t y m a t r i x analyzed by C M D S . While this solution appears to be straightforward, the most obvious s h o r t c o m i n g is that it is very ditlicult to relate one M D S solution to another, although a p r o g r a m such as P I N D I S , which may be found in the M D S ( X ) series m a y be useful in this context. A third p r o c e d u r e which has been used, and which has provided a m e a n i n g f u l interpretation of two m o d e data, is the external M D S analysis. This p r o c e d u r e initially obtains derived p r o x i m i t y measures fbr elements within one m o d e of the data, and subsequently analyzes them t h r o u g h C M D S . In the next phase of the analysis, the second m o d e of data is regressed or located into the first. For example, Fenton and Hills (1987), in exploring the perception of animals between animal liberationists and hunters, had subjects rate animal categories on a n u m b e r of elicited constructs, resulting in a two-way m o d e m a t r i x consisting of animal categories by constructs. O n e objective of this study was to identify the most salient dimensions individuals used to discriminate a m o n g the animal categories. In o r d e r to accomplish this, a C M D S was p e r f o r m e d on a m a t r i x of derived p r o x i m i t y measures which consisted of Euclidian distances a m o n g the animal categories across all constructs. Following the identification of space of suitable dimensions, each of the constructs representing the second m o d e of the data was then regressed into the space t h r o u g h the use of a p r o p e r t y fitting p r o g r a m , P R O F I T , from the M D S ( X ) p r o g r a m series. ]'hose constructs which were highly correlated with specific orientations in the space were then used to identify the way in which individuals a p p e a r e d to discriminate a m o n g the animal categories. MDS STUDIES IN TOURISM
RESEARCH
T h e r e are a n u m b e r of" examples of m u l t i d i m e n s i o n a l scaling procedures e m p l o y e d in the existing tourism literature. In an early application of the technique, A n d e r s s e n and C o l b e r g (1973) studied the similarity of would-be travelers' perceptions of M e d i t e r r a n e a n destinations. This kind of work is closely allied to m a r k e t research approaches to the image of one's p r o d u c t c o m p a r e d to its competitors' and affords the possibility of diachronic studies of p r o d u c t image. For example, if one destination is m a r k e t e d intensively as offering an exclusive and expensive style of holiday experience, then a series of M D S analyses should be able to follow the success of the image m a k i n g over time. Similarly, the choice of route to a destination is sometimes of interest. Pearce and P r o m n i t z (1984) d e m o n s t r a t e d that highways in Australia were j u d g e d to be very different in their tourist appeal. T h i s
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study also indicated that the perceptions people hold about tourist products and services can be clearly linked to their choices and behavior patterns. In this study, the researchers found one cluster of highways which was simply seen as undesirable, unattractive, and to be avoided at holiday times. The traffic flow figures for these highways supported the perceptual data. It would be valuable in many other image studies (including MDS studies) if the perceptions and cognitions of tourists could be linked more frequently to their behaviors in regard to those settings (Figure 1). In an attempt to refine and extend an earlier article on tourist roles by Cohen (1974), Pearce used multidimensional scaling techniques to provide a picture of how a student sample saw 15 travel related roles (Pearce 1982, 1985) (See Figure 2). In a recent extension of this approach, Smithson (1987) noted that the MDS picture provided contrasting degrees of fuzziness, as defined by fuzzy set theory. Those roles in the center of the space were rated as clearer and less confused than roles towards the periphery. Despite the fact that the behavioral ratings were organized to assess tourism related roles, the core role of tourist is the fuzziest in the whole set. Smithson's interpretation of the original MDS data with fuzzy set theory methods raises the possibility of other interpretive and statistical approaches adding on to MDS procedures. Recently, Canter has proposed the extensive use of facet theory to interpret, comment on, and organize basic MDS solutions (Canter 1985). Moscardo and Pearce (1986) used archival material as the input for their multidimensional scaling analysis of the similarity of 17 visitor centers in Britain. The data consisted of ratings of the centers on a number of dimensions and these ratings were converted into similarity scales as discussed earlier in this article. The resulting map of the visitor centers revealed several types of centers which appeared to function in different ways. One cluster of centers provided little more than pamphlets and a booking service, while another group offered the visitor detailed ecological and environmental interpretations of the surrounding area. In general, the more detailed visitor centers were those with which the visitors were most satisfied (Figure 3). A further study employing the MDS technique was conducted at Green Island, one of the most popular destinations on Australia's Great Barrier Reef. In this study the perceptions of tourists and national park staff were compared, and MDS results reflecting the views of each group were obtained. It can be seen that the national park staff not only group the activities differently to the tourists, but indeed use different dimensions or scales to organize their clusters of activities. National park staff emphasize management related issues in their mental maps of the activities (e.g., safe-dangerous, well promoted-not well promoted), while the tourists appear to focus on the experiential dimensions of the activities (how close they get to the reef, the enjoyment level of the activity, and its physical location) (Figures 4 and 5). Other research efforts using the technique have profitably explored tourists' perceptions of Finland as a destination (Haaht 1986) using a two mode, two-way P R E F MAP analysis of the rectangular matrix of countries by attributes'data. This study is allied to the correctional
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marketing use of M D S research and is functionally similar to the earlier Anderssen and Colbey (1973) analysis and use. A more creative use of the procedure is offered by Kemper, Roberts and Goodwin (1983). They employed a card sorting technique to explore the cultural perceptions of a New Mexico community from an anthropological perspective. They used 50 items relating to cultural interests, activities, or services in the card sorting task (e.g., fishing, weaving, pottery) and provided a dimensional solution of the 89 subjects' perceptions. Their analysis revealed a culture-nurture dimension in the data, an activepassive classification of the activities, and a local or widespread identity to the activities. Interestingly, the latter two dimensions are somewhat similar to those reported on the other side of the world in the Green Island study of tourists' perceptions. Within the wider domain of leisure research applications of the MDS, techniques have included a classification of leisure activity types (Becket 1976; Hirschman 1985; Ritchie 1975), the relationship between public and private recreational systems (Lovingood and Mitchell 1978), an exploration of the kinds of psychological benefits which a recreational park can produce (Uluch and Addoms 1981), and a test of Maslow's theory of motivation (Mills 1985).
Additional Uses
In addition to the studies cited, the multidimensional scaling procedures outlined above provide an exciting methodology for a host of tourism studies. One of the core areas of interest in contemporary tourism studies is how tourists perceive and classify the visited setting (Iso-Ahola 1983; Mayo and Jarvis 1983; Stringer and Pearce 1984). M D S procedures provide a technique for investigating the ways in which tourists rate and organize such stimuli as countries, cities, national parks, theme parks, museums, tourist sites, and information centers. Tourist services too can be examined with this approach and target stimuli might include airline companies, restaurants, package tours, destination resorts, and travel agents. If a large number of these studies were to be conducted by tourism researchers, one's knowledge of tourists' preferences and judgments would be substantially enhanced and could permit the investigation of cross-national and sampling differences in tourists' perceptions. Some researchers have argued that descriptive research is perhaps less sophisticated and less desirable than hypothesis testing approaches. Initially it might appear that the multidimensional scaling approach will only provide a plethora of descriptive information. It is possible, however, to use the approach to facilitate the testing of theoretical perspectives in tourism studies. For example, one might hypothesize that certain elements should be seen as closer together than others in the final M D S solution. For example, in the study of tourist roles, one might have argued that tourists should be seen more as businessmen than conservationists. The M D S picture obtained from 100 students would have supported this perspective. A sample of conservationists might also have been studied and their mental arrangement of tourist
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roles could also have been explored. O n e could then test the proposal that conservationists would see the tourist roles as even more like that of businessmen and other exploitative groups than the cluster of roles which include conservationists, explorers, and scientists. The basis fbr such a prediction could lie in the assumed value differences of the conservationist group and this difference could in thct be measured with a scale of values test (e.g., the Rokeach scale) or a measure such as the E n v i r o n m e n t a l Response Inventory ( M c K e c h n i e 1973). If one were to find the anticipated pattern of similarity with the M D S results, then the predictive power of these personality and individual difference measures tbr tourism related material would be enhanced. It is in thct surprising how little of the conventional psychological testing material has been used in evaluating tourists' behavior and responses. Therefore, one theoretical use of the M D S approaches is to specit~' the pattern of anticipated results according to a theoretical perspective and inspect the final structure for its adherence to this pattern. Additionally, one can compare the perceptions of two or more groups of people which could be two different types of tourists, tourists and locals, or tourists and the providers of tourist services. It is argued here that this hypothesis testing or exploring function of multidimensional scaling has m u c h to offer tourism research. It is hoped that the future use of the procedure will tollow some of these exciting possibilities tor research integration and conceptual development. 2][~ REFERENCES Andcrssen, P., and Colberg R. 1973 Multivariate analysis in travel research: a tool tot travel package design and market segmentation. The Travel Research Association, Fourth Annual Cnnti-rence Proceedings. Becker, B. W. 1976 Perceived Similarities A m o n g Recreational Activities. Journal of Leisure Research 8:112-122. Canter, O. 1985 Facet Theory: Approaches to Social Research. New" York: Springer-Verlag. Carroll, J. D., andJ..J. Chang 1970 Analysis of Individual Dift~'rences in Multidimensional Scaling via an N-way Generalization of Eckart-Young Decomposition. Psychometrika, 35:283-319. Cohen, E. 1974 Who is a lburist? Sociological Review 22(4): 527-53. Coxon, A. R M. 1982 The User's Guide to Multidimensional Scaling. London: Chaucer Press. Easterling, D. V. 1984 Ideological Shifts in the U.S. Senate between 1971 and 1978: A Principal Directions Scaling of Roll Call Votes. In theory and applications of nmhidimensional scaling, F. W. Young and R. M, Hamer, eds. Hillsdale NJ: Erlbaum. Eckart, C., and G. Young 1936 The Approximation of one Matrix by Another of a Lower Rank. Psychometrika 1:211-218. Fenton, D. M. 1985 Dimensions o(" Meaning in the Perception of Natural Settings and their Relationship to Aesthetic Response. Australian Journal of Psychology 37(3):325-339. Fentorl, D. M., a n d A . M Hills 1987 The Perception of Animals Amongst Animal Liberationists and Hunters: A Multidimensional Scaling Analysis. (Under review).
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Green, P. E. and E J. Carmone 1972 Marketing Research Applications of Nonmetric Scaling Methods. In Multidimensional Scaling: Theory and Applications in the Behavioural Sciences, Vol 2: pp. 183-210, A. K. Romney, R. N. Shepard, and S. B. Nerlove, eds. New York: Seminar Press. Haahti, A. J. 1986 Finland's Competitive Position as a Destination. Annals of Tourism Research 13:11-26. Halpern, A. R. 1984 Organization in Memory for Familiar Songs. Journal of Experimental Psychology: Learning, Memory, and Cognition 10(3): 496-512. Harshman, R. A., and W. S. De Sarbo 1984 An Application of PARAFAC to a Small Sample Problem, Demonstrating Preprocessing, Orthogonality Constraints, and Split-half Diagnostic Techniques. In Research methods for multimode data analysis, pp. 602-642, H. G. Law, C. W. Snyder, J. A. Hattie, and R. R McDonald, eds. New York: Praeger. Hirschman, E. C. 1985 A Multidimensional Analysis of Content Preferences for Leisuretime Media. Journal of Leisure Research 17 : 14-28. Hodson, F. R., D. G. Kendall, and P. Tautu eds. 1971 Mathematics in the Archaeological and Historical Sciences. Edinburgh: University Press. Iso-Ahola, S. E. 1980 The Social Psychology of Leisure and Recreation. Dubuque, Iowa: William C. Brown.
Johnson, S. C. 1967 Hierarchical Clustering Schemes. Psychometrika 32:241-254. Kemper, R. V., J. M. Roberts, and R. D. Goodwin 1983 Tourism as a Cultural Domain. Annals of Tourism Research 10: 149-171. Kruskal, J. B. 1964 Nonmetric Multidimensional Scaling: A Numerical Method. Psychometrika 29:115-129. Kruskal, J. B. and M. Wish 1978 Multidimensional Scaling. Sage University Paper Series on Quantitative Applications in the Social Sciences, 7-11. Beverly Hills: Sage Publications. Law, H. G., C. W. Snyder, J. A. Hattie, and R. R McDonald eds. 1984 Research Methods for Muhimode Data Analysis. New York: Praeger. Lovingood, R E., and L. S. Mitchell 1978 The Structure of Public and Private Recreational Systems: Columbia, South Carolina. Journal of Leisure Research 10:21-36. MacCallum, R. C. 1979 Recovery of Structure in Incomplete Data by ALSCAL. Psychometrika 44:6974. Mayo, E. J., andJarvis, L. P. 1981 The Psychology of Leisure and Travel. Boston: CBI Publishing. McKechnie, G. E. 1974 Manual for the Environmental Response Inventory. Palo Alto, California: Consulting Psychologists Press. Mills, A. S. 1985 Participation Motivations for Outdoor Recreation: A Test of Maslow's Theory. Journal of Leisure Research 17:184-199. Moscardo, G., and P. L. Pearce 1986 Visitor Centres and Environmental Interpretation: An Exploration of the Relationships Among Visitor Enjoyment, Understanding and Mindfulness. Journal of Environmental Psychology 6:89-108. Nassar, J. 1980 On Determining Dimensions of Environmental Perception. In Optimizing Environments: Research, Practice, and Policy, R. R Stough and A. Wandersman, eds. Environmental Design and Research Association. Pearce, R L. 1982 The Social Psychology of Tourist Behaviour. Oxford: Pergamon.
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Pearce, P. 1~. 1985 A Systcmatic C o m p a r i s o n of'l}'avel-related Roles. H u m a n Relations 38:1001 1011. Pcarce, P. L., and J. Promnitz 1984 Research tot ~I})urist Highways. Australian Road Research 14(3):156 160. Purcell, A. T. 1984 Multivariate Models and the Attribules of the Expcriencc of the Built Environment. E n v i r o n m e n t and P l a n n i n g I1:193 212. Richardson, M. W. 1938 Multidimensional Psychophysics. Psychological Bulletin 35:659-660. Richie, J. R. B 1975 O n the Derivation of Leisure Activity Types: A Perceptive M a p p i n g App,'oach. .Journal of Leisure Research 7:128- 164. Shcpard, R. N. 1962 Analysis of Proximities: M u h i d i m e n s i o n a l Scaling with an U n k n o w n Distance Function (part 1). Psychomctrika 27(1):125-139. 1972 A Taxnnomv of Some Principal ~l~pes of Data and of" M u h i d i m e n s i o n a l M e t h ods of their Ai{alvsis.. In Multidimensional Scaling: Theory and Applications In lhc Behavioural Sciences, \.'ol 1:(21 4 7 , ) R . N. Shcpard, A. K. R n m n e v and S. B. Nerlove, cds. New "~b,k: Seminar Press. Schiffman, S. S., M. L. Reynolds, and E W. 5:bung 1981 Introduction to M u h i d i m e n s i o n a l Scaling: Theory, Mcthods, and Applications. New ~'brk: Acadelnic Press. Smithson, M. 1986 Fuzzy Set Analysis tot Behavioural and Social Scicnccs. New ~;:)rk: Springer \~'rlag. SPSS Inc. 1986 SPSSx: User's Guide (2nd ed.). New "~})rk: McGraw-Hill. Stringcr, P. F., and Pearce, R L. 1984 Toward a symbiosis of Social Psychology and "li)urism Studies. Annals of ~Iburism Research 11 : 5-17. Uluch. R. S. , and Addoms, D. 1,. I981 Psychological and Recreational Benefits of a Recreational Park. olournal of Leisure Research 13: 43-56. Wish, M. 1971 Individual Differences in Perceptions and Preferences A m o n g Nations. In Attitude Research Reaches New Heights (pp. 312-318), C. W. King and D. Tigert, eds. Chicago: American M a r k e t i n g Association. }bung, G., and A. S. Householder 1938 Discussion of a Set of Points in Terms of T h e i r Mutual Distances. Psychometrika 3: 19-22. Submitted 1 9 J u n e 1987 Accepted 22 j u l y 1987 Final version submitted 7 August 1987 Rel;e'reed anonymously
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MULTIDIMENSIONAL SCALING AND TOURISM RESEARCH Mark F e n t o n Curtin University of Technology, Australia P h i l i p Pearce James Cook Univ. of North Queensland, Australia
Abstract: Multidimensional scaling (MDS) is a tbrm of analysis which permits the relationships a m o n g a set of elements to be represented as interelement distances in spaces. It is suitable for data collected according to a n u m b e r of difti~rent formats. This article describes a n u m b e r of the tormal and technical features of M D S analysis and its variants. The main purpose of M D S approaches lie in their capacity to explore the structure underlying a set of judgements. Existing and potential uses of the multidimensional scaling procedure in tourist studies are discussed. It is concluded that the multidimensional scaling approach can provide more than a complex technique tot simplifying data sets. It is also argued that the technique can be used to test hypotheses and conceptual arguments in the tourist literature. K e y w o r d s : multidimensional scaling, tourism research.
R~sumd: Fanalyse 5 l'~chelle muhidimensionnelle ct la recherche en tourisme. I2analyse 5 l'dchelle multidimensionnelle ( E M D ) est une mdthode d'analyse qui permet que les rapports entre les ~l~mcnts d'un ensemble soient reprdsent~s comme des distances entre dldments dans l'espace. Cette m6thode convient h des donndes qu'on a recueillies par plusieurs moyens difli~rents. Le present article ddcrit quelques-uncs des caract6ristiques formelIes et techniques de l'analyse E M D et de ses variantes. Le but principal des approches E M D se trouve dans leur capacitd d'explorer la structure qui est 5 la base d'un ensemble de jugements. On discute des usages actuels et ~ventuels du procddd de l'analyse ~l l'6chelle multidimensionnelle dans l'dtude du tourisme. On conclut que l'approche de l'dchelle muhidimensionnelle peut offrir plus qu'une technique con> plexe pour simplifier des ensembles de donn~es. O n soutient aussi qu'il est possible d'utiliser cette technique pour v6rifier des hypoth}ses et des arguments conceptuels dans les oeuvres de recherche touristique. M o t s clef: analyse 5 l'dchelle muhidimensionnelle, recherche en tourisme.
INTRODUCTION Imagine that a map of Australia lies across a desk. Recorded in kilometers are the distances among all major cities in Australia, resulting in a triangular data set which represents all the intercity distances. M a r k F e n t o n is a lecturer in psychology at the Curtin University of Technology (Bentley WA 6102, Australia). His research interests include environmental perception and computer ergonomics. P h i l i p Pearce is a senior lecturer in psychology at J a m e s Cook University. He has spent ten years conducting research into social psychological aspects of tourists. 236
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With this data set of all intercity distances, it would be possible to construct, on the basis of these distances, a map showing the location of each of these cities. Now this could take some time since each city would have to be positioned on the map in such a way that the map of distances represent the data matrix o'f distances among cities. Rather than developing the map by hand, the data could be subjected to a multidimensional scaling analysis (MDS), the result of which would be a map of Australian cities, where the mapped intercity distances would be identical to the matrix. Multidimensional scaling began primarily as a variant of factor analysis within the field of psychophysics in the late 1930s (Eckart and Young 1936; Richardson 1938; Young and Householder 1938). Later, through the papers of Shepard (1962, 1972), Kruskal (1964), and Carroll and Chang (1970), it was expanded into a broad family of scaling techniques. While it was initially developed within the area of psychology, it has been usefully applied to a number of areas outside the general scope of psychology, including marketing (Green and Carmone 1972), political science (Easterling 1984), and archaeology (Hodson, Kendall, and Tautu 1971). The twofold aim of MDS is to reduce data so as to make them more manageable and meaningful, and at the same time to identify whether there is any inherent underlying structure within the data. Both aims of MDS are related, as the recovery of underlying structure usually means the reduction of the entire data set to a manageable and limited number of dimensions, clusters, or groupings. Multidimensional scaling has many elements in common with factor analysis, but it differs from it in three important respects. First, while factor analysis, like MDS, attempts to identify the inherent structure within data, factor analysis requires that the variables to be analyzed must be measured on at least an interval scale. MDS does not necessarily require this assumption as it determines inherent structure on the ordered relations existing among elements. Second, an MDS solution is usually easier to interpret than a factor analysis solution, as the MDS model is based on the distance between points in a multidimensional space. In factor analysis, the model which is generated is based on the angles between vectors. A third important difference between MDS and factor analysis, which is related to the interpretation of the final configuration, is that the researcher using MDS usually finds relatively fewer dimensions than would occur if the data were analyzed through factor analysis. As Shepard (1972:3) has noted "the high dimensionality characteristic of factor-analytic results is in part a consequence of the rigid assumptions of linearity upon which the standard factoranalytic methods have been based", and, as such, one would expect a solution of lower dimensionality when the assumptions of linearity are removed. The data on which the MDS analysis is based consist of a series of "proximities" which indicate the degree of similarity or dissimilarity among elements within a defined set. The proximity measures may be either "direct" or "derived" measures of proximity. If the measures are direct, then the subject has usually provided a direct estimate of the degree of (dis)similarity between any pair of elements, either through a rating or
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classification task. Derived proximities, on the other hand, usually consist of some m e a s u r e of association a m o n g elements within a set which are not m a d e directly by a subject. MEASURES OF PROXIMITY
Oirec! Measures of ProxbniO, O n e of the most c o m m o n measures of direct p r o x i m i t y is paired comparisons. T h r o u g h pairwise j u d g m e n t s , the subject indicates the degree to which two elements are similar or dil'l~rent. In this task, a bipolar rating scale of which the endpoints are a n c h o r e d with the verbal labels o f " v e r y similar" and "very different" is used to record the judgment. While the use of the rating scale is the most c o m m o n tbrm of eliciting direct measures of p r o x i m i t y from subjects, Schiffrnan, Reynolds and Young (1981) have suggested that it is sometimes a difticuh and somewhat a m b i g u o u s task to p e r f o r m in terms of assigning a specific m e a n i n g to the n u m e r i c points on the scale. For this reason, Schiffman et al. (1981) have suggested that rather than m a k i n g j u d g ments of similarity with reference to a n u m e r i c scale, a less a m b i g u o u s and m o r e effective p r o c e d u r e is to have subjects simply place a mark on a line of which the e n d p o i n t s of the line arc a n c h o r e d with the verbal labels "exact same" and "most different." T h e length of the line is then m e a s u r e d in millimeters from the verbal label up to and including the mark, and as such rcpresents a direct m e a s u r e of proxiinity between elements. A second m e t h o d o f u b t a i n i n g direct measures of p r o x i m i t y is to have sutzjccts sort a large pool of elements into a n u m b e r of smaller groups which are perceived as being alike on some attribute of interest. T h e n u m b e r of groupings can be p r e d e t e r m i n e d by the researcher or determ i n e d d u r i n g the sorting by the subject. After completion, a inatrix is constructed of b i n a r y values representing the degrce of similarity between elements, where a 1 might indicate that the elements were sorted into the same group with a 0 indicating that the elements were sorted into different groups. A third m e t h o d of o b t a i n i n g some index of similarity a m o n g elements is to have subjects rank o r d e r the elements on a particular attribute. Alternatively, elements may be r a n k - o r d e r e d in terms of how similar they arc to a predefined standard. T h e completed m a t r i x represents a rectangular matrix of elements by attributes, or elements by standards, where the values in the body of the m a t r i x represent the r a n k i n g of the element in relation to the attribute or standard. While there are a n u m b e r of other variants of the three p r o c e d u r e s for o b t a i n i n g direct measures of p r o x i m i t y (see C o x o n 1982, C h a p . 10), the rating, grouping, and ranking p r o c e d u r e s are the most cominon within the behavioral sciences literature. Examples of obtaining direct proximities t h r o u g h the use of rating scales include research on the perception of natural settings (Fenton 1985) and the perception of nations (Wish 1971), while examples of the use of g r o u p i n g p r o c e d u r e s include the perception of tourist highways (Pearee and P r o m n i t z 1984),
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urban settings (Nassar 1980), and music (Halpern 1984). The ranking procedure is not as common as either the rating or grouping methods, but has been used by Harshman and De Sarbo (1984) in the context of marketing research. One important consideration which is often overlooked in planning a study, which uses MDS and is based on direct measures of proximity, is the number of elements that are going to be used and the time required to obtain direct measures of proximity among all elements. For example, if the researcher who decides to use the paired comparisons procedure wishes to know what the underlying dimensions are that subjects use in discriminating among four elements, then in order to form a complete proximity matrix six paired comparisons will have to be completed; with eight elements 28 paired comparisons will be required; with 12 elements 66 comparisons; and with 20 elements 190 comparisons. Clearly, as the number of elements increases, there is a corresponding and rapid increase in the number of paired comparisons required. In addition, Schiffman et al. (1981) indicate that while the time required to complete a paired comparisons task depends upon the type of elements used, paired comparisons among all possible pairs of 20 elements, with no readaption or rest intervals, could take upwards of l :/2 hours. In order to partly reduce the time required to complete a set of paired comparisons, MacCallum (1979:69) has suggested the use of an incomplete data design, where only a certain percentage of the proximity matrix is completed by any one individual. Monte Carlo studies, which have compared analyses based on different percentages of incomplete data, have shown "that very accurate recovery of true distances, stimulus coordinates, and weight vectors could be achieved with as much as 60% missing data as long as sample size was sufficiently large and the level of random error was low."
Indirect Measures of Proximity Indirect measures of proximity usually consist of some index of association, such as a correlational index, as in Pearson's r; a contingency measure, such as Cramer's V or Phi; or a distance measure as usually found in Euclidian, City Block, or Minkowski distances. Given that such indexes of proximity are normally based on aggregated data either across individuals, stimuli, or replications on the variable of interest, then the resulting spatial configuration may simply be an artifact of the process of aggregation. One of the most valuable reference sources for identifying the different types of indirect measures of proximity available is the SPSSx Users Guide (1986). Not only are the measures identified and the defining formulae supplied, but the SPSSx proximities program module will generate selected proximities on the basis of either the rows or columns of a square or rectangular matrix.
How M D S Works MDS consists of a broad family of scaling techniques, where the
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selection of any one p r o c e d u r e is d e p e n d e n t on the type of data to bc analyzed, decisions as to how the data are to be treated d u r i n g the analysis, and which end result is required. As such, the tbllowing discussion applies only to the most c o m m o n e l e m e n t a r y torm of M D S , which will be r e f e r r e d to as classical m u l t i d i m e n s i o n a l scaling ( C M D S ) . M a n y of the other M D S procedures are simply an extension of this basic model. Given a triangular matrix of either derived or direct proximities p r o d u c e d t h r o u g h any of the p r o c e d u r e s previously discussed, the ob.jective of M D S is to take the proximities a m o n g elements and represent them as distances in a space of minimal dimensionality so that the distances a p p r o x i m a t e as best as possible the proximities a m o n g elements. This is accomplished t h r o u g h an iterative cycle and begins with an estimated or r a n d o m starting configuration of" distances a m o n g elements. T h e distances in the starting configuration are then c o m p a r e d to the original p r o x i m i t y values a m o n g elements and a "goodness of fit function computed," which in most M D S procedures is usually identified as "stress." O n c e this function has been c o m p u t e d the starting configuration is adjusted so that it m o r e closely a p p r o x i m a t e s the original proximities. Again this adjusted contiguration is c o m p a r e d to the original p r o x i m i t y values with a goodness of" fit function being computed. This iterative cycle continues until the m a x i m u m n u m b e r of iterations specified by the user has been reached or the i m p r o v e m e n t in fit or stress is less than a critical interval, which leads to the completion of the iterative cycle. T h e process of locating elements in a space, where the distances a m o n g elements c o r r e s p o n d as m u c h as possible to the proximities, may be u n d e r t a k e n in a space of any dimensionality as specified by the user prior to the analysis. Solutions will normally be obtained in a n u m b e r of dimensions, b e g i n n i n g with a one-dimensional solution. As for the m a x i m u m dimensionality for the data set, Kruskal and Wish (1978:34), as a rule of' t h u m b , have indicated that in o r d e r tbr the solution to be statistically stable, the n u m b e r of elements minus one should be greater than four times the proposed dimensionality. O n c e a series of dimensional solutions is o b t a i n e d for a data set, the researcher is then taced with the problem of selecting the most a p p r o p r i a t e dimensionality and i n t e r p r e t i n g the dimensional solution.
Interpreting the M D S Solution It must be e m p h a s i z e d that there is no one index that will identify the correct dimensional representation for the data. Although the goodness of fit function for each configuration m a y partially answer this question, consideration must also be given to the interpretability of the dimensional space. W h e n using stress to identify the a p p r o p r i a t e dimensionality, it is usual to construct a plot showing the relationship between stress levels and dimensional solutions (i.e., Kruskal and Wish 1978, Fig. 16; Schifflnan et al. 1981, Fig. 1.6). W h e n inspecting the plot, the dimensionality after which there is little or no substantial i m p r o v e m e n t in stress is usually selected as the most appropriate dimensional solution.
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In addition to an evaluation of the stress value, careful consideration must be given to the interpretation of the dimensional solution. It may well be that the solution with the optimum stress value is not necessarily the most interpretable and meaningful solution, and solutions in a higher or lower dimensionality may also need to be considered.
Data Theory A n u m b e r of schemes have been developed for classifying the broad range of M D S procedures, the earliest of which was probably that developed by Shepard (1972). However, the most recent non-mathematical overview of MDS, which at the same time attempts a partial taxonomy of M D S models in terms of a general data theory, is that proposed by Schiffman et al. (1981). Th e concepts embedded within the data theory proposed by Schiffman et al. (1981) attempt to link attributes of the data with the model being used to understand the data. As such, three organizing concepts are used to define the data theory proposed: the shape of the data, the n u m b e r of"ways" of the data, and the nature of the M D S model.
Shape or Mode of the Data T h e data for an M D S analysis can be in the form of a rectangular or square matrix. A rectangular data matrix is sometimes also referred to as two-mode data since the proximities within a rectangular matrix emphasize the degree of relationship between two distant sets of elements. For instance, the columns of a rectangular data matrix may represent specific objects, places, or people, while the rows may consist of the rating scales on which the column elements are judged. This is a c o mmo n type of data matrix collected in behavioral science research, and is in fact the type of matrix that is most often analyzed through factor analysis. By contrast, the second data shape com m on to M D S data is the square data matrix which is also sometimes identified as consisting of one mode data. In this matrix, the proximities denote the degree of relatedness among one set of elements, rather than two, as in the case of rectangular data. If the square matrix is symmetrical (i.e., where there is no substantive difference between asking the degree of similarity between element A and B and element B and A), then a special case of the square matrix can be developed known as the triangular or offdiagonal data matrix. Such a triangular data matrix is the most common form of data matrix to be analyzed by MDS. In some circumstances, it may not be possible to assume symmetry in proximity measures. For example, asymmetric proximity measures may be found in interpersonal perception research, where person A may regard himself as similar to person B, but person B may regard himself as very dissimilar to person A. While it is possible to use a specific M D S program to analyze such data ( A L S C A L - - A M D S ) , it is possible under some circumstances to consider the asymmetry as noise, and to average the two proximity measures and form a triangular data matrix. A second alternative in dealing with this situation is to analyze
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the upper and lower triangles of the original square matrix separately and compare the resulting solutions.
The 'q4hy" ~ the Data The way of the data simply represents the dimensionality of the original data matrix to be analyzed. Any data matrix must in the first instance be two-way data representing the columns and rows of either a square or rectangular matrix. Three-way data usually takcs the form of several matrices, where the third way is usually represented by either individual subjects or replications over time. It is possible to go beyond three-way or even three mode data (of. Law, Snyder, Hattie and McDonald 1984 tot a review of such approaches), and there are M D S programs which will analyze such data (i.e., C A N D E C O M P and PARAFAC). However, the procedure is extremely rare. As Coxon (1982:187) indicates, "users are advised to proceed beyond three-way data with considerable caution. T h e y are in largely uncharted territoIt is appropriate when discussing data suitable tot M D S analysis to use both the n u m b e r of modes and n u m b e r of ways to define the original data matrix. For instance, a triangular data matrix of averaged proxiinity measures across subjects which represents the degree of dissimilarity a m o n g a n u m b e r of countries recently visited could be defined as one mode (countries), two-way data. If, on the other hand, one did not average across subjects but wished to include individual subjects' data matrices in the M D S analysis, one would then have two mode (countries, subjects),hrec-way data. Ahcrnatively, the researcher might ask sut~jects to complete a rectangular matrix consisting of ratings given to countries on a n u m b e r of predefined scales. If the researcher does not aggregate across subjects but includes each individual subject's rectangular matrix in the analysis, then there would be three mode (countries, rating scales, subjects), three-way data.
MDS Models There are two broad classes of M D S models that can be defined as either unweighted M D S or weighted M D S . O n l y the first of these two will be reviewed here. T h e most significant difference between the two types of M D S procedures is that weighted M D S specifically examine the variation a m o n g matrices that might occur in three-way data. In this case, and if" individuals are represented by different matrices, then it is possible to examine the weighting given by individuals to the averaged spatial configuration.
~ku,,eighted MDS The most c o m m o n unweighted M D S model is Classical Multidimensional Scaling ( C M D S ) . This model attempts to identify the underlying structure of" one mode two-way data (i.e., proximity data represented in a lower triangular matrix). In this model, the proximi-
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ties, which usually represent the degree of dissimilarity between elements, are represented as distances in a multidimensional space. There are a number of MDS programs which will analyze data of this type including MINISSA from within the MDS(X) set of programs, KYST, P O L Y C O N , M U L T I S C A L E , and A L S C A L . A L S C A L is perhaps tile most appropriate MDS program, as apart from it also being an integral part of the SPSSx statistical package, it has theoretically no limit to the size of the data which can be analyzed, although system memory will ultimately determine this. In addition, A L S C A L has a large number of options available through which the data can be analyzed. For instance, data can be analyzed assuming any level of measurement, as continuous or discrete, and with missing data. Of course, it must be emphasized that while a C M D S program will analyze two-way one mode data, and hopefully produce an interpretable dimensional solution, this may well be that due to some a priori theoretical reason, the researcher is not interested in identifying the underlying dimensional structure, but wishes to know if there is any clustering or grouping of the elements. In this case, rather than a dimensional analysis being most appropriate, a cluster analysis should be used, such as the program C L U S T E R or Q U I C K C L U S T E R from within the SPSSx package, or the clustering algorithm H I C L U S (Johnson 1967) which is available from within the MDS(X) program set. The second type of unweighted MDS is perhaps more appropriately referred to as multidimensional unfolding (MDU), and is used to analyze two-way, two mode data. Data suitable for this type of analysis typically consist of a rectangular data matrix, comprising ratings which have been given to a number of elements on the basis of a series of predefined rating scales. M I N I R S A from within the MDS(X) program series will perform a M D U analysis, but perhaps the most appropriate program is again A L S C A L from the SPSSx package. The M D U analysis produces a multidimensional solution which is very different from that achieved in classical MDS, since one is now identifying a spatial solution which represents the interrelationships between two sets of elements or data modes and not one. Given two sets of elements are represented in the derived spatial configuration, it is often referred to as a joint space solution. For instance, if individuals record their preference for visiting a number of different countries, then a M D U analysis of this two mode data (individuals, countries) would provide a spatial solution where both the individuals and countries were identified in a joint space, with some points in the space representing individuals and some points representing countries. Whenever M D U is used, care should be taken when interpreting the dimensional solutions that emerge as they are notoriously uninterpretable or "degenerate" (Purcell 1984; Schiffman et ah 1981). This instability is a result of the mathematical procedures in transforming joint proximities to joint distances. There are, however, a number of alternatives to the analysis of rectangular, two way two mode data, and since such data matrices are common in behavioral science research, such alternatives are worth
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identifying. First, if a large r e c t a n g u l a r data m a t r i x needed to be analyzed, principal c o m p o n e n t s or factor analysis could be used in preference to M D S , where the factor loadings could be used to interpret one m o d e of the data, while the factor scores could be used to identify the relationship of the second data m o d e to the first. O f course, as mentioned earlier, there are a n u m b e r of drawbacks to the use of factor analysis. T h e second alternative is to p e r f o r m two C M D S analyses on the data matrix. In this case, derived proximities would be obtained for both sets of elements and each derived p r o x i m i t y m a t r i x analyzed by C M D S . While this solution appears to be straightforward, the most obvious s h o r t c o m i n g is that it is very ditlicult to relate one M D S solution to another, although a p r o g r a m such as P I N D I S , which may be found in the M D S ( X ) series m a y be useful in this context. A third p r o c e d u r e which has been used, and which has provided a m e a n i n g f u l interpretation of two m o d e data, is the external M D S analysis. This p r o c e d u r e initially obtains derived p r o x i m i t y measures fbr elements within one m o d e of the data, and subsequently analyzes them t h r o u g h C M D S . In the next phase of the analysis, the second m o d e of data is regressed or located into the first. For example, Fenton and Hills (1987), in exploring the perception of animals between animal liberationists and hunters, had subjects rate animal categories on a n u m b e r of elicited constructs, resulting in a two-way m o d e m a t r i x consisting of animal categories by constructs. O n e objective of this study was to identify the most salient dimensions individuals used to discriminate a m o n g the animal categories. In o r d e r to accomplish this, a C M D S was p e r f o r m e d on a m a t r i x of derived p r o x i m i t y measures which consisted of Euclidian distances a m o n g the animal categories across all constructs. Following the identification of space of suitable dimensions, each of the constructs representing the second m o d e of the data was then regressed into the space t h r o u g h the use of a p r o p e r t y fitting p r o g r a m , P R O F I T , from the M D S ( X ) p r o g r a m series. ]'hose constructs which were highly correlated with specific orientations in the space were then used to identify the way in which individuals a p p e a r e d to discriminate a m o n g the animal categories. MDS STUDIES IN TOURISM
RESEARCH
T h e r e are a n u m b e r of" examples of m u l t i d i m e n s i o n a l scaling procedures e m p l o y e d in the existing tourism literature. In an early application of the technique, A n d e r s s e n and C o l b e r g (1973) studied the similarity of would-be travelers' perceptions of M e d i t e r r a n e a n destinations. This kind of work is closely allied to m a r k e t research approaches to the image of one's p r o d u c t c o m p a r e d to its competitors' and affords the possibility of diachronic studies of p r o d u c t image. For example, if one destination is m a r k e t e d intensively as offering an exclusive and expensive style of holiday experience, then a series of M D S analyses should be able to follow the success of the image m a k i n g over time. Similarly, the choice of route to a destination is sometimes of interest. Pearce and P r o m n i t z (1984) d e m o n s t r a t e d that highways in Australia were j u d g e d to be very different in their tourist appeal. T h i s
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study also indicated that the perceptions people hold about tourist products and services can be clearly linked to their choices and behavior patterns. In this study, the researchers found one cluster of highways which was simply seen as undesirable, unattractive, and to be avoided at holiday times. The traffic flow figures for these highways supported the perceptual data. It would be valuable in many other image studies (including MDS studies) if the perceptions and cognitions of tourists could be linked more frequently to their behaviors in regard to those settings (Figure 1). In an attempt to refine and extend an earlier article on tourist roles by Cohen (1974), Pearce used multidimensional scaling techniques to provide a picture of how a student sample saw 15 travel related roles (Pearce 1982, 1985) (See Figure 2). In a recent extension of this approach, Smithson (1987) noted that the MDS picture provided contrasting degrees of fuzziness, as defined by fuzzy set theory. Those roles in the center of the space were rated as clearer and less confused than roles towards the periphery. Despite the fact that the behavioral ratings were organized to assess tourism related roles, the core role of tourist is the fuzziest in the whole set. Smithson's interpretation of the original MDS data with fuzzy set theory methods raises the possibility of other interpretive and statistical approaches adding on to MDS procedures. Recently, Canter has proposed the extensive use of facet theory to interpret, comment on, and organize basic MDS solutions (Canter 1985). Moscardo and Pearce (1986) used archival material as the input for their multidimensional scaling analysis of the similarity of 17 visitor centers in Britain. The data consisted of ratings of the centers on a number of dimensions and these ratings were converted into similarity scales as discussed earlier in this article. The resulting map of the visitor centers revealed several types of centers which appeared to function in different ways. One cluster of centers provided little more than pamphlets and a booking service, while another group offered the visitor detailed ecological and environmental interpretations of the surrounding area. In general, the more detailed visitor centers were those with which the visitors were most satisfied (Figure 3). A further study employing the MDS technique was conducted at Green Island, one of the most popular destinations on Australia's Great Barrier Reef. In this study the perceptions of tourists and national park staff were compared, and MDS results reflecting the views of each group were obtained. It can be seen that the national park staff not only group the activities differently to the tourists, but indeed use different dimensions or scales to organize their clusters of activities. National park staff emphasize management related issues in their mental maps of the activities (e.g., safe-dangerous, well promoted-not well promoted), while the tourists appear to focus on the experiential dimensions of the activities (how close they get to the reef, the enjoyment level of the activity, and its physical location) (Figures 4 and 5). Other research efforts using the technique have profitably explored tourists' perceptions of Finland as a destination (Haaht 1986) using a two mode, two-way P R E F MAP analysis of the rectangular matrix of countries by attributes'data. This study is allied to the correctional
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marketing use of M D S research and is functionally similar to the earlier Anderssen and Colbey (1973) analysis and use. A more creative use of the procedure is offered by Kemper, Roberts and Goodwin (1983). They employed a card sorting technique to explore the cultural perceptions of a New Mexico community from an anthropological perspective. They used 50 items relating to cultural interests, activities, or services in the card sorting task (e.g., fishing, weaving, pottery) and provided a dimensional solution of the 89 subjects' perceptions. Their analysis revealed a culture-nurture dimension in the data, an activepassive classification of the activities, and a local or widespread identity to the activities. Interestingly, the latter two dimensions are somewhat similar to those reported on the other side of the world in the Green Island study of tourists' perceptions. Within the wider domain of leisure research applications of the MDS, techniques have included a classification of leisure activity types (Becket 1976; Hirschman 1985; Ritchie 1975), the relationship between public and private recreational systems (Lovingood and Mitchell 1978), an exploration of the kinds of psychological benefits which a recreational park can produce (Uluch and Addoms 1981), and a test of Maslow's theory of motivation (Mills 1985).
Additional Uses
In addition to the studies cited, the multidimensional scaling procedures outlined above provide an exciting methodology for a host of tourism studies. One of the core areas of interest in contemporary tourism studies is how tourists perceive and classify the visited setting (Iso-Ahola 1983; Mayo and Jarvis 1983; Stringer and Pearce 1984). M D S procedures provide a technique for investigating the ways in which tourists rate and organize such stimuli as countries, cities, national parks, theme parks, museums, tourist sites, and information centers. Tourist services too can be examined with this approach and target stimuli might include airline companies, restaurants, package tours, destination resorts, and travel agents. If a large number of these studies were to be conducted by tourism researchers, one's knowledge of tourists' preferences and judgments would be substantially enhanced and could permit the investigation of cross-national and sampling differences in tourists' perceptions. Some researchers have argued that descriptive research is perhaps less sophisticated and less desirable than hypothesis testing approaches. Initially it might appear that the multidimensional scaling approach will only provide a plethora of descriptive information. It is possible, however, to use the approach to facilitate the testing of theoretical perspectives in tourism studies. For example, one might hypothesize that certain elements should be seen as closer together than others in the final M D S solution. For example, in the study of tourist roles, one might have argued that tourists should be seen more as businessmen than conservationists. The M D S picture obtained from 100 students would have supported this perspective. A sample of conservationists might also have been studied and their mental arrangement of tourist
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MULTIDIMENSIONAL SCALIN(;
roles could also have been explored. O n e could then test the proposal that conservationists would see the tourist roles as even more like that of businessmen and other exploitative groups than the cluster of roles which include conservationists, explorers, and scientists. The basis fbr such a prediction could lie in the assumed value differences of the conservationist group and this difference could in thct be measured with a scale of values test (e.g., the Rokeach scale) or a measure such as the E n v i r o n m e n t a l Response Inventory ( M c K e c h n i e 1973). If one were to find the anticipated pattern of similarity with the M D S results, then the predictive power of these personality and individual difference measures tbr tourism related material would be enhanced. It is in thct surprising how little of the conventional psychological testing material has been used in evaluating tourists' behavior and responses. Therefore, one theoretical use of the M D S approaches is to specit~' the pattern of anticipated results according to a theoretical perspective and inspect the final structure for its adherence to this pattern. Additionally, one can compare the perceptions of two or more groups of people which could be two different types of tourists, tourists and locals, or tourists and the providers of tourist services. It is argued here that this hypothesis testing or exploring function of multidimensional scaling has m u c h to offer tourism research. It is hoped that the future use of the procedure will tollow some of these exciting possibilities tor research integration and conceptual development. 2][~ REFERENCES Andcrssen, P., and Colberg R. 1973 Multivariate analysis in travel research: a tool tot travel package design and market segmentation. The Travel Research Association, Fourth Annual Cnnti-rence Proceedings. Becker, B. W. 1976 Perceived Similarities A m o n g Recreational Activities. Journal of Leisure Research 8:112-122. Canter, O. 1985 Facet Theory: Approaches to Social Research. New" York: Springer-Verlag. Carroll, J. D., andJ..J. Chang 1970 Analysis of Individual Dift~'rences in Multidimensional Scaling via an N-way Generalization of Eckart-Young Decomposition. Psychometrika, 35:283-319. Cohen, E. 1974 Who is a lburist? Sociological Review 22(4): 527-53. Coxon, A. R M. 1982 The User's Guide to Multidimensional Scaling. London: Chaucer Press. Easterling, D. V. 1984 Ideological Shifts in the U.S. Senate between 1971 and 1978: A Principal Directions Scaling of Roll Call Votes. In theory and applications of nmhidimensional scaling, F. W. Young and R. M, Hamer, eds. Hillsdale NJ: Erlbaum. Eckart, C., and G. Young 1936 The Approximation of one Matrix by Another of a Lower Rank. Psychometrika 1:211-218. Fenton, D. M. 1985 Dimensions o(" Meaning in the Perception of Natural Settings and their Relationship to Aesthetic Response. Australian Journal of Psychology 37(3):325-339. Fentorl, D. M., a n d A . M Hills 1987 The Perception of Animals Amongst Animal Liberationists and Hunters: A Multidimensional Scaling Analysis. (Under review).
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Green, P. E. and E J. Carmone 1972 Marketing Research Applications of Nonmetric Scaling Methods. In Multidimensional Scaling: Theory and Applications in the Behavioural Sciences, Vol 2: pp. 183-210, A. K. Romney, R. N. Shepard, and S. B. Nerlove, eds. New York: Seminar Press. Haahti, A. J. 1986 Finland's Competitive Position as a Destination. Annals of Tourism Research 13:11-26. Halpern, A. R. 1984 Organization in Memory for Familiar Songs. Journal of Experimental Psychology: Learning, Memory, and Cognition 10(3): 496-512. Harshman, R. A., and W. S. De Sarbo 1984 An Application of PARAFAC to a Small Sample Problem, Demonstrating Preprocessing, Orthogonality Constraints, and Split-half Diagnostic Techniques. In Research methods for multimode data analysis, pp. 602-642, H. G. Law, C. W. Snyder, J. A. Hattie, and R. R McDonald, eds. New York: Praeger. Hirschman, E. C. 1985 A Multidimensional Analysis of Content Preferences for Leisuretime Media. Journal of Leisure Research 17 : 14-28. Hodson, F. R., D. G. Kendall, and P. Tautu eds. 1971 Mathematics in the Archaeological and Historical Sciences. Edinburgh: University Press. Iso-Ahola, S. E. 1980 The Social Psychology of Leisure and Recreation. Dubuque, Iowa: William C. Brown.
Johnson, S. C. 1967 Hierarchical Clustering Schemes. Psychometrika 32:241-254. Kemper, R. V., J. M. Roberts, and R. D. Goodwin 1983 Tourism as a Cultural Domain. Annals of Tourism Research 10: 149-171. Kruskal, J. B. 1964 Nonmetric Multidimensional Scaling: A Numerical Method. Psychometrika 29:115-129. Kruskal, J. B. and M. Wish 1978 Multidimensional Scaling. Sage University Paper Series on Quantitative Applications in the Social Sciences, 7-11. Beverly Hills: Sage Publications. Law, H. G., C. W. Snyder, J. A. Hattie, and R. R McDonald eds. 1984 Research Methods for Muhimode Data Analysis. New York: Praeger. Lovingood, R E., and L. S. Mitchell 1978 The Structure of Public and Private Recreational Systems: Columbia, South Carolina. Journal of Leisure Research 10:21-36. MacCallum, R. C. 1979 Recovery of Structure in Incomplete Data by ALSCAL. Psychometrika 44:6974. Mayo, E. J., andJarvis, L. P. 1981 The Psychology of Leisure and Travel. Boston: CBI Publishing. McKechnie, G. E. 1974 Manual for the Environmental Response Inventory. Palo Alto, California: Consulting Psychologists Press. Mills, A. S. 1985 Participation Motivations for Outdoor Recreation: A Test of Maslow's Theory. Journal of Leisure Research 17:184-199. Moscardo, G., and P. L. Pearce 1986 Visitor Centres and Environmental Interpretation: An Exploration of the Relationships Among Visitor Enjoyment, Understanding and Mindfulness. Journal of Environmental Psychology 6:89-108. Nassar, J. 1980 On Determining Dimensions of Environmental Perception. In Optimizing Environments: Research, Practice, and Policy, R. R Stough and A. Wandersman, eds. Environmental Design and Research Association. Pearce, R L. 1982 The Social Psychology of Tourist Behaviour. Oxford: Pergamon.
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Pearce, P. 1~. 1985 A Systcmatic C o m p a r i s o n of'l}'avel-related Roles. H u m a n Relations 38:1001 1011. Pcarce, P. L., and J. Promnitz 1984 Research tot ~I})urist Highways. Australian Road Research 14(3):156 160. Purcell, A. T. 1984 Multivariate Models and the Attribules of the Expcriencc of the Built Environment. E n v i r o n m e n t and P l a n n i n g I1:193 212. Richardson, M. W. 1938 Multidimensional Psychophysics. Psychological Bulletin 35:659-660. Richie, J. R. B 1975 O n the Derivation of Leisure Activity Types: A Perceptive M a p p i n g App,'oach. .Journal of Leisure Research 7:128- 164. Shcpard, R. N. 1962 Analysis of Proximities: M u h i d i m e n s i o n a l Scaling with an U n k n o w n Distance Function (part 1). Psychomctrika 27(1):125-139. 1972 A Taxnnomv of Some Principal ~l~pes of Data and of" M u h i d i m e n s i o n a l M e t h ods of their Ai{alvsis.. In Multidimensional Scaling: Theory and Applications In lhc Behavioural Sciences, \.'ol 1:(21 4 7 , ) R . N. Shcpard, A. K. R n m n e v and S. B. Nerlove, cds. New "~b,k: Seminar Press. Schiffman, S. S., M. L. Reynolds, and E W. 5:bung 1981 Introduction to M u h i d i m e n s i o n a l Scaling: Theory, Mcthods, and Applications. New ~'brk: Acadelnic Press. Smithson, M. 1986 Fuzzy Set Analysis tot Behavioural and Social Scicnccs. New ~;:)rk: Springer \~'rlag. SPSS Inc. 1986 SPSSx: User's Guide (2nd ed.). New "~})rk: McGraw-Hill. Stringcr, P. F., and Pearce, R L. 1984 Toward a symbiosis of Social Psychology and "li)urism Studies. Annals of ~Iburism Research 11 : 5-17. Uluch. R. S. , and Addoms, D. 1,. I981 Psychological and Recreational Benefits of a Recreational Park. olournal of Leisure Research 13: 43-56. Wish, M. 1971 Individual Differences in Perceptions and Preferences A m o n g Nations. In Attitude Research Reaches New Heights (pp. 312-318), C. W. King and D. Tigert, eds. Chicago: American M a r k e t i n g Association. }bung, G., and A. S. Householder 1938 Discussion of a Set of Points in Terms of T h e i r Mutual Distances. Psychometrika 3: 19-22. Submitted 1 9 J u n e 1987 Accepted 22 j u l y 1987 Final version submitted 7 August 1987 Rel;e'reed anonymously