College and Research Libraries Multidimensional Mapping of Book Circulation in a University Library William E. McGrath Circulated books classified according to academic subject areas and student majors were used to determine relative subject similarities in forty academic departments. -Multidimensional scal- ing was used to compute a best-fit solution of the similarities in three dimensions for under- graduate circulation, and two dimensions for graduates. Similarity, or "distances," between departments is shown in two-dimensional maps. The meaning of the dimensions and the ten- dency of departments to cluster within them is discussed. One dimension can confidently be regarded as ''hard-soft, '' a second may be regarded with much less confidence as ''pure ap- plied," and a third is not readily interpreted. Five principal clusters are strongly apparent: quantitative; social services; chemistry and life sciences; humanities; and engineering and earth sciences. Implications for collection development and storage are discussed, including applications for area bibliography, allocation of the budget to departments, organization of the collection, and online retrieval. n university administration, academic departments are al- most universally treated as in- dependent and homogeneous units. Each has a department head, sepa- rate budgets, an allotment of faculty, en- rollment quotas, objectives, and so on. Academic libraries also recognize this practice, primarily by budget allocation for books. From a democratic point of view, the system works and is practical. Yet, faculty members are the first to observe that each has interest in or some relationship to the work of other departments. So too, stu- dents take courses outside of their major. A political scientist, for example, may as- sign readings in history, anthropology, sociology, psychology, or other subjects, and will want to be assured that the library has appropriate materials in those areas. This is true to some extent for many other disciplines. One measure of this cross- disciplinary activity is the extent to which students charge out books in disciplines other than their own major. An earlier. pa- per analyzed this cross-disciplinary circu- lation, defining the extent that students from the University of Southwestern Lou- isiana (USL) charge out books in disci- plines not their major as ethnocentricity af- ter Donald T. Campbell, 1 and the extent to which books in a discipline were used by students in other disciplines as supportive- ness. 2 In that study and in this one, "de- partment" and "discipline" are used in- terchangeably. Theoretically, each discipline has some- thing to offer, and accordingly, books in every discipline have some probability, ranging from 0 percent to 100 percent, of being used by the other disciplines. In fact, of the forty-three disciplines ana- lyzed in the USL study, these percentages were wide-ranging, from 0 percent to 70 percent, and 2 percent to 87 percent for undergraduate and graduate ethnocen- tricity; and 25 percent to 100 percent, and William E. McGrath is associate professor, School of Information and Library Studies, State University of New York at Buffalo. 103 104 College & Research Libraries 13 percent to 98 percent for undergraduate and graduate supportiveness. If each discipline were to use the knowl- edge of every other, the total number of ways they could combine or permute is very large, far too many to comprehend individually. Of the forty in the USL study, the number of permutations just two at a time was 1,560. To consider larger permutations-three at a time, or four or five, and so on-is unthinkable. The num- bers become astronomical. Actually, the matrix of circulation data for the forty USL disciplines showed a large number of in- stances in which a discipline showed zero use by others and a few disciplines that were used by many others. Skewness of this sort is to be expected, but not appar- ent on simple inspection of the matrix combinations because there are so many, and because of the great variability in the extent to which any two disciplines are used by each other. These are the more complex cluster patterns. A well-defined cluster would be one in which all disci- plines in it were used by each other to the exclusion of all others. It is these clusters that offer the more intriguing aspects in the exploration of this type of data. Cer- tain quantitative disciplines such as phys- ics, engineering, and mathematics, for ex- ample, should cluster. On the other hand, some clusters may be hidden and revealed only by extensive analysis. Knowledge of these clusters should be highly useful in providing library service, particularly in collection development, al- location, organization, and storage of the collection and perhaps in retrieval from online catalogs. One could hypothesize, prior to their discovery, about the existence of clusters, such as a physical science cluster, but such hypotheses would be trivial in the sense that such clusters could either be found or not. We know so little about clusters and other hidden patterns that whatever anal- ysis is undertaken (and whether or not ex- plicit hypotheses are stated), findings are certain to uncover new knowledge. There- fore, it would be better to reserve such statements until the actual discovery of clusters. This type of study is sometimes de- March 1983 scribed as data-descriptive and hypothesis-generating. It is analogous to focusing a new telescope on the heavens and, for the first time, observing nebulae, globular clusters, galaxies, or other phe- nomena. Their explanation awaits their discovery. Not until then would it be ap- propriate to formulate and test hypothe- ses. This paper then is data-descriptive and will focus on the discovery of pat- terns. Many studies have been published on patterns of journal use, but few on pat- terns of book use. In recent years, these journal studies have employed citation data to examine the extent to which one or a group of authors is cited, or one or a group of journals is cited. Most of this re- search was intended to identify the most highly cited authors or journals, those with the highest impact factor and so on. Some of that research has employed novel ways to uncover patterns, notably the work of Henry Small and Belver Griffith in which they employed co-citation data; that is, the number of times two authors or two papers were cited together to map clusters of authors within a discipline or an invisible college.3 Their work and that of others has done much to discover inter- nal structure of disciplines and subdisci- plines and, to some extent, to identify new disciplines. But little work has been done on the interrelationships among many disciplines from the broad-based organi- zation of a university. Furthermore, little work has been done on the cross- disciplinary use of books as opposed to journals. Yet the largest percentage of use, perhaps as high as 70 percent to 80 percent in some libraries, is with books rather than journals. This is because students consti- tute the largest population of book users in a university library. Both undergradu- ates and graduates make heavy use of the book collection, and in most universities undergraduates far outnumber gradu- ates. To contrast, co-citation analysis exam- ines dynamic patterns of interdisciplinary and cross-disciplinary research, whereas cross-disciplinary book use analysis exam- ines the existing patterns of interdiscipli- nary content. A simpler way of saying this is that journals point to where disciplines are going, whereas books describe where disciplines are. Accordingly, this study describes cross-disciplinary patterns at one point at one university as revealed by student book circulation. METHOD Two interesting data-descriptive tech- niques are multidimensional scaling anal- ysis (MDS) and cluster analysis. They are used to reduce large numbers of combina- tions and permutations to something more comprehensible and to discover hid- den patterns of the data. MDS, developed in recent years to a high state of sophistica- tion by Torgerson/ Kruskal and Wish, 5 Shepard and ·others, 6 Schiffman, Rey- nolds, and Young/ et al., is used to map distances computed from similarities data between objects in space in as many as six dimensions. The objects are located in space by their Cartesian coordinates among the various dimensions. The map will also show any tendency of objects to cluster. Other tech- niques, such as tree-fitting and hierarchi- cal clustering, can be used to confirm or en- hance any clusters found in the MDS configuration. 8 Both clusters and dimen- Multidimensional Mapping 105 sions have meaning and can be submitted to hypothesis testing for explanation. Multidimensional scaling is sometimes described as a technique in which the stat- istician is able to regenerate a map show- ing distances between cities or points while knowing only the mileages between every pair, as in the table of miles in a road atlas. Likewise, a map can be generated whatever the data. In an interesting and innovative paper, Anthony Biglan gener- ated a three-dimensional map from fac- ulty perception of similarities between every pair of academic departments at the University of Illinois. 9 This paper, on the other hand, tabulates similarities between departments using the number of books charged out in each discipline by the stu- dents in every other discipline. (See table 1.) The method of data collection is de- scribed in the paper cited above. 10 The data are arrayed in two asymmetric matri- ces, one 40 x 40 for undergraduates, and one 40 x 17 for graduate students. "Asymmetric" means that data above the diagonal are not the same as data below the diagonal, representing two measures of similarity between each pair of disci- plines. In order to obtain a symmetric rna- TABLE 1 NAMES OF USL DEPARTMENTS AND ABBREVIATIONS Department Abbrevia tion Department Abbreviation Accounting ACCT Horticulture HORT Agriculture AGRI Industrial & Vocational Education INDVOC Ap~ied Art APPLART Journalism JOUR Arc itecture ARCH Management MGMT Biology BIOL Marketing MARK Chem1cal Engineering CHEMENG Mathematics MATH Chemistry CHEM Mechanical Entneering ME CHENG Civil Engmeering CIVENG Medical Recor s MEDREC Computer Science COMPSCI Microbiology MICROB Economics ECON Music MUSIC Education EDUC Nursing and Health NUHLTH Electrical Engineering ELENG Petroleum Engineering PETROLENG English ENGL Philosophy PHILOS Finance FINAN Phtsics PHYSICS Fine Arts FIN ART Po itical Science POL SCI French & German FRENGER Psychology PSYCH General Business GENBUS Sociology SOCIOL Geo~aphy GEOG Spanish SPAN Geo ogy GEOL Special Education SPECED History HIST Speech SPEECH rfome Economics HOMEC *Graduate circulation only. 106 College & Research Libraries trix, necessary for the MDS computations to take place, the two measures for under- graduate circulation were averaged. For example, psychology majors .charged out fifty-four biology books, while biology majors charged out eighteen psychology books; hence the average circulation simi- larity between psychology and biology is thirty-six. This similarity has meaning, of course, only in relation to the similarities between every other pair. (By convention, when large numbers are taken to mean more similarity, they are called "similari- ties"; otherwise they are "dissimilari- ties," as in mileages.) In these data, the number of books charged ranged from 0 to 2,629. To obtain a symmetric matrix for gradu- ate circulation, every possible pair of ma- jors was correlated. Thus, the input matrix contained correlation coefficients. From these two new m?trices, one undergradu- ate, one graduate, the MDS program then computed "distances" between every pair of disciplines. The program used in this study is called ALSCAL and was writ- ten by Young and Lewyckyj. 11 It is avail- able as a package. The Cartesian coordi- nates obtained from ALSCAL were later used as input data to a cluster analysis program in the BMDP. Biomedical Com- puter Programs package. 12 In MDS programs, Pythagorean dis- tances are computed in any number of di- mensions from one to six, specified by the program user. The several solutions are printed out in two-dimensional configura- tions. More than four dimensions are rarely needed to explain the data and can- not be visualized in a single configuration. (A three-dimensional solution requires three two-dimensional displays, a four re- quires six, a five requires ten, and a six re- quires fifteen.) March 1983 The "goodness" or "badness" of each solution is evaluated either by the familiar R 2 or a statistic called STRESS. These two ~tatistics are approximate!~ but inversely equivalent; the larger the R2 (up to 1.0), or the smaller the STRESS (down to 0.0), the better. RESULTS AND INTERPRETATION Preliminary results of this study were reported in another paper by this author in which it was suggested that the Carte- sian coordinates of the dimensional solu- tions might be used as quantitative de- scriptors to augment subject headings in an online database or for approval plans with book vendors .13 The data used in that paper have been more extensively ana- lyzed here. Table 2 gives the values for STRESS in three solutions for undergrad- uate circulation and four for graduate cir- culation. STRESS values for undergraduate circu- lation show steady improvement from two to four dimensions. Improvement drops off sharply from three to four di- mensions, indicating that four dimen- sions do not provide enough improve- ment to warrant interpretation and probably contain much statistical error or noise. Clusters A one-dimensional solution for under- graduates was not obtained. For a large number of objects, inadequacy of the one- dimensional solution can be demon- strated by analogy with a map of the United States.lt is not incorrect to say that one must travel 900 miles west to go from Boston to New Orleans. One does indeed travel that many miles westward. But one also travels 900 miles southward. Two TABLE 2 Dimensional Solution Four Three Two One STRESS FOR MULTIDIMENSIONAL SOLUTIONS FOR UNQERGRADUATE AND GRADUATE CIRCULATION Undergraduate STRESS STRESS Improvement STRESS 0.188 ~ 0.038 0.077f 0.226 f 0.121 0.327 0.101 0.182 Not Computed o:416 Graduate STRESS Improvement ! I 0.044 0.061 0.234 pieces of information, west and south, are needed to show that the best course is along the hypotenuse. Likewise, dis- tances can sometimes be better explained in three dimensions. A trip to Denver, for example, requires traveling one mile verti- cally, the third dimension in geography. The two-dimensional solution for un- dergraduate circulation has considerable pattern, though not entirely satisfactory (see figure 1). Three fairly dense, homoge- neous, and well-separated clusters can be seen: a business cluster, an engineering clus- ter, and a mathematics/physics ~luster, with an English/sociology/history cluster in the center. The remaining disciplines are more diffuse, and except for several close proximities, the clustering is less appar- ent. Some anomalies are apparent: jour- nalism and microbiology appear in the math/physics cluster, for example, and bi- ology appears with music and philoso- phy. The three-dimensional solution is more satisfactory. The presence of journalism near electrical engineering and other sci- Multidimensional Mapping 107 ence disciplines (see figures 1 and 2) can be explained by viewing the configuration from another perspective, Dimensions I and III in figure 3, in which journalism now appears with philosophy, music, and others. And in figure 4, journalism ap- pears somewhat off by itself. None of the two-dimensional figures display the clus- ters in a thoroughly satisfactory way. Fig- ure 2 perhaps best displays their homoge- neity, while figures 3 and 4 show them to overlap. Clusters would be best per- ceived, of course, in a single three- dimensional display. Labeling of the clusters was helped by the tree diagram shown in figure 5. The di- agram, of all forty disciplines, was ob- tained from the BMDP Biomedical Com- puter Programs cluster analysis using the Cartesian coordinates of the MDS three- dimensional solution as input data. The tree diagram enhances our comprehen- sion of the clusters by positioning pairs of similar disciplines, subclusters, and larger clusters adjacent to each other. The degree of similarity is indicated by the length of Dim . II Soft 2.0 tO O.O Dim.! -to -2.0 .speced Frenger • Applart Q Medrec Speech Finarte Arche Hart •lndvac Geag • • Agri •Civeng -2.0 -1.0 Ma~th Physic • • Eleng • • Compsci ~crob Jour Dim.II Hard 0.0 FIGURE 1 • Educ tO th 2.0 Two-Dimensional Map of Undergraduate Circulation, with Tentative Clusters Dim .! 108 College & Research Libraries March 1983 Dim. II 2.0 1.0 O.O Dim.! -1.0 Quantitative Cluster -2 .0 Dim . .II -2 .0 -1.0 0.0 FIGURE2 Chemeng Engineering Cluster 1.0 Ar~v~ng .~Geol Geog Earth Sciences 2.0 Dimensions I and II of Three-Dimensional Undergraduate Circulation, with Improved Clusters Dim . m Soft 2.0 Arch •Eng I D' I Bioi :Hist •Hort Dim. I 0.0~l~m~·~--~~~~L-~~------+-•A-g-ri------~~~~~~----~ -~ .0 -2 .0 -2.0 -to tO 2.0 FIGURE 3 Dimensions I and III of Three-Dimensional Undergraduate Circulation, with Overlapping Clusters Multidimensional Mapping 109 Dim.IIT Soft 2.0 1.0 O.O Dim . .II Dim.m Hard -2.0 -1.0 0.0 tO 2.0 FIGURE 4 Dimensions II and III of Three-Dimensional Map of Undergraduate Circulation, Showing Cluster Overlap from Another Perspective Distance 2 .2 I I I I I I I I I I I I I I I ~~g~~~6~ 5u~~~~~ ~§8g~~~~ ~~~~~~~ ~~~u~~~u ~xoo~~~u Engineering and Chemistry and Earth Sciences Life Sciences I I I I I I I I I I I I I I I I I I I I I I I I ~ ~~~~~ 8~~5~~~~~ g~~~g~~~ ~~~~~~~ w~uwuuQ~z ~ux ~~ooo ~~~~~~j §~§~~~g~§ sd~~~~~~ Humanities Social Quant itative Services FIGURE 5 Tree Diagram of Departmental Clusters Derived from Cluster Analysis of Three-DimensiOnal Coordinates of Undergraduate Circulation 110 College & Research Libraries the branches and trunks (vertical lines) of each cluster. The diagram is binary in that it joins pairs of departments or pairs of clusters. The diagram starts with the two most similar departments, sociology and psychology. It then joins this pair to an- other pair, economics and marketing, and so on at each level until they are merged into a large pair-wise cluster, and this clus- ter in turn is joined with another to form a still larger one. Note, for example, that nursing and home economics are adjacent to education and are contained in the larger cluster with economics, marketing, sociology, and psychology-that is, social sciences, whereas history, normally categorized as a social science, is grouped with liberal arts departments. These apparent anoma- lies can be explained by recalling that the similarities are based on the average of "use by" and "use of." Thus, though nursing students used many more home economics books than home economics students used nursing books, they are treated in this analysis as if they were used equally. Also, a great many home eco- nomics books were used by other depart- ments in the cluster. Although some im- provement of the clustering might be obtained by distinguishing between ''use by" and "use of" and by going to four di- mensions perhaps, we should remember that we are dealing with empirical data and that the results may bring some sur- prises. Thus, these results suggest that nursing and home economics, at USL, could be classified with the social sciences in a larger cluster which can be called the social services cluster, and that history should be regarded as a humanities disci- pline. A summary of the clusters appears in figure 6. These clusters are not unlike those found by Allan, who counted Dewey deci- mal classification numbers shared by pairs of academic departments at a midwestern university, then used a critical probabili- ties method to measure their similarity .14 Though the correspondence between the author's study and that of Allan's is not exact, the results suggest that similar clus- ters would be found from one university to another. It would be interesting to ex- March 1983 plore how and in what context this gener- alization would take place. Circulation by graduate students in nineteen major areas is shown in a consid- erably less complex two-dimensional so- lution in figure 7. STRESS values for grad- uate circulation (see table 2) show considerable improvement from one to two dimensions and little improvement from two to three, indicating that two di- mensions are quite enough for this num- ber of disciplines. Five simple and intui- tively acceptable clusters are apparent: chemistry I microbiology /biology, mathe- matics/computer science, geography/ge- ology, psychology/political science, and English/ speech/history. The simplicity of these clusters and their homogeneity re- flect a sharper focus by graduate students on their major, a conclusion also sup- ported in the paper on ethnocentricity and supportiveness. 15 The configuration should be interpreted as circulation by majors in subject space, slightly different than the interpretation for undergraduate circulation, which entails use of each oth- er's materials by any pair of majors. Dimensions Just as important as clusters in the anal- ysis of the multidimensional configura- tions is the interpretation of the dimen- sions themselves. Biglan labeled his three dimensions hard/soft, pure/applied, and life/ nonlife. That is, disciplines at one end of one of his dimensions can be considered ''hard,'' while those at the other end can be regarded as ''soft,'' and so on for pure/ applied and life/nonlife. I obtained mea- sures of these dimensions in an earlier study through a survey of faculty at USL using an entirely different method. 16 Those measures correlated quite well with Biglan's, but somewhat less well with those in this study (see table 3). However, there is one dimension in each of two-, three-, and four-dimensional solutions, that agrees fairly well with the hard/soft variable of the earlier USL faculty survey, with correlations of -0.61, 0.72, and 0.44, respectively. (The negative sign is mean- ingless since it is an arbitrary orientation of the plot.) On the other hand, there are 1. Quantitative Cluster Business l Accounting General Business Management Political Science Finance Mathe- { Mathematics matics Electrical Engineering Computer Science 4. Chemistry and Life Science Cluster Chemistry Microbiology Medical Records Multidimensional Mapping 111 2. Social Services Cluster l Social Economics Sciences Marketing Sociology Psychology Education Special Education Services 3. Humanities Cluster Speech Education Nursing Home Economics French/German Journalism English Industrial Vocational Education Biology History Fine Arts Horticulture Agriculture Music Philosophy Applied Arts 5. Engineering and Earth Sciences Engineer-l Chemical Engineering ing Petroleum Engineering Mechanical Engineering Physics Earth Sciences Geology l Civil Engineering Geography Architecture FIGURE 6 Clusters of Academic Departments Derived from a Cluster Analysis of the Three-Dimensional Coordinates of Undergraduate Circulation no substantial correlations between Biglan's pure/applied nor the earlier USL pure/applied and any of the several dimen- sions in this study-the highest (0.44) is with Dimension I of the four-dimensional solution. There are also no substantial cor- relations with Biglan' s life/nonlife variable. Since both the earlier USL and Biglan surveys were based on perceptions of fac- ulty, neither are empirically based on solid behavioral data, though some significant correlations with behavioral variables have been found. One attempt to validate Biglan' s dimensions, by Muffo and Lang- ston, found significant differences in fac- ulty salaries according to hard/soft, pure/ap- plied, and life/nonlife categories. 1 Biglan himself found significant correlations be- tween his dimensions and scholarly out- put.18 This author found low but signifi- cant correlations between the hard/soft variable from the earlier USL survey and circulation, and between the pure/applied variable and student enrollment. No sig- nificant correlations were found between life/nonlife and other variables in either the Biglan O! USL studies. David A. Kolb, examining data from a learning style inventory associated with the undergraduate majors of 800 man- agers, found strong similarities between Biglan' s hard/soft and pure/applied dimen- sions and what he called abstract/concrete and rejjective/active dimensions, respec- tively. 9 He further supported this associa- tion in an examination of extensive data from a 1969 Carnegie Commission of Higher Education study. The literature of vocational interest also contains studies on the similarities of oc- cupations. Robinson and others, for ex- ample, using smallest space analysis, a 112 College & Research Libraries March 1983 Dim. II 2.0 Pure? 0 0 Soft · Dim.! -2.0 Homec • -1.0 Dim. IT Applied? 0.0 OGeog Geol tO Hard Compsci Dim. I eMgmt 2.0 FIGURE 7 Two-Dimensional Map of Circulation by Graduate Majors technique related to multidimensional scaling, found two strong dimensions in several inventories of occupational simi- larity, the strongest of which was object ori- ented versus people oriented occupations. The other was doer versus thinker occupa- tions, which included commercial/business versus scientific components, possibly in a third dimension. They contended, how- ever, that two dimensions were sufficient to explain t.he bulk of variance. 20 The dimensions derived in this study, being empirically based, deserve to be in- terpreted or explained for what they are- not whether they are something else. One of these dimensions, on the basis of corre- lations discussed above, could be called hard/soft, but only if whatever it is that is ''hard'' or'' soft'' is measured with behav- ioral data, as it is in this study. The other two dimensions, though firmly implanted in the data, require further analysis. Any number of hypotheses could be generated to explain the dimensions, whether they are founded in the literature of learning theory, vocational interest, in- formation science, sociology of science, or library science, but the most immediate explanations in the context of this study would be found in the curriculum-in terms of undergraduate course require- ments, and in highly focused majors and electives for graduate students. Whether or not these dimensions are identified or otherwise explained, and even if they are no more descriptively identified as Dimensions I, II, or III, they should be useful in many ways- particularly if they agree with dimensions found in similar data from other institu- tions or in a larger database. IMPLICATIONS FOR COLLECTION DEVELOPMENT AND STORAGE Area Bibliographers Ideally, each academic department should have a librarian, expert in that de- partment's subject matter, who would be responsible for collection development. Unfortunately, no library has enough li- Multidimensional Mapping 113 TABLE 3 CORRELATIONS* BETWEEN BIGLAN'S DIMENSIONS USL CIRCULATION AND USL FACULTY SURVEY DIMENSIONS USL Faculty Survey USL Undergrad Circulation USLGrad Circulation+ H/S PIA LINL 2 I II 3 I II III 4 I II III N I II HIS -0.78 + + 0.45 0.66 0.60 -0.16 0.64 0.74 0.40 Biglan's Dimensions PIA + 0.78 + -0.17 0.14 0.08 -0.04 -0.02 not obtained -0.08 0.31 LINL + + 0.86 -0.09 0.53 -0.26 0.57 0.53 -0.06 0.10 USL Faculty Survey HIS PIA -0.24 -0.61 0.39 0.03 -0.72 0.32 -0.09 0.62 0.44 0.17 -0.23 -0.21 -0.07 0.12 0.44 0.04 0.06 -0.17 not obtained *Pearson product moment correlations, except as noted, N = 20 . tSpearman rank order correlations, N = 11 . :j:Not obtained . brarians for such one-to-one assignments. On the other hand, assignment of librari- ans to areas such as Asian studies, Slavic studies, and the like, may be equally prob- lematic, because they may cover a broad range of unrelated subjects for which the bibliographer may be not as familiar. Fur- thermore, these "areas" may not corre- spond at all with real use patterns of the collection. An alternative to these two ap- proaches would be to assign bibliogra- phers to departmental clusters based on circulation, such as those found in this study. Then, every cluster or subcluster could be covered to a hierarchical depth according to the number of bibliographers available. Thus, the "quantitative" clus- ter could be treated as one cluster with one bibliographer, or as two at the next level deeper with two bibliographers. Allocation A major concern of collection develop- ment librarians is that allocation to depart- ments may result in too small a budget for some departments and too large a budget for others. Faculty also voice this concern if they feel their allotment does not permit them to request books outside of their own narrowly defined areas. Knowledge of clusters would permit more flexible al- location. Each cluster would receive anal- location with further allocation to sub- clusters if desired. The denser the cluster-i.e., the more similar each depart- ment in the cluster and the further away the cluster is from others, the less critical the suballocation, since whatever books were purchased on a subject within the cluster would have a higher probability of being used by students majoring in any subject within the cluster. But depart- ments that are not obviously part of a clus- ter should receive an allocation indepen- dent of others, because their purchases are less likely to be used by others . If a de- partment is equidistant from all others- i.e., in the center, such as English and his- tory in this study-then the books they purchase have a high probability of being used by students in many departments. Indeed the data show this to be so, and thus they should also receive larger alloca- tions. Organization of Materials Storage of the collection according to cir- culation clusters would be a logical alter- native to the existing practice of storage in departmental, branch, or divisional li- braries based on campus geography or on the traditional divisions of humanities, science/technology, and social sciences. Books on ed:ucation and physics may be 114 College & Research Libraries housed together for no better reason than that the education and physics depart- ments happen to be in the same building. On the other hand, students in the social sciences are as likely to find many of their books in the humanities division as they are in the social sciences division. Psychol- ogy books are stored with philosophy books only because their classification numbers are adjacent in the classification scheme. The divisional arrangement has never been shown to be more effective than single sequence collections, and some libraries have abandoned efforts to maintain them. On the other extreme, separate libraries for every department might be considered ideal by faculty, but are far too costly and inefficient. If a library is forced to break up its collection and if it can afford to do so, then storage of collec- tions according to circulation clusters such as those found in this study would make sense and is worth considering. Such "cluster collections" may be more practi- cal, convenient, and satisfying to faculty and students who complain that "my books are scattered all over the library, and all over the campus, and why can't you librarians bring them together all in one place?" Surely this is a compromis- able problem. Online Retrieval Circulation dimensions found in this study could be used to augment retrieval in an online catalog. Traditional author, ti- tle, subject heading, and call number re- trieval is limited in that they are undimen- sional. Each are capable of describing only one thing about a book. They can not de- scribe other characteristics. To be sure, Boolean logic allows combinations and ex- clusions of authors, headings, and so on, but still the approach is limited to these traditional tags. As3uming that the circulation dimen- sions were valid and generalizable, their Cartesian coordinates could be used as an- other way to describe books in the collec- tion. This could be done in the cataloging process by assigning coordinates to each book in much the same manner as classifi- cation numbers are assigned. A book in March 1983 computer science might have, say, coordi- nates of 0.4 and -1.5 for Dimensions I and II, respectively. If it were understood that these dimensions were pure/applied and hard/soft, then these coordinates would re- trieve a "hard" and somewhat "applied" book. In the paper cited above, the author suggested that these dimensions could be used to identify books desired through ap- proval plans, but the question of how books could be assigned coordinates and who would do so is problematic. 21 Also, individual books would not necessarily have the same coordinates as their general subject. That is, one computer science book may be "hard" and "pure" while another may be "soft" and "applied." This would seem to require that further multidimensional analysis be done on each cluster to determine more refined co- ordinates for each subject within a cluster. CONCLUSION . Multidimensional mapping and cluster analysis of circulation provides the ability to sort out the complex overlapping inter- disciplinary and cross-disciplinary rela- tionships among the academic depart- ments served by the library. The insights gained offer the librarian several new ways in which to enhance library service, and to treat academic departments with more flexibility. The discovered dimen- sions may provide new theoretical per- spective on those relationships. Applica- tions would include assignments in area bibliography, allocation to clusters of de- partments, organization and storage of the collection, and perhaps in online re- trieval. FURTHER RESEARCH Clusters and dimensions could be im- proved by separating data for freshmen and sophomores, who have not yet con- centrated on their major, from juniors and seniors. The distinction between ''use by" and "use of" should be further ex- plored and separately submitted to MDS and cluster analysis . The dimensions need to be explained by hypothesizing correla- tions with other likely variables. An at- tempt should be made to verify and, if possible, generalize the clusters and di- mensions discussed here by examining Multidimensional Mapping 115 circulation or other data at other institu- tions and particularly in a large online util- ity serving many institutions. REFERENCES 1. Donald T. Campbell, "Ethnocentrism of Disciplines and the Fish-Scale Model of Omniscience," in Muzafer Sherif and Carolyn W . Sherif, eds., Interdisciplinary Relationships in the Social Sciences (Chicago: Aldine, 1969), p .328-48. 2. William E. McGrath, Donald J. Simon, and Evelyn Bullard, "Ethnocentricity and Cross- Disciplinary Circulation," College & Research Libraries 40:511-18 (Nov. 1979). 3. Henry G . Small and Belver C. Griffith, "The Structure of Scientific Literature, 1: Identifying and Graphing Specialties," Science Studies 4:17-40 (1974). 4. W . S. Torgerson, Theory and Method of Scaling (New York: Wiley, 1958) . 5. Joseph Kruskal and Myron Wish, Multidimensional Scaling (Beverly Hills, Calif.: Sage Publications, 1978). 6. Roger N. Shepard, A. K. Romney, and S. N erlove, eds ., Multidimensional Scaling: Theory and Appli- cations in the Behavioral Sciences (New York: Seminar Press, 1972) . 2v . 7. Susan S. Schiffman, M. Lance Reynolds, and Forrest W . Young, Introduction to Multidimensional Scaling: Thoery, Methods, and Applications (New York: Academic Pr., 1981). 8. Roger N. Shepard, "Multidimensional Scaling, Tree-fitting, and Clustering," Science 210:290-398 (Oct. 1980). 9. Anthony Biglan, ''The Characteristics of Subject Matter in Different Academic Areas,'' Journal of Applied Psychology 57:195-203. 10. McGrath and others, "Ethnocentricity." 11. Forrest W. 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