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We are faced with a dilemma then. Are we to believe the data presented in Figure
~ or those presented in Figure 2? Homans (1950) was the first to use these data in a
secondary analysis. He reported additional details that suggest that he was probably in
touch with the original research team. And in his report he used the data as they are
displayed in Figure I.
Moreover, there is additional ancillary evidence for the correctness of the data as
presented in Figure I. It tutus out that there is a contradiction in the presentation of
Figure 2 that makes it difficult to accept the data presented there as correct. Compare, for
example, the participation patterns displayed by the two women designated with red
arrows in Figure 2: woman ~ ~ and woman ~ 6. According to Figure 2, these two women
displayed identical patterns of participation. Yet, in that figure, woman ~ ~ was classified
as a primal member of her "clique'. while woman 16 was called secondary. This
contradiction implies that the correct data are those shown in Figure i.
T~ Or
s~s=P
cow:
Ape.... i..
polyp ~ -
~-
~ry. . .
Go- ~ ~ ~ ~ ~
Body.
al
13
4
l IS
tS
L7
8
By
10
11
12
13
t~
IS
t.
(~7
1
~~ ~ PI
1 2 3 4 5 ~ 7 8 4 10 11 ~ 13 ~
C C ~ C - ~ C
~ ~ C - ~ ~ C C -
- C C ~ ~ ~ C C C
C - ~ C C C ~ C -
p, p ~ _ p _ _
p _ p p _ p _
~ P ~ p _
- S - S S
S - S S &
S S ~ - - ~
P P p _ ~ At.
P P P - P P P
C ~ C ~ - ~ C
C - ~ ~ C ~ C ~
- ~ ~ C lO.-CI
S S
$
S
-
_
[S - S! q~
_
_
. _
Figure 2. Participation of the Southern Women in Events
Most analysts have apparently reached this conclusion. Most have used the data
as shown in Figure I. A few, however, have analyzed the data as presented in Figure 9.
and this produces a problem for any attempt to compare the results of one analysis with
those of another. When the two analyses are based on the use of different data sets
comparisons are, of course, not possible.
DYNAMIC SOCIAL NETWORK MODEM AND ISIS
43
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~ have assumed that the "correct" data are those shown in Figure I. For the
relatively small number of results that have been produced by analyses of the data of
Figure 2, I: have asked the original analysts to redo their analyses using the Figure ~ data
or ~ have redone them myself.
4. Finding Groups and Positions in the DOG Data
4.l Davis, Gardner and Gardner's Intuition-Based Groups (DGG41)
In their own analysis Davis Gardner and Gardner did not use any systematic
analytic procedures. They relied entirely on their general ethnographic knowledge of the
community and their intuitive grasp of the patterning in Table ~ to make sense of the data.
As Davis and Warner (1939) descnbed it, they drew on ". . . records of overt behavior
and verbalizations, which cover more than five thousand pages, statistical data on both
rural and urban societies, as well as newspaper records of social gatherings . . ."
DOG drew on all this material and used it both to assign the women to groups and
to determine individuals' positions within groups. They indicated that the eighteen
women were divided into two overlapping groups. They assigned women 1 through 9 to
one group and women 9 through IS to another. They assigned three levels in terms of
core~penphery participation in these groups. They defined women ~ through 4 and 13
through 15 as core members of their respective groups. Women 5 through 7 and ~ ~ and
12 they called primary. Women ~ and 9 on one hand and 9, 10, ~6, 17 and ~~ on the
other were secondary. Note that woman 9 was specified as a secondary member of both
groups because, they said, "in interviews" she was "claimed by both" (DOG. p. ~ 5 ~ ).
4.2 Homans' Intuition-Based Analysis (HOM50)
Like Davis, Gardner and Gardner before him, Homans ~950) interpreted these
data from an intuitive perspective. Unlike those earlier investigators, however, Homans
did not have years of ethnographic experience in Natchez to draw upon. His intuitions,
therefore, had to be generated solely by inspecting the DOG data and, presumably, by
conversations with the ethnographers.
Homans implied that he had re-analyzed the data using, a procedure introduced by
Forsyth and Katz (1946) whom he cited. Forsyth and Katz had suggested permuting the
rows and columns of a data matrix so as to display its group structure as clusters around
the principal diagonal of the matrix (upper left to lower right). Their procedure required
that both the rows and columns be rearranged until as far as possible more or less
solid blocks of non-blank cells are gathered together. Such blocks of cells, they
suggested, represent "well-knit~' groups.
l:t is doubtful that Homans actually used the Forsyth and Katz procedure. DOG
had already arranged the matrix in such a way that it displayed group structure.
Seemingly they had anticipated the Forsyth and Katz approach by six years. Homans.
44
DYNAMIC SOCIAL NETWORK MODEM ED ISIS
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then, did not rearrange the data matrix at all; he simply copied the arrangement of Figure
l, exactly as it was reported by DOG.
In any case, after inspecting the arrangement shown in Figure I, Homans grouped
~ 6 of the women and distinguished two levels of core and penpheral positions. In his
report Homans (p. 84) report wrote:
we generalize these observations by saying that the
women were divided into two groups. The pattern is frayed
at the edges, but there is a pattern. The first seven women,
Evelyn through Eleanor, were clearly members of one group;
numbers ~ ~ through ~ 5, Myra through Helen, were just as
clearly members of another. Some women participated
about equally with both groups but not very much with either;
Pear! twoman S] is an example. And some participated,
though not very often, only with the second group. Pearl,
Olivia, Flora [women 8, ~ 7 and ~ 8] and their like are
marginal group members.
This statement is somewhat ambiguous. ~ does assign women ~ through ~ to one
group and ~ ~ through 15, along with 8, 17 and IS to the other. Because woman ~ (PearI)
is assigned to both, the two groups overlap. In addition Homans characterized women 8
17 and IS to "marginal positions" but it is difficult to know whet he intended by the
phrase '`and their like.'? His statement, moreover, makes no mention at all of woman 9
(Ruth) or womanI6 (Dorothy). They were simply not assigned to either group or to any
position.
4.3 Phillips and Conviser's Analysis Based on Information Theory (P&C72)
Phillips and Conviser (1972) were the first to use a systematic procedure in the
attempt to uncover the group structure in the DGG data.3 They reasoned that a collection
of individuals is a group to He extent that all of the members of the collection attend the
same social events. So, to examine the DGG data. they needed an index of the variability
of attendance. They chose the standard information theoretic measure of entropy, H
(Shannon, 1964~. H provides an index of the viability of a binary (yes/no) variable. In
this case, it was applied to all the women (and all the events) in the DGG data. Thus, H
was used to provide an index of the degree to which different collections of women
attended different sets of events (and different sets of events attracted different collections
of women).
Phillips and Conviser set about to find groups by comparing various ways of
partitioning the women into subsets. They argued that any given partitioning produced
social groups if the entropy H summed for all of the subsets was less than the entropy for
3 It should be noted that Phillips and Conviser attributed the southern women data to Homans. Nowhere in
their paper did they acknowledge DGG.
DYNAMIC SOCIAL NETWORK MODEL~G ED ISIS
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the total set of women. In such an event, the women assigned to each subset would be
relatively homogeneous with respect to which events they attended.
They evaluated the utility of any proposed partitioning by cadculating the
information theoretic measure a. a is an index of the degree to which the overall entropy
of the total collectivity H is reduced by calculating the value Hi within each of the i
designated subsets and summing the results (Garner and McGill, ~ 956~. a is large when
all the women who are classed into each subset are similar with respect to their
attendance patterns. It is maximal only when the within-subset patterns are all identical.
To employ this approach then, it is necessary to partition the women in all
possible ways. calculate a for each partitioning, and see which partitioning produces the
largest value.
There is, however, a major difficulty with this approach. The number of possible
partitionings grows at an exponential rate with an increase in the number of individuals
examined. The number grows so rapidly that the partitions cannot all be examined, even
with as few as ~ ~ women to be considered.
So Phillips and Conviser worked out a way to simplify the problem. Like
Homans, they cited again the procedure suggested by Forsyth and Katz (19461. That
procedure rearranges the rows and columns in the data matrix in such a way that women
who attended the same events and events that were attended by the same women are
grouped together. When this is done, only those women who are close together in the
matrix are eligible to be in the same group. That being the cases only those relatively few
partitionings that include or exclude individuals in successive positions in the data matrix
need to be considered.
As ~ indicated above, the DOG data had already been arranged in the desired
order by the original authors. So, like Homans, Phillips and Conviser did not actually
have to rearrange them. They could proceed directly to partitioning. They began by
partitioning the women into two classes (1 versus 2 through IS, ~ and 2 versus 3 through
~ 8, ~ through 3 versus 4 through ~ 8, etc.~. They reported that, of all these two-group
partitions, the split of ~ through ~ ~ versus ~ 2 through ~ ~ yielded the largest value of a.
In checking their results, however, T discovered that their result was based on an
error in calculation. When ~ recalculated ~ discovered that the maximum value of a is
actually achieved with the ~ through 9 versus JO through ~~ split. This approach simply
partitions; it cannot distinguish core or peripheral positions, nor can it permit
overlapping.
4.4 Breiger's Matrix Algebraic Analysis (BGR74)
Breiger (1974) used matrix algebra to show that the original two-mode, woman by
event DGG data matrix could be used to generate a pair of matrices that are,
46
DYNAMIC SOCIAL NETWORK MODELING kD ISIS
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mathematically, dual. First, multiplying the original matrix by its transpose produces a
woman by woman matrix in which each cell indicates the number of events co-attended
by both the row and the column women. Second, multiplying the transpose by the
original matrix yields an event-by-event matrix where each cell is the number of women
who attended both the row event and the column event. The woman-by-woman matrix is
shown in Figure 3.4 And its dual, the event-by-event matrix. is shown in Figure 4.
1 1 1 1 ~ 1 1 ~ 1
1 2 3 4 ~ ~ 7 8 9 0 ~ 2 3 4 ~ 6 7 ~
E L T ~ ~ F E P R V M K S N H D O F
1 EVELYN 8 ~ 7 ~ 3 4 3 3 3 2 2 2 2 2 1 2 1 1
2 LAURA 6 7 6 6 3 4 4 2 3 2 1 1 2 2 2 ~ O O
3 THERESA' 7 6 8 6 4 4 4 3 4 3 2 2 3 3 2 2 1 1
4 BRENDA 6 6 ~ 7 ~ 4 4 2 3 2 1 1 2 2 2 1 0
C~LOi It 3 3 4 4 4 2 2 0 2 1 0 0 1 1 1 ~ ~ 0
6 FRANCES 4 4 4 4 2 4 3 2 2 1 1 1 1 1 1 1 0 0
7 ELEANOR 3 4 4 4 2 3 4 2 3 2 1 1 2 2 2 1 0 0
8 PEARL 3 2 3 2 0 2 2 3 2 2 2 2 2 2 1 2 1 1
9 RUTH 3 3 4 3 2 2 3 2 4 3 2 2 3 2 2 2 1 1
10 VERNE 2 2 3 2 1 1 2 2 3 4 3 3 4 3 3 2 1 1
11 MYRA 2 1 2 1 0 1 1 2 2 3 4 4 4 3 3 2 1 1
12 KATHERINE 2 1 2 1 0 1 1 2 2 3 ~ 6 6 ~ 3 2 1 1
13 SYLVIA 2 2 3 2 1 1 2 2 3 4 4 6 7 6 4 2 1 1
14 NORA 2 2 3 2 1 1 2 2 2 3 3 ~ 6 ~ 4 1 2 2
15 HELEN 1 2 2 2 1 1 2 1 2 3 3 3 4 4 ~ 1 1 1
16 DOROTHY 2 1 2 1 0 1 ~ 2 2 2 2 2 2 1 1 2 1 1
17 OLIVIA 1 0 1 0 0 ~ ~ 1 1 1 ~ 1 1 2 1 1 2 2
18 FLORA 1 ~ 1 ~ O ~ 0 1 1 1 1 1 1 2 ~ 1 2 2
_
Figure 3. The One-Mode, Woman by Woman, Matrix Produced by Matrix
Multiplication
~ 2 3 4 5 S 7 ~ 9 10- 11 12 13 14
E1 E2 E3 E4 E5 ES E7 E8 E9 E10 E11 E12 E13 E14
1 E1 3 2 3 2 3 3 2 3 1 ~ ~ ~ 0 0
2 E2 ~ 3 3 2 3 3 2 3 2 ~ 0 0 0 0
3 E3 3 3 6 4 6 ~ 4 ~ 2 ~ 0 ~ 0 0
4 E4 2 2 ~ 4 4 3 3 3 2 0 0 Q O O
5 ES 3 3 6 4 8 6 ~ 7 3 0 a G ~ 0
E6 3 3 ~ 3 6 ~ ~ 7 4 1 1 1 1 1
7 E7 2 2 4 3 6 ~ 10 8 ~ 3 2 4 2 2
8 E8 3 3 ~ 3 7 7 8 14 9 4 1 ~ 2 2
~ E9 1 2 2 ~ 3 4 ~ 9 12 4 3 ~ 3 3
10 E10 ~ ~ 0 0 C 1 3 4 4 ~ 2 ~ 3 3
11 E11 ~ 0 0 ~ 0 1 2 1 3 2 4 2 1 1
12 E12 0 0 0 ~ 0 1 4 ~ 5 ~ 2 6 3 3
13 E13 ~ 0 0 0 0 1 2 2 3 3 1 3 3 3
14 E 14 0 ~ 0 ~ 0 1 2 2 3 3 1 3 3 3
Figure 4. The One-Mode, Event by Event, Matrix Produced by Matrix
Multiplication
Breiger renamed DOG's "Myra." He listed her as "Myrnaq in his tables and diagrams. Breiger s
designation has been picked up in a number of later works includin;, the data set released as part of the
UCINET progran1 (Borgatti, Everett and Freeman. 1992).
DYNAMIC SOCIAL NETWORK HOD~:~ING ED ISIS
47
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woman 6, but the paired-comparison analysis places woman 5 closer to the core than
woman 6.
To evaluate the effectiveness of each of the ~ ~ orders provided by the analytic
procedures, ~ used gamma. Gamma provides an order-based measure of agreement. T
compared each of the orders suggested by the procedures with the idealized orders
provided by canonical analysis and p~red-compar~son analysis.
Because the two idealized orders are so similar. their gammas with the orders
~ ~ ~ . ~ ~ . . .
p~uuuc<;u by one analytic procedures were, of course, nearly Identical. The results for
both the canonical and the paired-comp~son standards are shown in Figure 14.
For both model-based standards. Homans' order produced the highest gamma.
One must be careful, however, in looking at these values because different gamma
calculations may be built on vastly different numbers of observations. In this case, the
value of I.0 associated with Homans' work was based on only 17 comparisons in the
order of the women. In contrast the values associated with the two analyses by Newman
were based on 58 and 59 comparisons respectively. Because Homans' report contained
relatively less information about who was in the core and who was peripheral it
generated fewer predictions about positions. The predictions it did make happened to
agree with the positional information produced by both cntena. But the Newman
analyses both produced large numbers of predictions, and they were still mostly in
agreement with those produced by the cntena.
Beyond Newman. the orders produced hv n~vi.c GY~rrlner ~nr1 f'~~rAnPr
~ —J ~ ~7 _ _A ~ A, ~ ,~ ~ ~ of_ A A_
themselves, by Doreian, by Freeman and White in their first analysis, and by Skvoretz
and Faust are consistently in agreement with the cntena. Their gammas are all above .9
and they are all based on at least 43 comparisons. At the opposite extreme, both
Bonacich analyses and the Borgatti and Everett bi-cTique analysis do not agree very well
with the cntena.
ID Code Analysis (;amma with Number of 4:;amma wilt, Number of
Cannonical Comps Paired-Companson Comps
1 DGG41 cams, Gardner and Gardner, Eggnog. 0.962 52 0.923 52
2 HOMED Homans, Intuidon 1.000 17 1.000 17
6 BCH78 Bonacich, Boolean Algebra -~.111 9 0.~00 10
7 DOR79 Doreian, PJgebra~c Topology 0.329 28 0.929 28
8 BCH91 Bonacich, Correspondence Analysis 0.313 67 0.324 68
12 FWl;93 Freeman and White, Full Lath ce 0.953 43 0.~53 43
13 FVV293 Freeman and White, Su~Latice 0.867 45 O.870 46
14 BEl97 Borgati and Everett, Bi-Clique O.385 39 0.350 40
17 S&F99 Skvore~and Faust,p~ 0.932 59 0.933 60
18 ROB00 Roberts, Correspondence Analysis 0.844 64 0.846 65
20 N~1 Newman, Weighted C~P4tendance 0.~6 58 O.932 59
Figure 14. Gammas Showing the Degree to which 11 Analvses A~ree`1 with the Twn
Standards In Assigning individuals to Core and Peripheral Positions
DY7 JAMIC SOCIAL NETWORK MODELING AND ANALYSIS
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So again, we have been able to uncover something close to a consensus this time
with respect to core and peripheral positions. And we have again been able to find out
something about the extent to which each of the analytic procedures approaches that
consensus.
6. Summary and Discussion
6.l Assignment to Groups
Each of the ~ ~ analyses reported here assigned the DGG women to groups.
Consensus analysis determined the agreement among the assignments. It turned out that
there was a strong core of agreement among most of the analytic devices. The agreement
was substantial enough to allow the model to be used specify a partition of the women
into groups~ne that captured the consensus of all the analyses. At the same time, the
consensus analysis was also able to provide ratings of the "competence' of each of the
analytic procedures.
The consensual assignment of women to groups and the "competence" ratings
of the analytic methods were reported above. The "competence" scores were reflected in
the first axis of an singular value decomposition of the matches generated by the methods
in assigning pairs of women to the same or to different groups. In that earlier
examination ~ reported only the first axis. But here. it is instructive to examine the
second and third axes. They are shown in Figure 15.
Fues3
BCH78 ~ ~ BeR74
~ DOR78
BE197 ~~
r
FRE8Q
Baled
nOM5O S&F— Romo BE3er
Bat ~ ·P""
SINEWS FR193
~1
FWI93
Figure 15. Axes 2 and 3 Produced by the Singular Value Decomposition of the
Matches in the Assignments of Women
68
DYNAMIC SOCIAL NETWORK HODE~G ED ISIS
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The arrangement of points representing the analytic methods in Figure 15 tells a
good deal about both the partitioning of women to groups and the competence of the
methods. The consensus put women ~ through A in the first group and women 10
through ~ ~ in the second. In Figure 15, the basis for determining why this was the "best"
partition becomes apparent. That partition was specified exactly by six of the analytic
procedures: P&C72 (The corrected version of Phillips and Conviser's inflation
theoretic algorithms, BCH91 (Bonacich's correspondence analysis), FRI93 (Freeman~s
first genetic a:[gonthm solution), BE297 (Borgatti and Everett's taboo search), BE397
(Borgatti and Everett's genetic aIgorithm) and ROB00 (Roberts' correspondence analysis
of normalized data). These analyses are all placed at a single point at the upper right of
the figure.
Other analyses that produced results that were quite close to that ideal pattern
are clustered closely around that point. For example, BBA75 and NEW01 produced the
same pattern with only one exception. They both assi;,ned woman ~ to the second group.
~ ~ ~ ~ ~ ~ A: ~ ~ 1~ ~ C) _ _ ~ ~ ~ _ .1 1 — —
=——~
r ~ ~~ ~ asslg~lt;u corn women ~ ana a to me second group. DGG41 put woman 9 in both
groups. And FW193 put woman 16 in both. Finally, S&F99 deviated only by failing to
include woman 16 in either group. Thus, in addition to the six "perfect" partitionings, six
additional procedures came very close to the ideal and are clustered in the region
surrounding these "perfect" solutions. This clustering is the key. It shows a clear
consensus around the I-9, 10-~8 division. This consensus is really remarkable in view of
the immense differences among the analytic procedures used.
Figure 16 re-labels all the points such that their departure from the "perfect"
partitioning is displayed. Note that the I-9, 10-IS partition is labeled "PERFECT."
Note also that departures from that ideal are generally placed farther from the PERFECT
point as the degree of their departure grows. They are, moreover, segregated in terms of
the kinds of departure they embody. All the points that fall on the left of the vertical axis
involve methods that failed to assign two or more of the women to groups. Overall, those
points are arranged in such a way that those falling further to the left are those that are
missing more women. Immediately to the right of the vertical, are the methods that
located women in the "wrong" group. And their height indicates the number of women
classified in "error." All the way to the right are the methods that assigned women to
both groups. And, to the degree that they assigned more women in that way, they are
farther to the right. Finally, it should be noted that there are two analyses that assigned
women to multiple groups on the left. But it is clear from their placement that this
analysis was more responsive to their inability to place women in groups than it was to
their dual assignments.
DYNAMIC SOCKS NETWO=MODEL~G ED TRYSTS
69
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2 MISSING AND 3 MISSING AND 1 MISSING FRFE T
20VERLAP 1 OV~RW P C
6 MISSING 4 MISSING | \ | / 1 WRONG SIDE /
O \ 0 2 MISSING
O ~ WRONG SIDE /
O O O
MISSING ~ l
I ~ OWR~P
2 WRONG SIDE
3 MISSING ~
6 WRONG SIDE
Figure 16. Axes 2 and 3 of the Matches Labeled by Structural Form
OveratI, then, it is clear that there was a consensus about assigning women to
groups. Six methods agreed, and most of the others departed relatively little from that
agreed-upon pattern.
6.2 Positions in Groups
In assigning positions to individuals, ~ used two, quite different, scaling
techniques. One was based on a dominance model. For each pair of women A and B. the
mode! placed A closer to the core than B. if and only if more procedures placed A closer
to the core than B. The other was probability-based. It placed A closer to the core than B
with some probability based on the proportion of procedures that placed A closer to the
core than B.
Despite their differences, the results of these two methods turned out to be
almost identical. They were similar enough that either could be taken as providing
something very close to an optimum assignment of individuals to positions. The
effectiveness of each of the analytic procedures was evaluated by their monotone
correlations with these optima. The results were very similar; the correlation between the
gammas produced by the dominance model and those produced by the probability mode!
was .983. So, even with without consensus amon, the procedures, 1 was able to find the
a3reed-upon order~ore to penphe~y and to evaluate the ability of each method to
uncover that order.
70
DYNAMIC SOCIAL NETWO~MODEL~G kD ISIS
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6.3 A Final Word
As a whole T believe that this meta-analysis has been productive. As far as
assigning women to groups was concerned, the results were dramatic. When it came to
assigning women to positions, the results were less dramatic, but still fairly convincing.
We end, then, with four strong results: (~) We have a consensual partitioning of women
into groups. (2) We have a consensual assignment of women into core and peripheral
positions. (3) We have a rating of the methods in teens of their competence in assigning
women to groups. And (4) we have a rating of the methods in terms of their ordinal
correlations with the standard positional assignments.
~ would like to wind up with two additional comparisons of the analytic
procedures examined here. These final comparisons will be restricted to the published
analyses of the DGG data; they will not include the unpublished analyses involving my
use of Osbourn's VERI or the analysis Newman ran at my request.
The first comparison is based on time. Figure ~ 7 shows the average competence
ratings of procedures published at various points of time. The data in Figure 17 show an
interesting secular trend. There has been a slow but consistent trend toward increasing
competence through time. Thus, the overall tendency in published reports using the
DOG data is clearly in the direction of greater competence.
In addition. it is possible to make some generalizations about the adequacy of the
various kinds of analytic procedures that have been used to find groups and positions
using the DOG data. Six procedures (BGR74, BCH7S, DOR79, E&B93, FWI93 and
FW293) all took essentially algebraic approaches. Five (P&C72, FRI93, FR293, BEl97
and BE297) used venous aigonthms to search for an optimal partition. Three analyses
(BBA75, BCH91 and ROB00) employed various versions of singular value
decomposition. Two (DGG41 and HOM50) were based simply on the authors'
intuititions. And three developed unique approaches. One (FRE92) looked at a kind of
transitivity. A second (BEl97) dealt with overlapping bictiques. And the third (S&F99)
developed a statistical model.
D YIJAMIC SOCIAL NETWORK MODELING AND ANAL YSIS
71
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1
0.8
O.6
0.4
0.2
to
. . .
I:. ' .: , :: -, .: ,-., .: , ,~
.. . .. . .. . . .
I:' '' : I:- . ' ' ( ,,,,:~`,,~"i , I'd ,': 'a ,.,,:'~',^~,'~'.','i,' ~ v~ .
',: ''j,,''''f''"'.,.,,';,;,. ',':. .': ;' , (- '. '.:' ' :' ' ' ' ' ' ~1 ~ i
. ' . ~ In,, ~~ .d F) ~ ~ . ~ . ~ q)y i`, ,~ ,~ ~ .' ~ '.~ ~ . ,.,, <, _
: :~ i. ~ ;. : .: . :.'^.,':; ,~:'.:~ . ~ :<~;:~ :., ;:.i-~~;^~ I .'. at ~~:~':<
.. " ,"':"':'"''' 'a , ant: :,'~., A ''_"-,','[ ' . '': :~:~:~
~ W ` ~ ~~ : ; ~,W,,,~ .,,{ - . . .,,,,, Al . . ~ 1 St.,; ,;
'~ ~~] ~ ~ ~~ :~ of; a,' ~ ~ ~ ~~: ~
, . ~ f ~ 2~r ' ~ ' '.,''.~'.;~~2 A; I' ' W.>' ~ ,' ,; ~'~v~' ',
i~ ~~
40s and SOs 70s
91-93 97-00
Figure 17. Competences of the Procedures Over Time
All in all, then, we have used seven distinct classes of procedures in analyzing the
DOG data. Figure ~ ~ shows the relative success of each class in terms of its average
competence.
Procedure N Average Score
Statistical hJlodel 1 0.957
Eigen Structure 3 0.954
C: ptimal Partition ~ 0.941
Transitivity 1 0.926
Cliques 1 0.916
Algebraic Duality 6 0.914
Intuition 2 0.887
Figure IS. Average Competences of the Various Classes of Procedures
A number of features of Figure 17 are worth noting. First, the statistical mode! of
the DOG data developed by Skvoretz and Faust was the winner. It won despite the fact
that. unlike most of the other procedures, it was not explicitly designed to uncover
groups. Group structure emerged as a sort of bi-product of a broader structural analysis.
72
DYNAMIC SOCIAL N~:TWORKMODEL~G AD ISIS
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The statistical model is not' however, the undisputed champion. It is followed so
closely by the three singular value decomposition analyses, that it has to share the crown
with them. And the five partitioning programs are right up there near the top.
There seems to be a step between all those procedures and the next three. Clearly
transitivity, bicliques and the algebra-based approaches did not do as well. And, finally,
the intuitive judgments fall at the bottom. In part that position is due to the vagaries of
Homans' report, but DGG themselves did very little better. This result is particularly
interesting given the fact that Davis, Gardner and Gardner's interpretation of their own
data is often taken as privileged. The assumption has been that because they had a huge
amount of ethnographic experience in the community, DGG had an edge- they somehow
knew the ' true" group structure. But, particularly in the light of the present results, there
is no compelling reason to award DGG any special exalted status vis-a-vis their ability to
assign individuals to groups. Indeed, their very intimacy with these IS women might
have led to various kinds of biased judgments.
References
Batchelder, W. H. and N. J. Bershad
1979 The statistical analysis of a Thurstonian mode! for rating chess
players. Journal of Mathematical Psychology, 19:39-60.
Batchelder, W. H., N. J. Bershad and R. S. Simpson
1992 Dynamic p~red-comparison scaling. Journal of Mathematical
Psychology, 36: ~ 85-212.
Batchelder, W. H. and A. K. Romney
986 The statistical analysis of a general Condorcet mode! for dichotomous
choice situations. In B. Grofman and G. Owen (Eds.) hnformation
Pooling and Group Decision Malting. Greenwich, Connecticut: JAl
Press, Inc.
Batchelder, W. H. and A. K. Romney
1988 Test theory without an answer key. Psychometr~ka 53:71-92.
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Representative terms from entire chapter:
social network
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