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Keynote borgatti
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- 2. Motivation • In some ways, personal or ego network analysis has been poor cousin of full network analysis – Concepts that are emblematic of network analysis, such as betweenness, closeness, and blockmodeling, are full network analysis concepts •Yet … – a great deal of network research is actually based on ego networks – Fundamental processes of tie formation and influence occur at the level of individual choices and behavior – It can be argued, like politics, that all network processes are local NOTE: I use “ego network” and “personal network” interchangeably
- 3. All is local • Part of the idea of network and complexity science is that faraway events can affect each other through causal chains – Butterfly flapping wings in China ultimately determines a hurricane in Florida •Yet I only interact with those that I interact with: if a faraway node affects me, it is through my interactions with my alters – My alters mediate my interaction with the world Ann affects Bill, but only because she affects Pam, who affects Holly who affects those that interact with Bill
- 4. This is why I like eigenvector centrality • Even though it is a global measure that requires full network data … … it is grounded in a principle of local action • The centrality of node iis a simple sum of the centralities of i’s alters (the js) – The centralities of the js are determined by their ties to nodes outside i’s circle but that doesn’t matter because that information is already encoded in each j’s score j jiji vav 1 vi is the centrality of i, λ is a constant, aij is the tie from i to j, vj is the centrality of j v(a) = .5/1.7 = 0.29 v(b) = (.29+.58)/1.7 = 0.50 v(c) = (.5+.5)/1.7 = 0.58 v(d) = (.29+.58)/1.7 = 0.50 v(e) = .5/1.7 = 0.29 a b c ed 0.29 0.50 .58 0.290.50 λ = 1.73205
- 5. Clarifying the topic … • Personal or ego networks can result from: – Data collected via ego network research design* –Subgraphs collected via full network design *Referred to in this workshop as “personal network research”
- 6. Objective • Compare the analysis of ego networks derived from these two different kinds of research designs – ENRD: ego network research design* –FNRD: full network research design • Given that I’m only interested in the direct network neighborhood of a node, can I just use ego network research design? – or are there reasons why FNRD is superior even for investigating local effects? *Referred to in this workshop as “personal network research”
- 7. Ego network research design (ENRD) • Sample a set of nodes (egos) from a population • For each ego, obtain list of nodes (alters) the ego has ties with –For each alter, ask ego about • Ego’s relationship with alter: are they friends? co‐workers? kin? • Ego’s perceptions of the alter’s attributes: how old is alter? How happy is alter? – Ideally, ask ego to indicate ties among the alters Mary
- 8. Results of ego network data collection • Ego – attributes •Alters – List of alters – Multiple kinds of ties to ego – Perceived attributes of alters – (ties among alters) Mary
- 9. Full network research design (FNRD) • Select a set of actors to be the nodes – Typically a culturally defined group such as a gang, an organization, a department, attendees of an event, etc. •Collect ties (usually of various kinds/relations) among the actors • For comparability with ENRD, sample egos from full network and extract the sub‐graph of ties and nodes incident on the ego
- 10. General comparison ENRD and FNRD Advantage: FNRD • Can answer context questions – how fragmented is the network as a whole? –How many links separate egos from each other along the shortest path?* • Have incoming ties as well as out – ENRD can ask ego who likes him, but is still ego naming the alters • Non‐ties are meaningful – Can model tie/non‐tie for each dyad as outcome of decision‐ making process – in ENRD can ask ‘who do you not like?’, but not ‘who do you have no tie to?’ Advantage: ENRD • Can employ standard sampling techniques – And so standard statistical methods • Cheaper & easier to deploy – Can collect richer data – more ties • Fewer privacy/ethical issues – May improve validity of data *how quickly can something flowing through the network reach this node?
- 11. Comparison – cont. • ENRD combines advantages of mainstream social science data with social network perspective •And many network phenomena and measures do not seem to require anything more than ego network data – E.g., degree centrality, homophily, structural holes • Or is this a misconception? Full Network Analysis Mainstream Social Science Ego Networks perspectivedata
- 12. What can you do with ego net data? • (if you only have) Ties to alters –Network size for each kind of tie (e.g., number of friends) • (if you also have) Alter attributes – Network composition (e.g., number of friends who are top‐level managers) • Testing homophily • (if you also have) Ties among alters – Structural holes – All group‐level network measures (e.g., density of ties among friends; avg distance; no. of components)
- 13. Number of ties • Basically, this is network size – Can be calculated different size for each type of tie, or all ties combined •Very well studied variable; has been very productive – Health, power, satisfaction • And there is still more to study – Number of negative ties is understudied • how many enemies, rivals, competitors, energy‐drains do you have? – Multiplex ties • Suppose most of your friends are also co‐workers – Most relationships A—B consist of both the friend and co‐worker tie • What are the consequences for ego? Less freedom? More strain?
- 14. Does FNRD have any advantages for studying network size? • In context of defined groups, concept of non‐ties is meaningful – E.g., can compare ego1’s number of work friends with ego2’s number of work friends, because we know many friends were possible in each work setting –If we want to use no. of friends as measure of ability to make friends, we want to divide by size of potential partners pool 1 2
- 15. Network Composition • Measures summarizing the kinds of people in a person’s ego network – Frequencies (e.g., number of rich friends) –Central tendency (e.g., avg wealth of friends) • Measures describing the amount of heterogeneity in a person’s ego network – Heterogeneity measures (e.g., Blau, IQV) • Measures describing the similarity of a person’s own attributes with those of their alters – E.g., homophily measures
- 16. Network Composition Property of network: Categorical AttributesContinuous Attributes Summary of kind of alters ego tends has, based on a given attribute (e.g., wealth) Example: Does ego have mostly rich or mostly poor friends? How many of each? Example: What is the average wealth of ego’s friends? Measures: frequencies, proportions Measures: mean, median Variability in the kinds of alter an ego has, based on given attribute Example: whether ego has equal number of rich, middle, and poor friends, or mostly one kind Example: variance in wealth of person’s friends Measures: Blau/Herfindahl heterogeneity; Agresti IQV Measures: std deviation, variance Similarity of ego to alters with respect to given attribute Example: Prop. of ego’s friends who are same wealth class as ego Example: Similarity between ego’s wealth and friends’ wealth Measures: E‐I index; PBSC; Yules Q; Q modularity Measures: avg euclidean distance; identity coef.
- 17. Direction of Causality SELECTION Ego selects alters based on attributes INFLUENCE Ego influences alters to have attribute Summary of kind of alter an ego tends to have, based on a given attribute (e.g., wealth) Ego tends to seekout rich friends Ego tends to give friends money, opportunities for investment Variability in the kinds of alter an ego has, based on given attribute Ego seeks out diversity and has the skills to manage it Ego encourages alters to develop unique perspectives Similarity of ego to alters with respect to given attribute Homophily: ego attracted by people similar to self Diffusion: ego’s attitudes are contagious
- 18. Measurement of homophily* • What we can measure is the extent to which alters resemble egos • So, can we measure homophilyusing ENRD data? – It would seem obvious that we can … *Actually, measurement of similarity – homophily implies a certain direction of causality which can only be inferred by other means, if at all
- 19. Who do youdiscuss important matters with? Male Female Male 1245 748 Female 970 1515 Age < 30 30-39 40-49 50-59 60+ < 30 567 186 183 155 56 30 - 39 191 501 171 128 106 40 - 49 88 170 246 84 70 50 - 59 84 100 121 210 108 60 + 34 127 138 212 387 White Black Hisp Other White 3806 29 30 20 Black 40 283 4 3 Hisp 66 6 120 1 Other 21 5 3 34 Source: Marsden, P.V. 1988. Homogeneity in confiding relations. Social Networks 10: 57‐76. General Social Survey 1985. Ego network study of 1500 Americans • Rows are egos • Columns are alters • Cells are no. of ties from type of ego to type of alter
- 20. Homophily at the individual level • Across all alters for a given ego, compute simple frequencies for the variable “has same attribute value as ego or not” –E.g., number of alters that are same gender as ego and number of alters that are not • Define a statistic such as percent homophily Same attrib value 1 0 Tie = 1 a b %H = 9/54 = 0.83 Same attrib value as ego 1 0 Tie = 1 45 9 %H = a/(a+b)
- 21. Alternative statistic: E‐I index • Given frequencies, compute – It is just a rescaling of %H = a/(a+b) •Example: Same attrib value 1 0 Tie = 1 a b Same gender as ego 1 0 Tie = 1 45 9 ab ab EI EI = (9‐45)/(9+45) = ‐0.667
- 22. But there is a small problem • Suppose we did know the full network. As a result, for a given ego we know their non‐ties as well • Both %H and E‐I show strong homophily –Yet probability of being same gender is same for ties and non‐ties – IOW, no preference for same gender. Independence. • The result from ENRD data is misleading Same attrib value 1 0 Has tie 1 45 9 0 45 9 %H = 0.83 EI = ‐0.667
- 23. With FNRD we can define better measures of homophily/influence • Yule’s Q takes into account non‐choices as well: • Example cases Same attrib value 10 Tie 1 a b 0 c d %H = 0.83, EI = ‐0.667, YQ = 0.00 bcad bcad YQ Same attrib value 1 0 Tie 1 45 9 0 45 9 Same attrib value 1 0 Tie 1 45 9 0 9 45 %H = 0.83, EI = ‐0.667, YQ = 0.92
- 24. Invariance property of Yule’s Q • Additional benefit of Yule’s Q is insensitivity to table marginals – What if you dichotomized at different level and now had twice as many 1s? •keeping preference for own kind the same – What if you had twice as many same‐gender pairs • but with same underlying preference for own kind? Same attrib 1 0 Tie 1 45 9 0 101 151 YQ = 0.76 %H = 0.83 EI = ‐0.67 Same attrib 1 0 Tie 1 180 18 0 202 151 YQ = 0.76 %H = 0.91 EI = ‐0.82 Twice as many ties and twice as many same gender dyads Yule’s Q is not “fooled” by multiplying a row or column by a constant • Takes into account category sizes An aside …
- 25. Homophily: preference vs opportunity • With ENRDs we have information on ties but not non‐ties –We can measure homophily as outcome, but not homophily as choice • Adequacy of homophily in ENRD depends on research question – If am American and 95% of my friends are American, this clearly has certain effects on me • even if this is only because 95% of people in my world are American • So ENRD is ok – But if I am trying to measure nationalistic tendencies, I need to know whether 95% is more or less than expected if a person were making choices without regard for nationality • If 95% of my non‐ties are also American, we know that I am not showing any preference for Americans – low nationalism score
- 26. Comparing individuals • With ENRD, can we at least compare egos to each other? – Some ego’s have higher E‐I index than others. Is this interpretable as preference? •In principle, yes – if egos are drawn from the same population, then … – … significantly higher homophily score indicates greater preference for own kind • In practice, not clear what “same population” means – People live in segregated worlds due to choices made by others • Example: Are male or female students here at UAB more homophilous with respect to ethnic background? • For each person, we measure homophily using %H or E‐I – Run t‐test/anova to compare genders • If all students face same ethnic environment, then significant difference in avg homophily is meaningful as difference in preference
- 27. Propinquity • Do people tend to have ties with people who are physically close by? 0 0.1 0.2 0.3 0.4 0 2040 60 80 100 Distance (meters) ProbofDailyCommunication From research by Tom Allen Distance short long Tie 1 10 500 0 10 500 • Same issues as homophily – Lack of non‐ties a problem for modeling choice
- 28. Theoretical criteria • Until now we have examined specific phenomena/measurements we are interested in – E.g., homophily •Another way to compare ENRD and FNRD is in terms of the explanatory mechanisms that are used to understand node outcomes
- 29. Perspectives of action in SNA Structuralist In the socialproduction of their existence, men inevitably enter into definite relations, which are independent of their will, namely relations of production appropriate to a given stage in the development of their material forces of production. The totality of these relations of production constitutes the economic structure of society, the real foundation, on which arises a legal and political superstructure and to which correspond definite forms of social conscious‐ ness. The mode of production of material life conditions the general process of social, political and intellectual life. It is not the consciousness of men that determines their existence, but their social existence that determines their consciousness. – Marx 1859 Preface to A Contribution to the Critique of Political Economy Cognitivist “If men define situations as real, they are real in their consequences” – W.I. Thomas Success information Actual no. of ties confidence Perceived no. of ties
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- 33. Perception and ENRD • With ENRD, all ties are perceived by ego • Therefore, ENRD works well when … •Predicting ego’s own behavior • Predicting ego outcomes based on ego’s behavior • Predicting ego outcomes AND we can assume ego is accurate in perceiving ties • Hard to use ENRD when the topic of interest is understanding perceptual accuracy – Can use hybrid designs where the alters are interviewed about ties with ego
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- 35. Variations in ego net research designs • Limited 2‐wave snowball • Key informant method –Focal individual method
- 36. 2‐wave snowball • Get alter list from ego • Now interview alters about egos and the other alters •Allows us to examine accuracy/differences in perceptions of ties
- 37. Key informant method • We are interested in ties among a set of people, but can’t interview them – E.g., politicians, celebrities, criminals •Key informants are asked to provide the entire network from their point of view • One version of this is the observational focal individual method – Follow key informants around all day and record interactions around them
- 38. Rushmore Chimpanzee study • Julie Rushmore – College of Veterinary Medicine; University of Georgia •Each of 37 chimps is chosen to be “focal” chimp for a day • Researcher follows focal chimp for entire day and records not only his/her interactions but also all other interactions within view • Result is 37 separate 37‐by‐37 matrices – a 3‐way, 1‐mode data cube rushmore@uga.edu
- 39. Sample Data AJ AL ATAZ BB BL BO BU ES AJ 33 33 33 33 17 17 20 33 AL 33 42 42 32 11 11 14 32 AT 33 42 42 32 11 11 14 32 AZ 33 42 42 32 11 11 14 32 BB 33 32 32 32 11 11 14 33 BL 17 11 11 11 11 17 17 11 BO 17 11 11 11 11 17 17 11 BU 20 14 14 14 14 17 17 14 ES 33 32 32 32 33 11 11 14 AJ AL AT AZ BB BL BO BU ES AJ 24 26 24 22 0 0 0 42 AL 24 24 24 19 0 0 0 24 AT 26 24 24 20 0 0 0 25 AZ 24 24 24 19 0 0 0 24 BB 22 19 20 19 0 0 0 20 BL 0 0 0 0 0 0 0 0 BO 0 0 0 0 0 0 0 0 BU 0 0 0 0 0 0 0 0 ES 42 24 25 24 20 0 0 0 Interactions observed while following AJ Interactions observed while following KK Only first 9 chimps shown from a 37 by 37 matrix
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Correlations among focal matrices AJ AL ATAZ BB BL BO BU ES EU KK LK LR ML MS MU MX NP OG OM OT OU PB PG QT RD ST TG TJ TS TT TU UM UN WA WL YB AJ 1.00 0.66 0.39 0.15 0.58 ‐0.11 0.36 0.25 0.63 0.18 0.68 0.63 0.53 0.58 ‐0.08 0.22 0.26 0.00 0.34 0.24 0.52 0.27 0.34 0.52 0.18 0.15 0.37 0.21 0.17 0.51 0.31 0.00 0.05 0.14 0.06 0.36 0.67 AL 0.66 1.00 0.62 0.55 0.67 0.06 0.45 0.30 0.61 0.34 0.57 0.70 0.56 0.65 ‐0.13 0.23 0.27 0.00 0.48 0.29 0.59 0.24 0.37 0.51 0.38 0.28 0.35 0.34 0.30 0.57 0.29 ‐0.09 0.06 0.01 0.20 0.33 0.76 AT 0.39 0.62 1.00 0.64 0.47 0.26 0.33 0.54 0.44 0.29 0.51 0.63 0.36 0.45 ‐0.12 0.13 0.32 0.17 0.42 0.40 0.56 0.41 0.28 0.32 0.59 0.25 0.27 0.57 0.55 0.54 0.41 ‐0.03 0.27 0.16 0.26 0.48 0.54 AZ 0.15 0.55 0.64 1.00 0.33 0.36 0.31 0.55 0.31 0.32 0.34 0.42 0.26 0.36 ‐0.10 0.05 0.22 0.22 0.47 0.56 0.52 0.45 0.12 0.28 0.57 0.23 0.42 0.68 0.63 0.51 0.45 ‐0.03 0.22 0.05 0.28 0.31 0.31 BB 0.58 0.67 0.47 0.33 1.00 0.35 0.68 0.49 0.74 0.26 0.65 0.64 0.57 0.67 ‐0.14 0.12 0.47 0.09 0.43 0.32 0.59 0.31 0.51 0.57 0.40 0.29 0.32 0.34 0.42 0.56 0.27 ‐0.09 0.15 0.10 0.18 0.42 0.73 BL ‐0.11 0.06 0.26 0.36 0.35 1.00 0.38 0.56 0.16 ‐0.03 0.16 0.14 0.12 0.22 ‐0.17 ‐0.08 0.40 0.08 0.20 0.25 0.24 0.23 0.34 0.06 0.53 0.10 0.06 0.33 0.43 0.13 0.10 ‐0.11 0.13 ‐0.08 0.20 0.30 0.09 BO 0.36 0.45 0.33 0.31 0.68 0.38 1.00 0.63 0.74 0.19 0.59 0.64 0.58 0.62 ‐0.17 ‐0.14 0.37 0.24 0.39 0.28 0.45 0.35 0.25 0.45 0.48 0.13 0.29 0.49 0.47 0.60 0.38 ‐0.14 ‐0.02 ‐0.16 ‐0.10 0.47 0.53 BU 0.25 0.30 0.54 0.55 0.49 0.56 0.63 1.00 0.49 0.09 0.59 0.57 0.32 0.49 ‐0.20 ‐0.03 0.44 0.28 0.51 0.57 0.58 0.65 0.22 0.33 0.75 0.23 0.41 0.80 0.74 0.54 0.56 ‐0.13 0.19 ‐0.10 0.10 0.73 0.40 ES 0.63 0.61 0.44 0.31 0.74 0.16 0.74 0.49 1.00 0.34 0.82 0.75 0.61 0.78 ‐0.13 0.04 0.35 0.20 0.48 0.39 0.62 0.43 0.33 0.74 0.37 0.16 0.35 0.47 0.41 0.72 0.49 ‐0.13 0.11 0.01 0.08 0.54 0.77 EU 0.18 0.34 0.29 0.32 0.26 ‐0.03 0.19 0.09 0.34 1.00 0.21 0.30 0.13 0.27 0.09 0.10 0.11 0.40 0.22 0.22 0.15 0.10 0.04 0.38 0.07 0.00 0.24 0.22 0.19 0.33 0.19 0.09 0.14 0.30 0.20 0.04 0.30 KK 0.68 0.57 0.51 0.34 0.65 0.16 0.59 0.59 0.82 0.21 1.00 0.78 0.48 0.73 ‐0.16 0.11 0.41 0.23 0.54 0.50 0.67 0.62 0.26 0.70 0.48 0.23 0.40 0.57 0.45 0.69 0.62 ‐0.12 0.10 0.03 0.11 0.68 0.70 LK 0.63 0.70 0.63 0.42 0.64 0.14 0.64 0.57 0.75 0.30 0.78 1.00 0.49 0.72 ‐0.20 0.10 0.46 0.20 0.49 0.42 0.66 0.47 0.25 0.59 0.53 0.20 0.43 0.60 0.45 0.71 0.55 ‐0.15 0.06 ‐0.04 0.07 0.66 0.76 LR 0.53 0.56 0.36 0.26 0.57 0.12 0.58 0.32 0.61 0.13 0.48 0.49 1.00 0.46 ‐0.12 ‐0.02 0.11 0.00 0.47 0.24 0.63 0.27 0.46 0.58 0.40 0.10 0.21 0.27 0.29 0.46 0.20 ‐0.10 ‐0.05 ‐0.09 ‐0.04 0.35 0.55 ML 0.58 0.65 0.45 0.36 0.67 0.22 0.62 0.49 0.78 0.27 0.73 0.72 0.46 1.00 ‐0.13 0.31 0.65 0.21 0.46 0.40 0.57 0.42 0.28 0.58 0.40 0.25 0.28 0.47 0.42 0.66 0.46 ‐0.14 0.16 0.14 0.43 0.54 0.76 MS ‐0.08 ‐0.13 ‐0.12 ‐0.10 ‐0.14 ‐0.17 ‐0.17 ‐0.20 ‐0.13 0.09 ‐0.16 ‐0.20 ‐0.12 ‐0.13 1.00 0.02 ‐0.17 0.18 ‐0.13 ‐0.10 ‐0.13 ‐0.11 ‐0.09 ‐0.10 ‐0.21 0.02 ‐0.04 ‐0.14 ‐0.12 ‐0.07 ‐0.07 0.76 0.58 0.44 0.04 ‐0.15 ‐0.10 MU 0.22 0.23 0.13 0.05 0.12 ‐0.08 ‐0.14 ‐0.03 0.04 0.10 0.11 0.10 ‐0.02 0.31 0.02 1.00 0.39 0.00 ‐0.01 ‐0.01 0.00 0.03 0.03 0.00 0.05 0.20 ‐0.08 0.07 ‐0.07 0.14 0.05 ‐0.04 0.13 0.31 0.58 0.09 0.09 MX 0.26 0.27 0.32 0.22 0.47 0.40 0.37 0.44 0.35 0.11 0.41 0.46 0.11 0.65 ‐0.17 0.39 1.00 0.23 0.20 0.23 0.27 0.25 0.23 0.17 0.36 0.06 0.07 0.31 0.36 0.31 0.23 ‐0.11 0.16 0.24 0.47 0.42 0.36 NP 0.00 0.00 0.17 0.22 0.09 0.08 0.24 0.28 0.20 0.40 0.23 0.20 0.00 0.21 0.18 0.00 0.23 1.00 0.34 0.50 0.23 0.48 0.00 0.18 0.21 ‐0.01 0.23 0.46 0.36 0.30 0.55 0.17 0.25 0.31 0.13 0.33 0.07 OG 0.34 0.48 0.42 0.47 0.43 0.20 0.39 0.51 0.48 0.22 0.54 0.49 0.47 0.46 ‐0.13 ‐0.01 0.20 0.34 1.00 0.77 0.71 0.72 0.37 0.50 0.55 0.16 0.43 0.55 0.52 0.41 0.49 ‐0.09 0.13 ‐0.03 0.18 0.53 0.48 OM 0.24 0.29 0.40 0.56 0.32 0.25 0.28 0.57 0.39 0.22 0.50 0.42 0.24 0.40 ‐0.10 ‐0.01 0.23 0.50 0.77 1.00 0.72 0.86 0.26 0.44 0.52 0.15 0.47 0.65 0.58 0.42 0.64 ‐0.06 0.21 0.03 0.24 0.53 0.36 OT 0.52 0.59 0.56 0.52 0.59 0.24 0.45 0.58 0.62 0.15 0.67 0.66 0.63 0.57 ‐0.13 0.00 0.27 0.23 0.71 0.72 1.00 0.70 0.49 0.62 0.61 0.21 0.44 0.58 0.57 0.56 0.52 ‐0.11 0.13 ‐0.01 0.19 0.59 0.69 OU 0.27 0.24 0.41 0.45 0.31 0.23 0.35 0.65 0.43 0.10 0.62 0.47 0.27 0.42 ‐0.11 0.03 0.25 0.48 0.72 0.86 0.70 1.00 0.21 0.40 0.58 0.22 0.37 0.71 0.59 0.51 0.70 ‐0.07 0.20 0.00 0.15 0.70 0.33 PB 0.34 0.37 0.28 0.12 0.51 0.34 0.25 0.22 0.33 0.04 0.26 0.25 0.46 0.28 ‐0.09 0.03 0.23 0.00 0.37 0.26 0.49 0.21 1.00 0.27 0.32 0.06 0.09 0.04 0.12 0.12 ‐0.02 ‐0.08 0.07 0.04 0.14 0.28 0.40 PG 0.52 0.51 0.32 0.28 0.57 0.06 0.45 0.33 0.74 0.38 0.70 0.59 0.58 0.58 ‐0.10 0.00 0.17 0.18 0.50 0.44 0.62 0.40 0.27 1.00 0.30 0.14 0.35 0.39 0.33 0.52 0.41 ‐0.10 0.00 0.00 0.05 0.43 0.69 QT 0.18 0.38 0.59 0.57 0.40 0.53 0.48 0.75 0.37 0.07 0.48 0.53 0.40 0.40 ‐0.21 0.05 0.36 0.21 0.55 0.52 0.61 0.58 0.32 0.30 1.00 0.25 0.20 0.71 0.59 0.47 0.43 ‐0.15 0.09 ‐0.15 0.16 0.64 0.35 RD 0.15 0.28 0.25 0.23 0.29 0.10 0.13 0.23 0.16 0.00 0.23 0.20 0.10 0.25 0.02 0.20 0.06 ‐0.01 0.16 0.15 0.21 0.22 0.06 0.14 0.25 1.00 ‐0.02 0.27 0.30 0.34 0.20 0.00 0.12 ‐0.03 0.15 0.27 0.28 ST 0.37 0.35 0.27 0.42 0.32 0.06 0.29 0.41 0.35 0.24 0.40 0.43 0.21 0.28 ‐0.04 ‐0.08 0.07 0.23 0.43 0.47 0.44 0.37 0.09 0.35 0.20 ‐0.02 1.00 0.40 0.34 0.31 0.39 0.13 0.18 0.07 0.07 0.24 0.34 TG 0.21 0.34 0.57 0.68 0.34 0.33 0.49 0.80 0.47 0.22 0.57 0.60 0.27 0.47 ‐0.14 0.07 0.31 0.46 0.55 0.65 0.58 0.71 0.04 0.39 0.71 0.27 0.40 1.00 0.69 0.72 0.80 ‐0.09 0.21 ‐0.03 0.15 0.67 0.36 TJ 0.17 0.30 0.55 0.63 0.42 0.43 0.47 0.74 0.41 0.19 0.45 0.45 0.29 0.42 ‐0.12 ‐0.07 0.36 0.36 0.52 0.58 0.57 0.59 0.12 0.33 0.59 0.30 0.34 0.69 1.00 0.60 0.56 ‐0.08 0.23 0.03 0.21 0.52 0.37 TS 0.51 0.57 0.54 0.51 0.56 0.13 0.60 0.54 0.72 0.33 0.69 0.71 0.46 0.66 ‐0.07 0.14 0.31 0.30 0.41 0.42 0.56 0.51 0.12 0.52 0.47 0.34 0.31 0.72 0.60 1.00 0.72 ‐0.09 0.15 0.03 0.10 0.52 0.59 TT 0.31 0.29 0.41 0.45 0.27 0.10 0.38 0.56 0.49 0.19 0.62 0.55 0.20 0.46 ‐0.07 0.05 0.23 0.55 0.49 0.64 0.52 0.70 ‐0.02 0.41 0.43 0.20 0.39 0.80 0.56 0.72 1.00 ‐0.06 0.21 0.01 0.10 0.56 0.36 TU 0.00 ‐0.09 ‐0.03 ‐0.03 ‐0.09 ‐0.11 ‐0.14 ‐0.13 ‐0.13 0.09 ‐0.12 ‐0.15 ‐0.10 ‐0.14 0.76 ‐0.04 ‐0.11 0.17 ‐0.09 ‐0.06 ‐0.11 ‐0.07 ‐0.08 ‐0.10 ‐0.15 0.00 0.13 ‐0.09 ‐0.08 ‐0.09 ‐0.06 1.00 0.59 0.49 0.01 ‐0.14 ‐0.10 UM 0.05 0.06 0.27 0.22 0.15 0.13 ‐0.02 0.19 0.11 0.14 0.10 0.06 ‐0.05 0.16 0.58 0.13 0.16 0.25 0.13 0.21 0.13 0.20 0.07 0.00 0.09 0.12 0.18 0.21 0.23 0.15 0.21 0.59 1.00 0.62 0.38 0.10 0.11 UN 0.14 0.01 0.16 0.05 0.10 ‐0.08 ‐0.16 ‐0.10 0.01 0.30 0.03 ‐0.04 ‐0.09 0.14 0.44 0.31 0.24 0.31 ‐0.03 0.03 ‐0.01 0.00 0.04 0.00 ‐0.15 ‐0.03 0.07 ‐0.03 0.03 0.03 0.01 0.49 0.62 1.00 0.45 ‐0.08 0.05 WA 0.06 0.20 0.26 0.28 0.18 0.20 ‐0.10 0.10 0.08 0.20 0.11 0.07 ‐0.04 0.43 0.04 0.58 0.47 0.13 0.18 0.24 0.19 0.15 0.14 0.05 0.16 0.15 0.07 0.15 0.21 0.10 0.10 0.01 0.38 0.45 1.00 0.08 0.20 WL 0.36 0.33 0.48 0.31 0.42 0.30 0.47 0.73 0.54 0.04 0.68 0.66 0.35 0.54 ‐0.15 0.09 0.42 0.33 0.53 0.53 0.59 0.70 0.28 0.43 0.64 0.27 0.24 0.67 0.52 0.52 0.56 ‐0.14 0.10 ‐0.08 0.08 1.00 0.46 YB 0.67 0.76 0.54 0.31 0.73 0.09 0.53 0.40 0.77 0.30 0.70 0.76 0.55 0.76 ‐0.10 0.09 0.36 0.07 0.48 0.36 0.69 0.33 0.40 0.69 0.35 0.28 0.34 0.36 0.37 0.59 0.36 ‐0.10 0.11 0.05 0.20 0.46 1.00 High correlation between AJ and AL indicates that the pattern of interactions among all chimps when AJ is present is very similar to the pattern when AL is present AJ AL AT AZ AJ 1.00 0.66 0.39 0.15 AL 0.66 1.00 0.62 0.55 AT 0.39 0.62 1.00 0.64 AZ 0.15 0.55 0.64 1.00
- 41. MDS of correlations AJ AL AT AZ BB BL BO BU ES EU KKLK LR ML MS MU MX NP OG OM OT OU PB PG QT RD ST TG TJ TS TT TU UM UN WA WL YB • Nodes near each other provide similar “views” of the network structure • Nodes in the core have similar views of the network –would be good choices as “key informants” • Nodes in periphery, like MU, would see a distorted view of the network
- 42. Research Agenda • Interesting research question is the relationship between network position and perception of the network • Previous work has centered on centrality greater accuracy • But aside from degree of accuracy is: what exactly is the perception from a given position? – Systematically different perceptions by Bill versus Holly – “point of view” research
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- 44. Friends named, by week Newcomb T. (1961). The acquaintance process. New York: Holt& Winston.Copyright (c) 2011 Steve Borgatti & David Dekker. Do not distribute. T0 T1 T2T3 T4 T5 T6 T7 T8 T10 T11 T12 T13 T14 T15 P1 0 1 4 1 7 5 6 6 6 7 2 7 3 7 9 P2 1 1 1 4 9 10 9 9 8 9 9 12 10 10 12 P3 6 1 3 4 8 6 7 6 5 7 8 8 3 4 7 P4 2 2 3 3 7 8 9 9 7 8 7 9 6 8 10 P5 6 1 4 3 6 5 8 8 9 8 8 9 8 9 10 P6 0 3 3 2 5 4 3 5 5 4 3 7 6 6 9 P7 2 3 3 3 7 7 8 7 6 3 3 4 5 6 5 P8 0 0 3 0 5 3 3 4 4 6 6 6 3 7 8 P9 0 1 4 4 9 9 9 9 8 6 9 9 7 8 10 P10 0 0 0 0 0 0 2 1 1 2 1 7 4 4 2 P11 3 4 2 6 6 5 7 4 7 7 5 8 7 8 7 P12 3 4 2 3 3 4 3 4 5 6 7 4 5 6 9 P13 0 1 4 4 8 6 9 6 7 7 5 6 7 7 8 P14 1 4 3 3 1 6 9 8 4 2 9 6 7 2 8 P15 5 3 0 0 0 2 5 0 0 3 2 0 0 1 1 P16 2 2 3 4 4 6 4 5 3 4 4 5 6 6 7 P17 1 5 2 2 7 6 5 5 7 5 8 7 7 7 10
- 45. No. of friends over time 0 2 4 6 8 10 12 14 T0 T1 T2T3 T4 T5 T6 T7 T8 T10 T11 T12 T13 T14 T15 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 Weeks No. of friends named
- 46. Individual degree trajectories y = 0.7321x + 1.7429 R² = 0.7161 0 2 4 6 8 10 12 14 T0 T2 T4T6 T8 T11 T13 T15 P2 P2 Linear (P2) y = ‐0.1321x + 2.5238 R² = 0.1069 0 1 2 3 4 5 6 T0 T2 T4 T6 T8 T11 T13 T15 P15 P15 Linear (P15) y = 0.3071x + 3.2762 R² = 0.5628 0 1 2 3 4 5 6 7 8 9 T0 T2 T4 T6 T8 T11 T13 T15 P11 P11 Linear (P11) y = 0.3821x + 1.6762 R² = 0.3897 0 2 4 6 8 10 T0 T2 T4 T6 T8 T11 T13 T15 P1 P1 Linear (P1)
- 47. Slopes and intercepts • Intercept is general tendency to name others as friends – Gregariousness •Slope is increase in friends over time • Can model via HLM – Time is L1 unit – Person is L2 unit • L2 regression models slope & intercept as function of ego characteristics – Optimism – Social ability person intercept slope 1 1.676 0.382 2 1.743 0.732 3 4.362 0.146 4 2.848 0.461 5 3.000 0.475 6 1.133 0.400 7 3.914 0.111 8 0.095 0.471 9 2.800 0.500 10 ‐1.029 0.329 11 3.276 0.307 12 1.933 0.325 13 2.638 0.379 14 2.581 0.286 15 2.524 ‐0.132 16 2.248 0.261 17 2.086 0.439 high increase low increase decline
- 48. Beyond network size • One ego might show no change in no. of friends and indeed not gained or lost any ties • Another ego might show no change as well, but have lost all initial ties and replaced them with equal number of completely new alters •Need to do an analysis at the tie/alter level Copyright (c) 2011 Steve Borgatti & David Dekker. Do not distribute.
- 49. T1Size T1 ties 3 T2Size T2 ties 3 NewTies Ties added at T2 2 LostTies Ties lost 2 KeptTies Ties present both time periods 1 AbsentTies Ties ABSENT both time periods 12 Changes for node RUSS Changes within ego networks T1 T2 How many ties that each node add/drop between time points?
- 50. Egonet changes T1 Size T2 Size New Ties Lost Ties Kept Ties Abse nt Ties HOLLY 33 2 2 1 12 BRAZEY 3 3 2 2 1 12 CAROL 3 3 1 1 2 13 PAM 3 3 1 1 2 13 PAT 3 3 2 2 1 12 JENNIE 3 3 0 0 3 14 PAULINE 3 3 1 1 2 13 ANN 3 3 1 1 2 13 MICHAEL 3 3 0 0 3 14 BILL 3 3 1 1 2 13 LEE 3 3 1 1 2 13 DON 3 3 0 0 3 14 JOHN 3 3 1 1 2 13 HARRY 3 3 1 1 2 13 GERY 3 3 1 1 2 13 STEVE 3 3 0 0 3 14 BERT 3 3 1 1 2 13 RUSS 3 3 2 2 1 12 Women Men ------ ------ 1 Mean 1.750 2.200 2 Std Dev 0.661 0.600 3 Sum 14.000 22.000 4 Variance 0.438 0.360 5 SSQ 28.000 52.000 6 MCSSQ 3.500 3.600 7 Euc Norm 5.292 7.211 8 Minimum 1.000 1.000 9 Maximum 3.000 3.000 10 N of Obs 8.000 10.000 Difference Sig ========== ===== -0.450 0.157 Number of ties KEPT Significance for t‐test obtained via randomization method WomenMen
- 51. Modeling homophily dynamics • Suppose blue nodes have tendency to … –Add blue friends over time – Drop red friends over time T1 T2 For clarity of exposition, the pictures are full networks, but the point is egonet change Blue egos show tendency to drop red alters T1 T2
- 52. Modeling change as a function of group membership ‐1 0 1 07 151 2 1 14 112 20 Chi‐Square 22.25 p = 0.001 Pearson Corr 0.10 P = 0.029 ‐1 0 1 Odds Odds Ratio 0 0.044 0.944 0.013 0.013 12.540 1 0.096 0.767 0.137 0.159 Whether alter is same group as ego Relationship improved (1), worsened (‐1) or stayed same P‐value constructed via QAP permutation test
- 53. The NEW ties Num New Number of New ties 2 Num FoF Number of ties between New nodes and T1 alters.2 Den FoF NumFoF divided by max possible (NumFoF expressed as a density). 0.3 3 FoF/ T1 NumFoF divided by number of T1 alters 0.6 7 FoF/ New NumFoF divided by number NumNew 1 RED are T1 BLUE are T2 GRAY are in both Making friends with friends’ friends
- 54. E0A0 = Null triads (no ties) E0A1 = Ego has not ties but the two potential alters are tied. E1A0 = Ego has tie to one alter; other potential alter is isolate. E1A1 = Ego has tie to one alter, who is tied to the other potential alter. E2A0 = (Brokerage) Ego has ties to both alters, who are not tied to each other. E2A1 = (No brokerage) Ego has ties to both alters, who are tied to each other. T1 T2 E0A0 E0A1 E1A0E1A1 E2A0 E2A1 E0A0 56 2 20 2 0 0 80 E0A1 6 14 0 4 0 1 25 E1A0 15 4 14 2 0 0 35 E1A1 3 4 0 1 1 1 10 E2A0 0 0 2 0 0 0 2 E2A1 1 0 0 0 0 0 1 81 24 36 9 1 2 153 Changes in ego’s triads RED are T1 BLUE are T2 GRAY are in both
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- 56. Summary • Distinguished between ego networks and ego network research design (personal network analysis) • Asked whether there are any advantages/disadvantages to ENRD vsFNRD when only interested in ego network variables
- 57. Summary effects vs underlying tendencies • Measurements of network size, homophily, propinquity etccan be used in two ways – Summary of ego’s exposure to what flows • Function of opportunities provided by environment – Indication of ego’s strategies in tie formation • Choices being made by the ego • Examples – Network size vs ability to make friends – Observed exogamy vs preference for out marriage ENRD FNRD Overall effects Underlying tendencies Consequences of homophily Reveal cognitive characteristics
- 58. Structuralist vs cognitivist mechanisms •Some theoretical mechanisms imply that perceptions of the network don’t matter – Information benefits of central position • Others depend crucially on perceptions – My behavior is based on my perceptions • Outcomes vs behavior • In pure ENRDs, all ties are perceived – Lack of true incoming ties – Very strong for understanding behavior – For understanding outcomes, we need additional assumption of accuracy of perception – People vary in perception accuracy
- 59. More generally • FRNDs useful for studying global network phenomena (of course) • But fundamental processes of tie formation and influence occur at the level of individual choices and behavior –Personal network analysis at the center of the network dynamics field (or should be) • When larger network properties change, it is because of ego actions • Lot of interesting work to be done on ego network change • ENRDs – Can employ standard sampling techniques • And so standard statistical methods – Cheaper & easier to deploy • Can collect richer data – more ties • Excellent fit with qualitative/case‐oriented methods – Fewer privacy/ethical issues • May improve validity of data
- 60.