(1979). Social Networks and Psychology. Connections, 2 - INSNA

More documents

Recommendations

Info

- 1 0 8 -Clearly, in order to find such a minimal distance matrix min at least one of whose elements is lessthan the corresponding element in d, it will be necessary to have some choice of routes, i .e ., we musthave two or more informants . The method used to find min is given by Acton (1970) .We do not place too much reliance on min as representing any structure of interest to networkers .Instead, we define a category matrix cat ., which we claim represents the cognitive network from the viewpointof each informant . 13We obtain this as follows : in the course of obtaining min, several possible routes from i to j willhave been selected . In general there may be more than one such minimal route ; if a choice still exists wechoose the route needing fewest intermediaries . Then we define catij to be one more than the number ofintermediaries used to proceed from i to j . In other words, if i perceives direct interaction with j,defined here min-- = dij, then catij = 1 . If, however, mini] is such that i-7 k-aj then catij = 2, and soon . We can see the meaning of the category matrix diagrammatically (Figure 1) .FIGURE 1 . Diagrammatic description of category matrix : catii = 0 ; cat ij = cat ik = catie = 1 ;catim = . . . .= cat ir = 2 .The element catij is the number of the row in the network which i places j upon . Increasing the rownumber implies a more complicated interaction pattern, or that j is "not so easy to communicate withdirectly ."We claim that it is precisely the number of this row which represents the reality of the social network,rather than the route used to get there . This is especially true of the second row : in Fig . 1 wehave drawn 14 ja p ; i_-?k--Pp . Now both routes place p in the second row, and we appear to have overlappingpossibilities for the actual interaction route . This does not matter ; in fact, in physical structuredgroups there is often more than a 2 to 1 overlap ratio in the second row . In other words, on average, thetotal number of elements in the first rows of each of i's first row is usually 2 or more times the numberof distinct elements, implying a great deal of overlapping as described . It is tempting to hypothesizethat such overlap is essential to the healthy functioning of groups .We hypothesize that each informant knows, and understands the structure of his own first row (i .e .,he "knows who he knows"), and has a very good (70%) knowledge of his second row (a subset of his firstrow's first row) . This knowledge deteriorates as we descend the rows, as would be anticipated : clearlyan informant will have little or no knowledge of the interaction structure of a subset of the group withwhom he has little interaction . However, he will have sufficient knowledge to know how that little interactiontakes place, and who among his first or second rows is necessary to this interaction .We must stress the important fact that a position in a given row is a measure not of amount ofperceived interaction, but the degree of directness of such interaction .After the catij matrix is derived, we factor it, using the varimax rotation, by rows . Experimentationshowed that the varimax rotation gives the most intuitively useful results . Stingily, people with at leasta 0 .6 factor loading are chosen for inclusion in a "group ." CATIJ Row 1 links are then used to show theties between groups (and their members with all other groups and their members) . "Groups" are defined aspeople who have similar views on their relationship to the universe . This may result because of cliqueingor not, and in general ethnographic evidence must be relied upon to decide the meaning of factors and groupmembership .In two publications (Bernard and Killworth, 1973 ; Killworth and Bernard, 1974b) we have tested thevalidity of the CATIJ technique . We found that CATIJ filters out random error in dij (i .e ., that the CATIJmatrix is reasonably stable to perturbations in the original data) . (Of course, the errors in raw sociometricdata are probably not random . So far, we have no way to deal with this .) Furthermore, we havefound that factoring the CATIJ matrix produces excellent results, while factoring a sociogram producesvery poor results (i .e ., low connectivity even within subgroups) . Factoring CATIJ has turned up subgroupingswhich were not discerned by standard sociometric tests . In one memorable case, we had analyzed aprison living unit and found a totally unintuitive factor group of 3 inmates who had no apparent sociallinks . This bothered us until we learned, a week later, that the three had attempted an escape together .
-109-We have compared the connectivity of entire populations (sociometric "universes") using both CATIJand limited choice sociograms . By the time we got to seven unreciprocated choices, the links in the sociogramapproached the complexity of our own diagrams produced by CATIJ . In fact, in one test there were morelinks in the unreciprocated 7-choice sociogram than in the CATIJ row 1 matrix . 16% of the CATIJ row 1links were missed, however, by the sociogram . These links were the ones which formed vital between-grouplinks (Killworth and Bernard, 1974b) . (See Granovetter, 1973 for a discussion of the importance of weakties in the structuring of groups .)Software for CATIJThe KBPAK is available from the authors . It is written in FORTRAN IV, and runs nicely on IBM equipment. There are four programs . ZERO checks for "illegal" entries, repeated entries, and, when 100% ofa group has given data, that everyone has been mentioned by each informant once and only once . Errors areprinted out so the data may be cleaned .Program ONE produces the CATIJ matrix, and prints dij, mini J•, and catij, mutual connections (i .e .,those persons who have mutual CATIJ row 1 connections), all row 1 connections, and the number of CATIJentries produced by dij entries . This last bit of data is peculiar . It specifies how many dij rankingswere required in order to produce the complete CATIJ matrix . We continue to produce this table because wehave no formula to determine the minimal number of rankings required to produce a CATIJ on a given sizedata set . Users are requested to send us this bit of data . Program ONE also punches a CATIJ deck . Intape version, a CATIJ deck pops out automatically, but may be suppressed .Program FIVE uses the CATIJ deck and produces general statistics on the CATIJ matrix . It shows howmany row 1 connections people have to and from others, and computes the mean, etc .Program TEN computes and prints the correlation matrix of CATIJ . The matrix if factored by rows,rather than by the usual columns (see Killworth and Bernard, 1974a for reasons for this procedure) .Program TEN prints out the correlation matrix, the eigenvalues and factor matrix, the suggested subgroups(using the stingy 0 .6 criterion), and a variety of other data concerning between-group-links, and so forth .Details of the output are in our users' manual (Killworth and Bernard, 1975) for CATIJ . A bank of morethan 100 data sets, collected for analysis by the CATIJ technique is also available (see Bernard, Killworth,and Kuznicki, 1975) .ReferencesActon, Forman, 1970 . Numerical Methods that Work . New York : Harper and Row .Bernard, H . Russell, and Peter D . Killworth . 1973 ."On the Social Structure of an Ocean Going Vessel andOther Important Things" Social Science Research 2(2) :145-84 .Bernard, H . Russell, and Peter D . Killworth . 1975 . "On the Structure of Affective and Effective SociometricRelations in a Closed Group Over Time ." Technical Report 4#BK-107-75 . Office of Naval Research,Code 452, Arlington, Virginia .Bernard, H . Russell, and Peter D . Killworth . 1977 . "Informant Accuracy in Social Network Data II ." HumanCommunication Research . 4(1) : 3-18 .Bernard, H . Russell, Peter D . Killworth, and Richard Kuznicki . 1975 . "KBDATA : A Bank of Effective SociometricData Sets ." Technical Report #BK-109-75 . Office of Naval Research, Code 452, Arlington,Virginia .Bernard, H . Russell, Peter D . Killworth, and Lee Sailer . 1978 . "Informant Accuracy in Social Network DataIV ." Technical Report #BK-116-78 . Office of Naval Research, Code 452, Arlington, Virginia .Granovetter, M .S . 1973 . "The Strength of Weak Ties ." American Journal of Sociology 79 :1360-80 .Killworth, Peter D ., and H . Russell Bernard . 1974a . "CATIJ : A New Sociometric and Its Application to aPrison Living Unit : Human Organization 33(4) :335-50 .Killworth, Peter D ., and H . Russell Bernard . 1974b "The CATIJ Technique : Some Descriptive Tests of ItsAdequacy ." Technical Report #BK-104-74 . Office of Naval Research, Code 452, Arlington, Virginia .Killworth, Peter D ., and H . Russell Bernard . 1975 "How to Use the KBPAK ." Technical Report #BK-106-75 .Office of Naval Research, Code 452, Arlington, Virginia .Killworth, Peter D ., and H . Russell Bernard . 1976 "Informant Accuracy in Social Network Data ." HumanOrganization 35(3) :269-86 .Killworth, Peter D ., and H . Russell Bernard, 1978 "Informant Accuracy in Social Network Data III ."Journal of Social Networks, in press .
Page 1 and 2: The International Network for Socia
Page 3 and 4: NETWORK NOTEBOOKTheEditors'Request
Page 5 and 6: - 63 -ditions of stagflationary cri
Page 7 and 8: Michael Pearlman . 1977a . "Great B
Page 9 and 10: - 67 -MIGRATION AND SETTLEMENT . (S
Page 11 and 12: -69-PAPERSRUDIMENTARY NETWORKS AMON
Page 13 and 14: provided the following improved spe
Page 15 and 16: - 73 -analysis and differentiates h
Page 17 and 18: - 75 -normally been intentionally e
Page 19 and 20: - 77 -classes" which are "in betwee
Page 21 and 22: - 79 -charisma . As a consequence,
Page 23 and 24: - 81 -URBAN SOCIOLOGY IN BRITAIN AN
Page 25 and 26: - 83 -Footnotes1 . Michael Harloe (
Page 27: - 85 -help make sense of interlocki
Page 30 and 31: - 88 -I have been illustrative rath
Page 32 and 33: - 9 0 -The only trouble with that c
Page 34 and 35: - 9 2 -RESEARCH REPORTSDATA OF MICR
Page 36 and 37: staff--two of whom are native Miski
Page 38 and 39: - 9 6 -SI'EQAL JOURNAL ISSUESAbstra
Page 40 and 41: - 98 -fits in a given industry of f
Page 42 and 43: - 100 -THESIS SUMMARIESTHE CONTENT
Page 44 and 45: - 1 0 2 -Since the theory postulate
Page 46 and 47: - 1 0 4 -financial dependence, inte
Page 48 and 49: - 1 0 6 -John Foster, 1974 . Class
Page 52 and 53: ANU-MACRONET2 . A PROGRAM FOR COMPU
Page 54 and 55: ABSTRACTSABRAMS, Philip (Sociology,
Page 56 and 57: This analysis is based upon Franco
Page 58 and 59: on the fact that they and those who
Page 60 and 61: NEWBY, Howard (Sociology, Essex) "U
Page 62 and 63: - 120 -SMITH, Christopher J . (Okla

(1979). Social Networks and Psychology. Connections, 2 - INSNA

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?