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5th edition of Theory, Methods and Applications of Social Networks.International Seminar "Personal Networks: Methods and Applications"
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
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 worldAnn affects Bill, but only because she affects Pam, who affects Holly who affects those that interact with Bill
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 i is 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 ed0.29 0.50 .58 0.290.50
λ = 1.73205
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”
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”
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’sattributes: how old is alter? How happy is alter?
– Ideally, ask ego to indicate ties among the alters
Mary
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
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
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?
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?
FullNetworkAnalysis
MainstreamSocial Science
EgoNetworks
perspectivedata
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)
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?
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
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
Network CompositionProperty of network: Categorical Attributes Continuous 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/Herfindahlheterogeneity; 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 euclideandistance; identity coef.
Direction of CausalitySELECTION
Ego selects alters based on attributes
INFLUENCEEgo 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 seek out 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
Measurement of homophily*
• What we can measure is the extent to which alters resemble egos
• So, can we measure homophily using 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
Who do you discuss important matters with?
Male FemaleMale 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 10640 - 49 88 170 246 84 7050 - 59 84 100 121 210 108
60 + 34 127 138 212 387
White Black Hisp OtherWhite 3806 29 30 20Black 40 283 4 3Hisp 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
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 homophilySame attrib
value1 0
Tie = 1 a b
%H = 9/54 = 0.83
Same attribvalue as ego1 0
Tie = 1 45 9
%H = a/(a+b)
Alternative statistic: E‐I index
• Given frequencies, compute
– It is just a rescaling of %H = a/(a+b)
• Example:
Same attribvalue
1 0Tie = 1 a b
Same genderas ego
1 0Tie = 1 45 9
ababEI
EI = (9‐45)/(9+45) = ‐0.667
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 attribvalue
1 0Hastie
1 45 90 45 9
%H = 0.83EI = ‐0.667
With FNRD we can define better measures of homophily/influence
• Yule’s Q takes into account non‐choices as well:
• Example cases
Same attribvalue
1 0
Tie1 a b0 c d
%H = 0.83, EI = ‐0.667, YQ = 0.00
bcadbcadYQ
Same attribvalue
1 0
Tie 1 45 90 45 9
Same attribvalue
1 0
Tie 1 45 90 9 45
%H = 0.83, EI = ‐0.667, YQ = 0.92
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 attrib1 0
Tie1 45 90 101 151
YQ = 0.76%H = 0.83EI = ‐0.67
Sameattrib1 0
Tie1 180 180 202 151
YQ = 0.76%H = 0.91EI = ‐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 …
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
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
Propinquity
• Do people tend to have ties with people who are physically close by?
0
0.1
0.2
0.3
0.4
0 20 40 60 80 100Distance (meters)
Prob
of D
aily
Com
mun
icat
ion
From research by Tom Allen
Distanceshort long
Tie1 10 5000 10 500
• Same issues as homophily– Lack of non‐ties
a problem for modeling choice
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
Perspectives of action in SNAStructuralistIn the social production of their existence,men inevitably enter into definite relations,which are independent of their will, namelyrelations of production appropriate to a givenstage in the development of their materialforces of production. The totality ofthese relations of production constitutes theeconomic structure of society, the realfoundation, on which arises a legal andpolitical superstructure and to whichcorrespond definite forms of social conscious‐ness. The mode of production of material lifeconditions the general process of social,political and intellectual life. It is not theconsciousness of men that determines theirexistence, but their social existence thatdetermines their consciousness.
– Marx 1859 Preface to A Contribution to theCritique 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
Information benefitsof structural holes
• Burt argues that ego2 has an information advantage over ego1
• It is shape of actual network of information flow, not ego’s perception that matters
Ego 1
Ego 2
Feelings of support & belonging
• Actual shape of network may be secondary to ego’s perception
Ego 1 Ego 2
Power
• Ability to get things done may depend on the relationship between actual and perceived networks (Krackhardt) – i.e., accuracy
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
VARIANT EGO NETWORK DESIGNS
Variations in ego net research designs
• Limited 2‐wave snowball• Key informant method
– Focal individual method
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
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
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
Sample Data
AJ AL AT AZ BB BL BO BU ESAJ 33 33 33 33 17 17 20 33AL 33 42 42 32 11 11 14 32AT 33 42 42 32 11 11 14 32AZ 33 42 42 32 11 11 14 32BB 33 32 32 32 11 11 14 33BL 17 11 11 11 11 17 17 11BO 17 11 11 11 11 17 17 11BU 20 14 14 14 14 17 17 14ES 33 32 32 32 33 11 11 14
AJ AL AT AZ BB BL BO BU ESAJ 24 26 24 22 0 0 0 42AL 24 24 24 19 0 0 0 24AT 26 24 24 20 0 0 0 25AZ 24 24 24 19 0 0 0 24BB 22 19 20 19 0 0 0 20BL 0 0 0 0 0 0 0 0BO 0 0 0 0 0 0 0 0BU 0 0 0 0 0 0 0 0ES 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
Correlations among focal matricesAJ AL AT AZ 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 0.67AL 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 0.76AT 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 0.54AZ 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 0.31BB 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 0.73BL ‐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 0.09BO 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 0.53BU 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 0.40ES 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 0.77EU 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 0.30KK 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 0.70LK 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 0.76LR 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 0.55ML 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 0.76MS ‐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 ‐0.10MU 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 0.09MX 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 0.36NP 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 0.07OG 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 0.48OM 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 0.36OT 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 0.69OU 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 0.33PB 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 0.40PG 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 0.69QT 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 0.35RD 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 0.28ST 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 0.34TG 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 0.36TJ 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 0.37TS 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 0.59TT 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 0.36TU 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 ‐0.10UM 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 0.11UN 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 0.05WA 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 0.20WL 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 0.46YB 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 AZAJ 1.00 0.66 0.39 0.15AL 0.66 1.00 0.62 0.55AT 0.39 0.62 1.00 0.64AZ 0.15 0.55 0.64 1.00
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
TGTJ
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
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
LONGITUDINAL ANALYSIS
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 T2 T3 T4 T5 T6 T7 T8 T10 T11 T12 T13 T14 T15P1 0 1 4 1 7 5 6 6 6 7 2 7 3 7 9P2 1 1 1 4 9 10 9 9 8 9 9 12 10 10 12P3 6 1 3 4 8 6 7 6 5 7 8 8 3 4 7P4 2 2 3 3 7 8 9 9 7 8 7 9 6 8 10P5 6 1 4 3 6 5 8 8 9 8 8 9 8 9 10P6 0 3 3 2 5 4 3 5 5 4 3 7 6 6 9P7 2 3 3 3 7 7 8 7 6 3 3 4 5 6 5P8 0 0 3 0 5 3 3 4 4 6 6 6 3 7 8P9 0 1 4 4 9 9 9 9 8 6 9 9 7 8 10P10 0 0 0 0 0 0 2 1 1 2 1 7 4 4 2P11 3 4 2 6 6 5 7 4 7 7 5 8 7 8 7P12 3 4 2 3 3 4 3 4 5 6 7 4 5 6 9P13 0 1 4 4 8 6 9 6 7 7 5 6 7 7 8P14 1 4 3 3 1 6 9 8 4 2 9 6 7 2 8P15 5 3 0 0 0 2 5 0 0 3 2 0 0 1 1P16 2 2 3 4 4 6 4 5 3 4 4 5 6 6 7P17 1 5 2 2 7 6 5 5 7 5 8 7 7 7 10
No. of friends over time
0
2
4
6
8
10
12
14
T0 T1 T2 T3 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 frie
nds n
amed
Individual degree trajectories
y = 0.7321x + 1.7429R² = 0.7161
0
2
4
6
8
10
12
14
T0 T2 T4 T6 T8 T11 T13 T15
P2
P2
Linear (P2)
y = ‐0.1321x + 2.5238R² = 0.1069
0
1
2
3
4
5
6
T0 T2 T4 T6 T8 T11 T13 T15
P15
P15
Linear (P15)
y = 0.3071x + 3.2762R² = 0.5628
0123456789
T0 T2 T4 T6 T8 T11 T13 T15
P11
P11
Linear (P11)
y = 0.3821x + 1.6762R² = 0.3897
0
2
4
6
8
10
T0 T2 T4 T6 T8 T11 T13 T15
P1
P1
Linear (P1)
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 slope1 1.676 0.3822 1.743 0.7323 4.362 0.1464 2.848 0.4615 3.000 0.4756 1.133 0.4007 3.914 0.1118 0.095 0.4719 2.800 0.50010 ‐1.029 0.32911 3.276 0.30712 1.933 0.32513 2.638 0.37914 2.581 0.28615 2.524 ‐0.13216 2.248 0.26117 2.086 0.439
high increase
low increase
decline
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.
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?
Egonet changesT1Size
T2Size
NewTies
LostTies
KeptTies
AbsentTies
HOLLY 3 3 2 2 1 12BRAZEY 3 3 2 2 1 12CAROL 3 3 1 1 2 13PAM 3 3 1 1 2 13PAT 3 3 2 2 1 12JENNIE 3 3 0 0 3 14PAULINE 3 3 1 1 2 13ANN 3 3 1 1 2 13MICHAEL 3 3 0 0 3 14BILL 3 3 1 1 2 13LEE 3 3 1 1 2 13DON 3 3 0 0 3 14JOHN 3 3 1 1 2 13HARRY 3 3 1 1 2 13GERY 3 3 1 1 2 13STEVE 3 3 0 0 3 14BERT 3 3 1 1 2 13RUSS 3 3 2 2 1 12
Women Men ------ ------
1 Mean 1.750 2.2002 Std Dev 0.661 0.6003 Sum 14.000 22.0004 Variance 0.438 0.3605 SSQ 28.000 52.0006 MCSSQ 3.500 3.6007 Euc Norm 5.292 7.2118 Minimum 1.000 1.0009 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
Wom
enMen
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 egonetchange
Blue egos show tendency to drop red alters
T1 T2
Modeling change as a function of group membership
‐1 0 10 7 151 21 14 112 20
Chi‐Square 22.25 p = 0.001Pearson Corr 0.10 P = 0.029
‐1 0 1 Odds Odds Ratio0 0.044 0.944 0.013 0.013
12.5401 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
The NEW ties
NumNew Number of New ties 2
NumFoF
Number of ties between New nodes and T1 alters. 2
DenFoF
NumFoF divided by max possible (NumFoF expressed as a density).
0.33
FoF/T1
NumFoF divided by number of T1 alters
0.67
FoF/New
NumFoF divided by number NumNew 1
RED are T1BLUE are T2GRAY are in both
Making friends with friends’ friends
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 E1A0 E1A1 E2A0 E2A1E0A0 56 2 20 2 0 0 80E0A1 6 14 0 4 0 1 25E1A0 15 4 14 2 0 0 35E1A1 3 4 0 1 1 1 10E2A0 0 0 2 0 0 0 2E2A1 1 0 0 0 0 0 1
81 24 36 9 1 2 153
Changes in ego’s triads
RED are T1BLUE are T2GRAY are in both
CONCLUDING REMARKS
Summary
• Distinguished between ego networks and ego network research design (personal network analysis)
• Asked whether there are any advantages/disadvantages to ENRD vs FNRD when only interested in ego network variables
Summary effects vs underlying tendencies
• Measurements of network size, homophily, propinquity etc can 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
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
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
Gracias!Thank you for inviting me!
Jose‐Luis MolinaPilar Marques
Carlos Lozares and the QUIT
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