Relations, Species, and Network Structure

Description of Networks N Type of Animal Positive or Negative Relation Observed or Reported Relation baboonf dominance between baboons Hall and baboonm1 dominance between male baboons Ha

Relations, Species, and Network Structure*

John Skvoretz

Department of Sociology, University of South Carolina

Katherine Faust

Department of Sociology, University of California, Irvine

* For their encouragement and suggestions on the research, we thank H Russell Bernard, Linton

Freeman, and A Kimball Romney Discussion with Tom Snijders on the p* models was most

helpful We also thank Mike Burton for suggesting the matrix permutation approach On a more

personal note, we would like to acknowledge and celebrate the influence of Linton Freeman on

our careers On a visit to Lehigh University in the Fall of 1968 to give a talk, Lin advised John, a

double major in Sociology and Mathematics, to do his graduate work at Pittsburgh with a young

professor named Tom Fararo, thereby setting in motion a life-long interest in networks and

structure And, it was after Lin joined the School of Social Sciences at the University of

California, Irvine in 1979 as dean and catalyst for the Social Networks Program that Katie's

research interests turned to social networks It was also Lin who encouraged Katie to go to the

University of South Carolina, thereby making possible the collaboration that led to this research

ABSTRACT: The research we report here tests the "Freeman-Linton Hypothesis" which we take

as arguing that the structure of a set of relational ties over a population is more strongly

determined by type of relation than it is by the type of species from which the population is drawn Testing this hypothesis requires characterizing networks in terms of the structural properties they exhibit and comparing networks based on these properties We introduce the idea of a structural signature to refer to the profile of effects of a set of structural properties used

to characterize a network We use methodology described in Faust and Skvoretz (forthcoming) for comparing networks from diverse settings, including different animal species, relational contents, and sizes of the communities involved Our empirical base consists of 80 networks from three kinds of species (humans, non-human primates, non-primate mammals) and covering distinct types of relations such as influence, grooming, and agonistic encounters The methods

we use allow us to scale networks according to the degree of similarity in their structuring and then to identify sources of their similarities Our work counts as a replication of a previous study that outlined the general methodology However, as compared to the previous study, the current one finds less support for the Freeman-Linton Hypothesis

"My overall goal is to learn something basic about the foundations and consequences

of the sociability of social animals."

Linton Freeman, 1999, Research in Social Networks

(http://eclectic.ss.uci.edu/~lin/work.html)

" just as the physical differences between men and apes diminish in importance and cease to be a bar to a relationship when they are studied against the background of

mammalian variation, the differences in behavior diminish in importance when they

are seen in their proper perspective."

" human and animal behavior can be shown to have so much in common that the gap

ceases to be of great importance."

Ralph Linton, 1936, The Study of Man (New York: The Free Press)

The passages of Ralph Linton quoted above suggest that the behavioral commonalities between humans and animals are substantial The claim would extend to social behavior, in particular, behavior in regard to others of the same species, "the sociability of the social animals." This view is echoed in Lin Freeman's work That is, both authors would contend that the networks of baboons and school children, of cattle and bank clerks, and of fraternity brothers and ponies would be similarly structured whenever the nature of the behavior defining the connections was common to both networks In this paper we explore what we will call the Freeman-Linton Hypothesis, named after the scholars quoted above In particular, we examine 80 different networks from three types of species (humans, non-human primates, and non-primate mammals),varying in size from 4 to 73 units Many distinct types of relations are included: from liking, influence and grooming to disliking and victory in agonistic encounters Our specific research question is whether patterning in a network can be better predicted by type of animal or type of relation The Freeman-Linton hypothesis leads us to expect that type of relation will matter much more than type of social animal

To investigate this hypothesis requires a methodology that allows the comparison of many networks even though they may vary dramatically in size, in type of social animal, and in

relational contents The methodology should provide an abstract way of characterizing the structure of a network apart from the particular individuals involved It should also provide a set

of guiding principles for what it means to say that two networks are similarly structured The method we build on has been described in detail elsewhere (Faust and Skvoretz forthcoming) Inthe next section we outline the steps in that method We then apply it to our networks,

replicating the original analysis, which was restricted to a smaller set of networks (42 in

number) We also extend the original analysis to consider systematically sources of variation in network structuring among networks of different species and different types of relations We conclude the paper with a discussion of directions for future work with particular attention to the theoretical questions our project may address

Representation of the Structural Signature of a Network

Faust and Skvoretz (forthcoming) propose a method that allows researchers to measure the similarity between pair of networks and to look at the overall patterning of similarities among a large collection of networks from diverse settings Their basic argument is that two networks aresimilarly structured, that is, have the same structural "signature," to the extent that the networks exhibit the same structural properties and to the same degree One way to quantify the

magnitudes and directions of network's structural properties is to use a statistical model In that case, two networks are similarly structured if the probability of a tie between i and j is affected

by the same set of structural factors to the same degree in both networks To explicate this idea, consider a single structural factor, say, mutuality and two networks: A is a network of advice tiesbetween sales personnel and B is a network of helping relations between blue-collar workers Mutuality, the tendency for actor i to return a tie to actor j if j sends a tie to i, might be one structural factor that affects the probability of a tie between two actors in either network A or network B Tendencies toward mutuality have long been a concern of social network analysts (Katz and Powell 1955; Katz and Wilson 1956) and the measurement of mutuality remains a focus of contemporary research (Mandel 2000) It is a "structural" factor because it refers to a

property of the arrangement of ties in any pair in the graph rather than to properties of the

individuals composing the pair

With just this one factor, Faust and Skvoretz would propose that networks A and B are similarly structured if a tendency toward mutuality is present or absent in both networks and to the same degree Specifically, their method calibrates the strength of such structural tendencies in terms ofmeasures of impact that are invariant across networks that differ in size and overall density Therefore, strictly speaking, networks A and B are similarly structured if the standardized

tendency toward mutuality is identical in both networks Of course, with just one structural factor, fine discriminations among the structural patterns in different networks are just not possible Networks that may be structurally distinct for other reasons (such as different

tendencies towards transitivity) would be classed as similar because only one structural factor, mutuality, has been taken into account

As additional factors are considered, finer and finer discriminations among entire sets of

networks become possible But these finer distinctions require measuring multiple structural properties of the networks One could amass a collection of graph-based indices calculated on each network (mutuality, transitivity, ) and then compare these collections, but a more coherentapproach is to estimate a set of effects simultaneously in the context of a statistical model for the network Thus the first step in the comparison methodology proposed by Faust and Skvoretz (forthcoming) is to estimate statistical models for the probability of a graph in which the set of predictor variables is expanded beyond simple mutuality Until recently, no statistical models were able to incorporate any structural effects beyond mutuality However, with the

development of family of models known as p* such investigations became possible (Anderson et

al 1999; Crouch et al 1998; Pattison and Wasserman 1999; Wasserman and Pattison 1996; Robins, Pattison, and Wasserman 1999) Faust and Skvoretz use a p* model that includes six structural properties: mutuality, transitivity, cyclical triples, and star configurations (in-stars, out-stars, and mixed stars) as illustrated in Figure 1 The model is based on what Frank and Strauss (1986) call a "Markov" graph assumption This assumption stipulates that the state of a tie between i and j can only be influenced by the state of a tie between two other actors if at least one of these other actors is i or j Put another way, there is no impact "at a distance," meaning that the state of the tie between x and y cannot impact the state of the tie between w and z if x and y are complete different persons than w and z Furthermore, the model assumes that the Markov graph effects are homogeneous, that is, unrelated to specific labeled identities of actors Thus these effects are "purely structural" in that they do not depend the labels attached to the nodes

Figure 1 Network Properties Included in the p* Models

e Transitive triple f Cyclic triple

A p* model expresses the probability of a digraph G as a log-linear function of a vector of

parameters , an associated vector of digraph statistics x(G), and a normalizing constant Z( ):

(1)

The normalizing constant insures that the probabilities sum to unity over all digraphs The parameters express how various "explanatory" properties of the digraph affect the probability of its occurrence The explanatory properties of the graph include the structural factors, like

mutuality and transitivity mentioned above The model we use stipulates that the probability of agraph is a log-linear function of the number of mutual dyads, the number of out 2-stars, the number of in 2-stars, the number of mixed 2-stars, the number of transitive triples, and the number of cyclical triples If the resulting parameter estimate for a specific property is large and positive, then graphs with that property have large probabilities For example, if mutuality has a positive coefficient, then a graph with many mutual dyads has a higher probability than a graph with few mutual dyads Or, if the cyclical triple property has a negative coefficient, then a graph with many cyclical triples has a lower probability than a graph with few cyclical triples Thus, the resulting parameter estimates associated with the structural properties capture the importance

of these properties for characterizing the network under study The set of parameters forms thestructural signature of the network.[1]

The equation (1) form of the model cannot be directly estimated Rather the literature proposes

an indirect estimation procedure in which focuses on the conditional logit, the log of the

probability that a tie exists between i and j divided by the probability it does not, given the rest ofthe graph (Strauss and Ikeda 1990; Wasserman and Pattison 1996) Derivation of this

conditional logit shows it to be an indirect function of the explanatory properties of the graph Specifically, it is a function of the difference in the values of these variables when the tie

between i and j is present versus when it is absent, as specified in the following equation:

(2)

where G-ij is the digraph including all adjacencies except the i,jth one, G+ is G-ij with xij=1 while

G- is G-ij with xij=0 In the logit form of the model, the parameter estimates have slightly

different interpretations For instance, if the cyclical triple property has a negative coefficient, then in the equation (1) version, we may say that a graph with many cyclical triples has a lower probability than a graph with few cyclical triples In the equation (2) version, the interpretation

is that the log odds on the presence of a tie between i and j declines with an increase in the number of cyclical triples that would be created by its presence (Technically, however,

interpretation is best phrased in terms of the probability of the graph.) The importance of the logit version of the model lies in the fact that, as Strauss and Ikeda (1990) show, the logit versioncan be estimated, albeit approximately, using logistic regression routines in standard statistical packages.[2]

The significance for our problem of identifying the structural signature of a network is that it is possible to build and estimate models that capture multiple structural effects We are no longer limited to a structural signature built on only one or two factors In the research we report in the next section each network has a six-dimensional signature defined by the parameter estimates forthe effects of the six structural factors diagrammed in Figure 1 We also present several ways to

compare the signatures of different networks, looking for similarities and differences One of these ways extends the work of Faust and Skvoretz (forthcoming) who use parameter estimates from different networks to generate sets of predicted tie probabilities for focal networks and thencompare the sets of predicted probabilities using an Euclidean distance function Another way, new to the present research, explores the structural signatures based directly on the parameter estimates.

In all comparisons, we seek to assess the tenability of the Freeman-Linton hypothesis

Specifically, we want to compare the structural signatures of human networks to the structural signatures of the networks of other species If we find, in fact, that the signatures differ, we want

to see how much of the difference can be accounted for by "controlling for" relational type That

is, the Freeman-Linton hypothesis would predict that any difference in the aggregate between human networks and the networks of other species would disappear once we take into account relational type In other words, the hypothesis holds that the nature of the behavior defining the connections, not species of social animal, is the fundamental factor determining a network's properties and thus its structural signature These are the implications of the hypothesis we seek

to evaluate

Comparisons of Structural Signatures

Table 1 lists the 80 networks we use to evaluate the Freeman-Linton hypothesis and to illustrate our methodology of comparison The networks range in size from four colobus monkeys to 73 high school boys The ties composing the networks also vary from advice relations and

friendship ties to victories in agonistic encounters Each of the networks that we compare is represented by a 0,1 adjacency matrix (created by dichotomizing all non-zero entries equal 1 if the original relation was valued) More details about each of the networks can be found in the Appendix

Table 1 Description of Networks

N Type of Animal

Positive or Negative Relation

Observed or Reported Relation

baboonf dominance between baboons (Hall and

baboonm1 dominance between male baboons (Hall

baboonm2 dominance between male baboons (Hall

baboonm3 outcomes of agonistic bouts between

banka advice in a bank office (Pattison et al.)

11 human positive reportedbankc confiding in a bank office (Pattison et al.)

11 human positive reportedbankf close friends in a bank office (Pattison et

banks satisfying interaction in a bank office

bkfrac rating of interaction frequency in a

fraternity (Bernard et al.) 58 human positive reportedbkhamc rating of interaction frequency between

ham radio operators (Bernard et al.) 44 human positive reportedbkoffc top rank order of interaction frequency in

bktecc top rank order of interaction frequency in

a technical group (Bernard et al.) 34 human positive reportedcamp92 top rank order of interaction frequency in

"Camp" (Borgatti et al.) 18 human positive reportedcattle contests between dairy cattle (Schein and

cole1 friendship at time 1 between adolescents

cole2 friendship at time 2 between adolescents

colobus1 non-agonistic social acts between colobus

colobus2 non-agonistic social acts between colobus

colobus3 non-agonistic social acts between colobus

eiesk1 EIES data, rating of acquaintanceship

eiesk2 EIES data, rating of acquaintanceship

eiesm EIES data (Freeman and Freeman)

32 human positive observedfifth friendships between fifth graders

fourth friendships between fourth graders

ka advice between managers (Krackhardt)

21 human positive reportedkapfti1 instrumental work relations in a tailor

kapfti2 instrumental work relations in a tailor

kf Krackhardt, friendship between managers

21 human positive reportedkids1 initiated agonism between children

kids2 dominance among nursery school boys

medical physicians (Coleman, Katz and Menzel)

32 human positive reportednewc0 top rankings of friendship in a fraternity,

newc0n bottom rankings of friendship in a

fraternity, week 0 (Newcomb) 17 human negative reportednewc1 top ranking of friendship in a fraternity,

newc1n bottom rankings of friendship in a

fraternity, week 1 (Newcomb) 17 human negative reportednewc10 top ranking of friendship in a fraternity,

newc10n bottom rankings of friendship in a

fraternity, week 10 (Newcomb) 17 human negative reportednewc11 top ranking of friendship in a fraternity,

newc11n bottom rankings of friendship in a

fraternity, week 11 (Newcomb) 17 human negative reported

newc12 top ranking of friendship in a fraternity,

newc12n bottom rankings of friendship in a

fraternity, week 12 (Newcomb) 17 human negative reportednewc13 top ranking of friendship in a fraternity,

newc13n bottom rankings of friendship in a

fraternity, week 13 (Newcomb) 17 human negative reportednewc14 top ranking of friendship in a fraternity,

newc14n bottom rankings of friendship in a

fraternity, week 14 (Newcomb) 17 human negative reportednewc15 top ranking of friendship in a fraternity,

newc15n bottom rankings of friendship in a

fraternity, week 15 (Newcomb) 17 human negative reportednewc2 top ranking of friendship in a fraternity,

newc2n bottom rankings of friendship in a

fraternity, week 2 (Newcomb) 17 human negative reportednewc3 top ranking of friendship in a fraternity,

newc3n bottom rankings of friendship in a

fraternity, week 3 (Newcomb) 17 human negative reportednewc4 top ranking of friendship in a fraternity,

newc4n bottom rankings of friendship in a

fraternity, week 4 (Newcomb) 17 human negative reportednewc5 top ranking of friendship in a fraternity,

newc5n bottom rankings of friendship in a

fraternity, week 5 (Newcomb) 17 human negative reportednewc6 top ranking of friendship in a fraternity,

newc6n bottom rankings of friendship in a

fraternity, week 6 (Newcomb) 17 human negative reportednewc7 top ranking of friendship in a fraternity,

newc7n bottom rankings of friendship in a

fraternity, week 7 (Newcomb) 17 human negative reportednewc8 top ranking of friendship in a fraternity,

newc8n bottom rankings of friendship in a

fraternity, week 8 (Newcomb) 17 human negative reportednfponies threats between ponies (Tyler)

13 mammal negative observedprison friendship in a prison (MacRae)

67 human positive reportedrhesus1 fights between adult female rhesus

rhesus2 fights between yearling rhesus monkeys

rhesus4 fights between adult rhesus monkeys

rhesus5 fights between adult rhesus monkeys

rhesus6 fights between adult rhesus monkeys

sampdes disesteem between monks (Sampson)

18 human negative reportedsampdlk dislike between monks (Sampson)

18 human negative reportedsampes esteem between monks (Sampson)

18 human positive reportedsampin influence between monks (Sampson)

18 human positive reportedsamplk liking between monks (Sampson)

18 human positive reportedsampnin negative influence between monks

sampnpr negative praise (blame) between monks

samppr praise between monks (Sampson)

18 human positive reportedthird friendship between third graders

vcbf best friends between seventh graders

vcg get on with between seventh graders

(Wasserman and Pattison 1996) 29 human positive reportedvcw work with between seventh graders

(Wasserman and Pattison 1996) 29 human positive reported

First, for each data set, we estimate the standardized coefficients for a p* model that expresses the conditional probability of a tie as a function of six structural factors: mutuality, out 2-stars, in2-stars, mixed 2-stars, transitive triples, and cyclical triples Second, we use these standardized parameter estimates and the standardized change scores in these structural factors to calculate thepredicted probability of a tie in each i,j pair in each data set using as coefficients the parameter estimates from its own model and from each of the remaining 79 models Thus for each data set,

we have 80 sets of predicted probabilities, one from each set of parameter estimates including the set of estimates from the focal data set itself The third step uses the Euclidean distance function:

(3)

where d(t,y) is the distance between a target network t and a predictor network y, pt(i,j) is the probability of the tie between i and j in network t calculated from its own p* estimates, py(i,j) is the probability of the tie between i and j in network t predicted by the p* parameter estimates from network y, and gt is the size of network t The distance is a (dis)similarity score between the predicted probabilities from the estimates derived from t, the target network itself, and the predicted probabilities from the estimates derived from y, one of the other 79 networks

The 80 by 80 matrix of dissimilarity scores is the input data for two of our three comparisons of network structural signatures The first operation follows the methodology of Faust and

Skvoretz (forthcoming) and uses correspondence analysis to represent the proximities among all

of the networks The resulting configuration is interpreted in light of the type of social animal and the type of relation The second operation uses matrix permutation tests to model the

dissimilarity scores as linear functions of predictor variables including type of social animal and type of relation The third comparison of the structural signatures of the 80 networks directly inspects the standardized parameter estimates themselves, comparing their mean values across categories of animal type and relation type

Correspondence analysis results Correspondence analysis involves a singular value

decomposition of an appropriately scaled matrix Entries in the input matrix are divided by the square root of the product of the row and column marginal totals, prior to singular value

decomposition Correspondence analysis is used because it does not require symmetric input data Since correspondence analysis requires that data refer to similarities rather than

dissimilarities, we rescale the Euclidean distances by subtracting each from a large positive constant prior to doing the correspondence analysis (Carroll, Kumbasar, and Romney 1997) The matrix of similarities we analyze is not symmetric, that is, the distance between network x's prediction for network y and network y's prediction for its own data does not, in general, equal the distance between y's prediction for network x and network x's prediction for its own data In the following graphs we present the column scores from correspondence analysis of the matrix

of similarities among the networks Column scores show similarities among networks in terms

of the predictions they make for other networks Thus in the figures two networks are close together if they similarly predict other networks in the collection

The following graphs show the results of the correspondence analysis in the aggregate and then disaggregated by species and type of relation Species is a categorical variable taking on three values, humans, non-human primates and non-primate mammals We highlight the contrast between humans and non-human primates because we have relatively few (only 2) networks among mammals in our set of 80 cases Relations are first categorized by how they were

collected: observation or reported by respondent Obviously this is confounded with the type of

animal since only humans provided reports of their ties to others Second, we categorize the relation as either positive or negative Grooming, advice seeking, liking, etc are considered positive, whereas dominance, agonistic encounters, and disliking are negative This leads to fourtypes: observed positive, observed negative, reported positive, or reported negative.

Figures 2-6 display results of the correspondence analysis Figure 2 shows the location of each data set in the first two dimensions The closer together two networks are the more similar are their predictions for the other networks in the collection Thus, for example, "baboonnm2" is relatively far from "kids1" and so the two networks make very different predictions for other networks Figures 3 through 6 analyze the location of the networks based on type of animal and type of relation We present 68.2% confidence ellipses around the networks, centered on a category’s means along the first two dimensions with orientation determined by the covariance

of the scores of the category’s networks on the two dimensions Larger ellipses mean more variability in the location of networks of a certain type in the two dimensional space For

mutually exclusive categories like, say, humans and non-human primates, the smaller the overlap

of the respective ellipses, the more distinctive is the region in two dimensional space occupied bynetworks in one category as opposed to the other

Figures 2-6 display results of the correspondence analysis Figure 2a shows the location of each network in the first two dimensions The color and shape of the points code whether the valence

of the relation is "positive" or "negative" (as defined below), whether it was recorded by

observers or reported by network participants, and the kind of animal involved (human or human primate) Figure 2b is another version of the same figure, but with each point labeled by the network it represents These labels and descriptions of the networks are in Table 1 In both figures 2a and 2b the closer together two networks are the more similar are their predictions for the other networks in the collection Thus, for example, "baboonnm2" is relatively far from

non-"kids1" and so the two networks make very different predictions for other networks Figures 3 through 6 analyze the location of the networks based on type of animal and type of relation We present 68.2% confidence ellipses around the networks, centered on a category's means along thefirst two dimensions with orientation determined by the covariance of the scores of the category'snetworks on the two dimensions Larger ellipses mean more variability in the location of

networks of a certain type in the two dimensional space For mutually exclusive categories like, say, humans and non-human primates, the smaller the overlap of the respective ellipses, the moredistinctive is the region in two dimensional space occupied by networks in one category as opposed to the other

Figure 2 Correspondence Analysis of Similarities between Networks, Column Scores

Figure 3 Confidence Ellipses for Type of Animal Overlaid on Correspondence Analysis

of Similarities between Networks, Column Scores

Figure 4 Confidence Ellipses for Positive or Negative Relation Overlaid on Correspondence Analysis of Similarities between Networks, Column Scores

Figure 5 Confidence Ellipses for Observed or Reported Relation Overlaid on Correspondence Analysis of Similarities between Networks, Column Scores

Figure 6 Confidence Ellipses for Type of Relation (Observed or Reported, Positive or Negative) Overlaid on Correspondence Analysis of Similarities between Networks, Column

Scores

Each of the classifications contributes to understanding the clustering of the networks in the two dimensional space Despite some overlap, human and primate networks are found in different regions, and so too are positive vs negative and observed versus reported networks Positive reported networks are clearly distinguished from negative reported networks - their confidence ellipses do not overlap at all Positive observed and negative observed overlap and both are more variable than either of the reported relations Problematic for the Freeman-Linton

hypothesis is the clear distinction between the networks of different species particularly humans

vs nonhuman primates The data remain problematic for this hypothesis in an analysis of variance comparing column scores along the first three dimensions between categories of the classificatory variables, as reported in Table 2 Table 2 uses the proportion reduction in error (PRE) in dimension scores due to the categorical grouping variables, as measured by the

correlation ratio squared, Type of animal is an important distinction along the first and second dimensions of the correspondence analysis The kind of relation, especially the four

types differentiating observed vs reported and positive vs negative simultaneously, is an

important aspect of all three dimensions But it is difficult to maintain the position that type of relation is more important than type of animal in distinguishing among the networks To

investigate this issue, we return to the distances between the networks and examine them directly

to answer the question: if we control for relation type, does the effect of animal type disappear?

Dimensions by Type of Animal, and Type of Relation

Reported Relation

Positive or Negative Relation

1 Type of animal: human, non-human primate, non-primate mammal

2 Type of Relation: observed positive, observed negative, reported positive, reported negative

Matrix permutation test results A matrix permutation test allows us to test directly whether

distances between networks are significantly smaller when they are measured on the same kind

of animal than when they are measured on different kinds of animals, whether they are smaller when both networks express the same type of relation, and then, controlling for the kind of relation, does the greater similarity (i.e., smaller distances) between networks from the same species disappear We take the matrix of distances as the dependent variable and regress it on matrices which express hypotheses about species and relations as the basis for similarity betweennetworks, using the methodology described in Krackhardt (1988) To execute the test, we build 0,1 matrices in which the ij cell is coded 1 if networks i and j are of the same type, that is, are measured over the same type of animal, or the same type of relation We then use these matrices

as predictors with the dependent variable being the matrix of Euclidean distances between

predicted probabilities We first consider the bivariate relationship between the various

classificatory variables and distance and then pass to a multiple regression analysis of the

distances A permutation test is used to assess the significance of the regression coefficients The results are presented in Table 3

Table 3 Standardized Regression Coefficients Predicting Distances between Networks

using Matrix Permutation Regression, 80 Networks

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

Model 7

Model 8 Model 9

accounting for the distances between networks (r2=.249), followed by observed vs reported relations (r2=.177) Although the coefficient for positive vs negative relations is significant and

in the right direction, this classification accounts for relatively little of the variation in distance between networks (r2=.012) Model 4 is the most comprehensive model for relation type alone

It has a main effect for both observed vs reported and for positive vs negative, and an

interaction effect between the two classifications Even this model accounts for less variation in distance than the classification by type of animal It is important to note that the coefficient for positive or negative relation changes sign from model 3 to model 4, indicating an instability of results when the interaction between positive vs negative relation and observed vs reported relation is included in the model

Models 5 through 9 are the multiple regressions and their results are consistent Namely, animal type is a significant factor no matter what aspect of relational type is controlled Model 9 is the most comprehensive model with an r2 of 275 and in this model, animal type has the largest standardized coefficient While aspects of relation type, net of animal type, are associated with distance between networks, the direction is opposite that expected for the positive vs negative classification However, it is difficult to interpret this effect since it occurs in the context of an interaction effect between positive/negative and observed/reported

The conclusion from the matrix permutation tests is very clear The Freeman-Linton hypothesis fails to receive confirmation in these 80 networks The effects of type of animal on similarity of network do not disappear when type of relation is taken into account In these 80 networks, contrary to the results of previous research (Faust and Skvoretz, forthcoming), animal type matters much more than relation type We continue to explore reasons for the impact of animal type by inspecting variation in the p* parameter estimates directly, that is, by directly comparing the structural signatures of the networks.[3]

Analysis of parameter estimates Table 4 presents some descriptive statistics regarding

parameter estimates from the p* models Figure 7 graphs the mean parameter values for humans

vs primates Since only 2 of the 80 networks refer to nonprimate mammals, they are dropped from further consideration Relations measured on humans comprise 66 of the networks and relations measured on nonhuman primates make up the remaining 12 networks Table 4 shows that a particular structural effect cannot be estimated in some networks For instance, an out 2-stars effect cannot be estimated in 32 of the 66 networks The 32 networks refer principally to the Newcomb data in which each individual has the same outdegree in our recoding of the

rankings respondents gave to others With no variance in outdegree, no out 2-star effect can be estimated Among the 12 primate networks, mutuality cannot be estimated in two of them In general, when we found it impossible to estimate a p* model with all six effects in it, we

estimated reduced models with various combinations of five (or four, if necessary) effects,

selecting the specific combination with the best fit.[4]

Table 4 Descriptive Statistics for p* Parameter Estimates by Animal Type

and with Type by Positive or Negative Relation

Mutuality

MeanSDN

0.400.2166

-0.550.819

0.440.2245

0.320.1821

0.550.442

-0.860.567

Out 2-Stars

MeanSD

N 0.080.56

34

0.201.3912

0.070.6128

0.150.226

0.530.68

3

0.091.589

SDN

0.490.5566

-0.391.1510

0.220.3045

1.060.5521

0.381.342

-0.581.128

Mixed 2-Stars

MeanSD

N -0.210.29

66

-0.681.279

-0.310.2445

-0.000.2721

0.020.182

-0.881.397

Transitive

MeanSD

N 0.100.64

66

0.691.6210

0.420.4545

-0.590.4121

0.090.582

0.841.798

Cyclic Triples Mean

SD

N -0.010.25

65

-0.531.198

-0.060.2444

0.100.2621

0.211.052

-0.781.216

Figure 7 Mean P* Parameter Estimates by Type of Animal