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Tom A.B. Snijders Multilevel Flavours Manchester Keynote 1 / 63
The Multiple Flavours of Multilevel Issuesfor Networks
Tom A.B. Snijders
University of OxfordUniversity of Groningen
June 19, 2012
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 2 / 63
Network analysis,certainly multilevel network analysis,is a cooperative venture ...
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 3 / 63
Multiple Flavours
As a statistician, for me originallymultilevel analysis was about nested data sets.
Then I learned that for sociologists, there is interestin the theoretical distinction between the levels:e.g., pupils in schools exemplifynot only multiple populations for whichinference sample ⇒ population is important,but also individuals in social contexts, anddifferent sets of actors mutually interacting.
This variety further multiplieswhen you think of network analysis.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 4 / 63
Multiple Flavours
As a statistician, for me originallymultilevel analysis was about nested data sets.
Then I learned that for sociologists, there is interestin the theoretical distinction between the levels:e.g., pupils in schools exemplifynot only multiple populations for whichinference sample ⇒ population is important,but also individuals in social contexts, anddifferent sets of actors mutually interacting.
This variety further multiplieswhen you think of network analysis.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 4 / 63
Multiple Flavours
As a statistician, for me originallymultilevel analysis was about nested data sets.
Then I learned that for sociologists, there is interestin the theoretical distinction between the levels:e.g., pupils in schools exemplifynot only multiple populations for whichinference sample ⇒ population is important,but also individuals in social contexts, anddifferent sets of actors mutually interacting.
This variety further multiplieswhen you think of network analysis.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 4 / 63
Multiple Flavours Whose pictures?
Where are we @?
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 5 / 63
Multiple Flavours Whose pictures?
Where are we @?
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 6 / 63
Multiple Flavours Whose pictures?
Where are we @?
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 7 / 63
Multiple Flavours Whose pictures?
Where are we @?
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 8 / 63
Multiple Flavours Whose pictures?
Where are we @?
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 9 / 63
Multiple Flavours
What is essential for ‘multilevel’ point of view:
Units of different natures;
these have their own type of influence on variables;
random/unexplained variability associated with each ‘level’.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 10 / 63
Multiple Flavours
What is essential for ‘multilevel’ point of view:
Units of different natures;
these have their own type of influence on variables;
random/unexplained variability associated with each ‘level’.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 10 / 63
Multiple Flavours
What is essential for ‘multilevel’ point of view:
Units of different natures;
these have their own type of influence on variables;
random/unexplained variability associated with each ‘level’.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 10 / 63
Multiple Flavours
What is essential for ‘multilevel’ point of view:
Units of different natures;
these have their own type of influence on variables;
random/unexplained variability associated with each ‘level’.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 10 / 63
Multiple Flavours
1 levels in one network
2 multiple parallel networks:replication, populations of networks
3 multiple actor setsand multiple types of relation
4 large networks
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 11 / 63
Multiple Flavours
1 levels in one network
2 multiple parallel networks:replication, populations of networks
3 multiple actor setsand multiple types of relation
4 large networks
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 11 / 63
Multiple Flavours
1 levels in one network
2 multiple parallel networks:replication, populations of networks
3 multiple actor setsand multiple types of relation
4 large networks
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 11 / 63
Multiple Flavours
1 levels in one network
2 multiple parallel networks:replication, populations of networks
3 multiple actor setsand multiple types of relation
4 large networks
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 11 / 63
Levels in One Network
1One Network, Multiple Levels
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 12 / 63
Levels in One Network
David Krackhardt, in his 2012 Sunbelt Keynote Lecture,talked about the multiple levels of analysis in a network:
in a network with N actors,level L is represented by those issueswhere the number of cases is of order NL .
Thus,
Level 1 Actors / Nodes
Level 2 Dyads / Ties
Level 3 Triads
Higher Larger subgroups ∼ hypergraph models
Level 0 Network
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 13 / 63
Levels in One Network
David Krackhardt, in his 2012 Sunbelt Keynote Lecture,talked about the multiple levels of analysis in a network:
in a network with N actors,level L is represented by those issueswhere the number of cases is of order NL .
Thus,
Level 1 Actors / Nodes
Level 2 Dyads / Ties
Level 3 Triads
Higher Larger subgroups ∼ hypergraph models
Level 0 Network
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 13 / 63
Levels in One Network
David Krackhardt, in his 2012 Sunbelt Keynote Lecture,talked about the multiple levels of analysis in a network:
in a network with N actors,level L is represented by those issueswhere the number of cases is of order NL .
Thus,
Level 1 Actors / Nodes
Level 2 Dyads / Ties
Level 3 Triads
Higher Larger subgroups ∼ hypergraph models
Level 0 Network
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 13 / 63
Levels in One Network
David Krackhardt, in his 2012 Sunbelt Keynote Lecture,talked about the multiple levels of analysis in a network:
in a network with N actors,level L is represented by those issueswhere the number of cases is of order NL .
Thus,
Level 1 Actors / Nodes
Level 2 Dyads / Ties
Level 3 Triads
Higher Larger subgroups ∼ hypergraph models
Level 0 Network
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 13 / 63
Levels in One Network
David Krackhardt, in his 2012 Sunbelt Keynote Lecture,talked about the multiple levels of analysis in a network:
in a network with N actors,level L is represented by those issueswhere the number of cases is of order NL .
Thus,
Level 1 Actors / Nodes
Level 2 Dyads / Ties
Level 3 Triads
Higher Larger subgroups ∼ hypergraph models
Level 0 Network
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 13 / 63
Levels in One Network
David Krackhardt, in his 2012 Sunbelt Keynote Lecture,talked about the multiple levels of analysis in a network:
in a network with N actors,level L is represented by those issueswhere the number of cases is of order NL .
Thus,
Level 1 Actors / Nodes
Level 2 Dyads / Ties
Level 3 Triads
Higher Larger subgroups ∼ hypergraph models
Level 0 Network
.Tom A.B. Snijders Multilevel Flavours Manchester Keynote 13 / 63
Levels in One Network
The recognition and distinction of actors and dyadsis fundamental for the graph-theoretic basisof network analysis.
Triads are fundamental for the sociological approachto social networks since Simmel.
Hypergraph models are not used so very much.They are a natural representation, e.g., foractivities occurring in groups andemails with multiple recipients.
Theoretical interest for the distinctionbetween the actor and dyad levelsbecomes even more interesting with multivariate networks.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 14 / 63
Levels in One Network
The recognition and distinction of actors and dyadsis fundamental for the graph-theoretic basisof network analysis.
Triads are fundamental for the sociological approachto social networks since Simmel.
Hypergraph models are not used so very much.They are a natural representation, e.g., foractivities occurring in groups andemails with multiple recipients.
Theoretical interest for the distinctionbetween the actor and dyad levelsbecomes even more interesting with multivariate networks.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 14 / 63
Levels in One Network
The recognition and distinction of actors and dyadsis fundamental for the graph-theoretic basisof network analysis.
Triads are fundamental for the sociological approachto social networks since Simmel.
Hypergraph models are not used so very much.They are a natural representation, e.g., foractivities occurring in groups andemails with multiple recipients.
Theoretical interest for the distinctionbetween the actor and dyad levelsbecomes even more interesting with multivariate networks.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 14 / 63
Levels in One Network
The recognition and distinction of actors and dyadsis fundamental for the graph-theoretic basisof network analysis.
Triads are fundamental for the sociological approachto social networks since Simmel.
Hypergraph models are not used so very much.They are a natural representation, e.g., foractivities occurring in groups andemails with multiple recipients.
Theoretical interest for the distinctionbetween the actor and dyad levelsbecomes even more interesting with multivariate networks.
.Tom A.B. Snijders Multilevel Flavours Manchester Keynote 14 / 63
Levels in One Network
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 15 / 63
Levels in One Network
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 16 / 63
Levels in One Network Relations impinge on relations
Multilevel issues in multivariate networks
... on the variety of how relations can affect relations ...
(cf. also the algebraic approach;e.g., work by Pattison & Breiger.)
Here the various levels are not nested:
ties, dyads, actors, triads, subgroups, ...,
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 17 / 63
Levels in One Network Relations impinge on relations
Multilevel issues in multivariate networks
... on the variety of how relations can affect relations ...
(cf. also the algebraic approach;e.g., work by Pattison & Breiger.)
Here the various levels are not nested:
ties, dyads, actors, triads, subgroups, ...,
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 17 / 63
Levels in One Network Relations impinge on relations
Multilevel issues in multivariate networks
... on the variety of how relations can affect relations ...
(cf. also the algebraic approach;e.g., work by Pattison & Breiger.)
Here the various levels are not nested:
ties, dyads, actors, triads, subgroups, ...,
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 17 / 63
Levels in One Network Relations impinge on relations
Different relations can impinge on one anotherin many different ways.
Dyad level
direct association(within tie)entrainment
mixed reciprocity
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 18 / 63
Levels in One Network Relations impinge on relations
Different relations can impinge on one anotherin many different ways.
Dyad level
direct association(within tie)entrainment
mixed reciprocity
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 18 / 63
Levels in One Network Relations impinge on relations
Different relations can impinge on one anotherin many different ways.
Dyad level
direct association(within tie)entrainment
mixed reciprocity
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 18 / 63
Levels in One Network Relations impinge on relations
Different relations can impinge on one anotherin many different ways.
Dyad level
direct association(within tie)entrainment
mixed reciprocity
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 18 / 63
Levels in One Network Relations impinge on relations
Different relations can impinge on one anotherin many different ways.
Dyad level
direct association(within tie)entrainment
mixed reciprocity
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 18 / 63
Levels in One Network Relations impinge on relations
Actor level
mixed popularity
mixed activity
mixed twopathity
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 19 / 63
Levels in One Network Relations impinge on relations
Actor level
mixed popularity
mixed activity
mixed twopathity
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 19 / 63
Levels in One Network Relations impinge on relations
Actor level
mixed popularity
mixed activity
mixed twopathity
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 19 / 63
Levels in One Network Relations impinge on relations
Actor level
mixed popularity
mixed activity
mixed twopathity
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 19 / 63
Levels in One Network Relations impinge on relations
Actor level
mixed popularity
mixed activity
mixed twopathity
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 19 / 63
Levels in One Network Relations impinge on relations
Actor level
mixed popularity
mixed activity
mixed twopathity
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 19 / 63
Levels in One Network Relations impinge on relations
Triad level
mixedtransitive closure
agreement ⇒red tie
. . . and other tie orientations . . .
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 20 / 63
Levels in One Network Relations impinge on relations
Triad level
mixedtransitive closure
agreement ⇒red tie
. . . and other tie orientations . . .
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 20 / 63
Levels in One Network Relations impinge on relations
Triad level
mixedtransitive closure
agreement ⇒red tie
. . . and other tie orientations . . .
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 20 / 63
Levels in One Network Relations impinge on relations
Triad level
mixedtransitive closure
agreement ⇒red tie
. . . and other tie orientations . . .
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 20 / 63
Levels in One Network Relations impinge on relations
Triad level
mixedtransitive closure
agreement ⇒red tie
. . . and other tie orientations . . .
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 20 / 63
Levels in One Network Relations impinge on relations
This type of cross-network dependencies is discussedfor cross-sectional observationsin Wasserman & Pattison (1999),with examples in Lazega & Pattison (1999).
For longitudinal observationsdependencies are multiplied,because we must distinguish betweenthe dependent and the explanatory(antecedent – subsequent) relations.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 21 / 63
Levels in One Network Multivariate SAOMs
Stochastic Actor-Oriented Models
Dynamics of multivariate networks can be represented bystochastic actor-oriented models as a direct extensionof such models for single networks.
(Snijders, Lomi & Torlò, Social Networks, in press.)
Multivariate dynamics modeled as continuous-time Markovchain, with state = the multivariate network,where tie variables change one by one.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 22 / 63
Levels in One Network Multivariate SAOMs
This can be extended by dependentbehaviour variables and/or two-mode networks.
Note that in Markov process modeling,extending the state space meansrelaxing the Markov assumption:the current state then provides more information.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 23 / 63
Levels in One Network Example: Vanina’s MBA study
Example
Research withVanina Torlò, Alessandro Lomi, Christian Steglich.
International MBA program in Italy;75 students; 3 waves.
1 Friendship
2 Advice:To whom do you go for help if you missed a class, etc.
3 Communication:With whom do you talk regularly.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 24 / 63
Levels in One Network Example: Vanina’s MBA study
Example
Research withVanina Torlò, Alessandro Lomi, Christian Steglich.
International MBA program in Italy;75 students; 3 waves.
1 Friendship
2 Advice:To whom do you go for help if you missed a class, etc.
3 Communication:With whom do you talk regularly.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 24 / 63
Levels in One Network Example: Vanina’s MBA study
Example
Research withVanina Torlò, Alessandro Lomi, Christian Steglich.
International MBA program in Italy;75 students; 3 waves.
1 Friendship
2 Advice:To whom do you go for help if you missed a class, etc.
3 Communication:With whom do you talk regularly.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 24 / 63
Levels in One Network Example: Vanina’s MBA study
Results will be presented comparingunivariate and multivariate models.
The difference shows which parts of the rulesgoverning the dynamics of each of the networksare mediated by the other networks.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 25 / 63
Levels in One Network Example: Vanina’s MBA study
Results: Friendship, univariate – multivariateuni multi
Effect par. (s.e.) par. (s.e.)
Out-degree –1.840 (0.233) –4.311 (0.395)Reciprocity 1.604 (0.097) 0.756 (0.184) ⇐Transitive triplets 0.188 (0.017) 0.150 (0.024)3-cycles –0.095 (0.030) –0.065 (0.037)Indegree popularity (p) 0.218 (0.062) 0.292 (0.104)Outdegree popularity (p) –0.383 (0.065) –0.237 (0.085) ←Outdegree activity (p) –0.079 (0.041) 0.156 (0.044) ⇐Sex alter –0.016 (0.070) –0.061 (0.078)Sex ego –0.158 (0.070) –0.102 (0.079)Same sex 0.277 (0.065) 0.144 (0.078) ←Same nationality 0.240 (0.080) 0.208 (0.091)Performance alter –0.015 (0.023) –0.017 (0.030)Performance ego –0.076 (0.024) –0.081 (0.025)Performance similarity 0.764 (0.188) 0.367 (0.224) ←
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 26 / 63
Levels in One Network Example: Vanina’s MBA study
Results: Friendship (across networks)
Effect par. (s.e.)
Advice ⇒ Friendship 0.842 (0.256)Reciprocal advice ⇒ Friendship 0.222 (0.209)Advice ind. ⇒ Friendship popularity –0.211 (0.071)Advice outd. ⇒ Friendship activity –0.143 (0.077)Communication ⇒ Friendship 1.694 (0.197)Reciprocal Comm. ⇒ Friendship 0.415 (0.225)Comm. ind. ⇒ Friendship popularity 0.112 (0.096)Comm. outd. ⇒ Friendship popularity –0.087 (0.058)Comm. outd. ⇒ Friendship activity –0.231 (0.061)
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 27 / 63
Levels in One Network Example: Vanina’s MBA study
Results: Advice, univariate – multivariateuni multi
Effect par. (s.e.) par. (s.e.)
Out-degree –2.267 (0.321) –5.129 (0.661)Reciprocity 1.329 (0.131) 0.314 (0.170) ⇐Transitive triplets 0.320 (0.038) 0.174 (0.045) ⇐3-cycles –0.065 (0.061) –0.103 (0.069)Indegree popularity (p) 0.245 (0.057) 0.293 (0.094)Outdegree popularity (p) –0.346 (0.143) 0.073 (0.225) ←Outdegree activity (p) –0.088 (0.062) 0.150 (0.080) ←Sex alter –0.043 (0.092) –0.002 (0.103)Sex ego –0.269 (0.096) –0.174 (0.102)Same sex 0.168 (0.086) 0.080 (0.102)Same nationality 0.450 (0.124) 0.371 (0.127)Performance alter 0.129 (0.036) 0.164 (0.047)Performance ego –0.107 (0.034) –0.071 (0.037)Performance similarity 0.735 (0.245) –0.003 (0.268) ⇐
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 28 / 63
Levels in One Network Example: Vanina’s MBA study
Results: Advice (across networks)
Effect par. (s.e.)
Friendship ⇒ Advice 0.670 (0.367)Reciprocal friendship ⇒ Advice –0.113 (0.210)Friendship ind. ⇒ Advice popularity –0.269 (0.130)Friendship outd. ⇒ Advice activity –0.199 (0.077)Communication ⇒ Advice 1.533 (0.339)Reciprocal Comm. ⇒ Advice 0.632 (0.253)Comm. ind. ⇒ Advice popularity 0.100 (0.124)Comm. outd. ⇒ Advice activity –0.189 (0.077)
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 29 / 63
Levels in One Network Example: Vanina’s MBA study
Communication, univariate – multivariateuni multi
Effect par. (s.e.) par. (s.e.)
Out-degree –1.116 (0.237) –1.977 (0.433)Reciprocity 1.334 (0.068) 0.941 (0.110) ⇐Transitive triplets 0.127 (0.010) 0.104 (0.011) ←3-cycles –0.035 (0.025) 0.006 (0.023)Indegree popularity (p) 0.216 (0.043) 0.254 (0.063)Outdegree popularity (p) –0.429 (0.077) –0.481 (0.081)Outdegree activity (p) –0.057 (0.027) 0.096 (0.035) ⇐Sex alter –0.016 (0.058) –0.012 (0.057)Sex ego –0.160 (0.054) –0.114 (0.061)Same sex 0.206 (0.054) 0.139 (0.055)Same nationality 0.009 (0.061) –0.083 (0.065)Performance alter –0.007 (0.019) –0.009 (0.023)Performance ego –0.080 (0.019) –0.048 (0.023)Performance similarity 0.580 (0.129) 0.552 (0.161)
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 30 / 63
Levels in One Network Example: Vanina’s MBA study
Results: Communication (across networks)
Effect par. (s.e.)
Friendship ⇒ Comm. 1.792 (0.216)Reciprocal friendship ⇒ Comm. –0.011 (0.165)Friendship ind. ⇒ Comm. popularity –0.051 (0.055)Friendship outd. ⇒ Comm. activity –0.101 (0.038)Closure friendship ⇒ Comm. –0.127 (0.033)Advice ⇒ Comm. 0.945 (0.256)Reciprocal Advice ⇒ Comm. 0.720 (0.227)Advice ind. ⇒ Comm. popularity 0.027 (0.045)Advice outd. ⇒ Comm. activity 0.051 (0.053)Advice ind. ⇒ Comm. activity –0.127 (0.043)
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 31 / 63
Levels in One Network Example: Vanina’s MBA study
Results: Communication (across networks)
Effect par. (s.e.)
Friendship ⇒ Comm. 1.792 (0.216)Reciprocal friendship ⇒ Comm. –0.011 (0.165)Friendship ind. ⇒ Comm. popularity –0.051 (0.055)Friendship outd. ⇒ Comm. activity –0.101 (0.038)Closure friendship ⇒ Comm. –0.127 (0.033) ⇐Advice ⇒ Comm. 0.945 (0.256)Reciprocal Advice ⇒ Comm. 0.720 (0.227)Advice ind. ⇒ Comm. popularity 0.027 (0.045)Advice outd. ⇒ Comm. activity 0.051 (0.053)Advice ind. ⇒ Comm. activity –0.127 (0.043)
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 31 / 63
Levels in One Network Example: Vanina’s MBA study
Dyad level
Dyad level C
A
F
All relations positively associated within dyads,direct effects stronger than reciprocal effects.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 32 / 63
Levels in One Network Example: Vanina’s MBA study
Actor level, incoming
Actor level:incoming ties(popularity)(red =negative association)
C
A
F
At actor-level for incoming ties:friendship and advice negatively associated,positive association communication ⇒ friendship.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 33 / 63
Levels in One Network Example: Vanina’s MBA study
Actor level, outgoing
Actor level:outgoing ties(activity)(red =negative association)
C
A
F
At actor-level for outgoing ties:all relations weakly negatively related;
A → C is mixed effect:incoming advice ties lead to less comm. activity.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 34 / 63
Levels in One Network Example: Vanina’s MBA study
Triad level
negative mixed closureFriendsh. ; Comm.
F F
C
Note that this is an effect additional to thepositive triadic closure of friendshipand the direct dyadic effect of friendship on communication.This will be taken up below.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 35 / 63
Levels in One Network Example: Vanina’s MBA study
Conclusions: levels
Dyad level and actor level tell different stories.
Individuals specialize:
Tied dyads tend to have multiplex ties:advice and friendship.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 36 / 63
Levels in One Network Example: Vanina’s MBA study
Conclusions: levels
Dyad level and actor level tell different stories.
Individuals specialize: learning⇔ sociability
Tied dyads tend to have multiplex ties:advice and friendship.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 36 / 63
Levels in One Network Example: Vanina’s MBA study
Conclusions: levels
Dyad level and actor level tell different stories.
Individuals specialize: advice⇔ friendship
Tied dyads tend to have multiplex ties:advice and friendship.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 36 / 63
Levels in One Network Example: Vanina’s MBA study
Conclusions: levels
Dyad level and actor level tell different stories.
Individuals specialize: advice⇔ friendship
Tied dyads tend to have multiplex ties:advice and friendship.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 36 / 63
Levels in One Network Example: Vanina’s MBA study
Conclusions: dyad level
Cross-dependencies between networks changethe representation of the internal dynamics:Observed reciprocation and homophily for networksare partly accounted for by multiplex entrainmentand reciprocation & homophily in the other networks;this is the case especially for advice;
homophily in friendship mediated by communication;
performance homophily remains only for communication;
homophily in advice remains only for nationality.
Communicate with those having similar performance,
and they will advise you.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 37 / 63
Levels in One Network Example: Vanina’s MBA study
Conclusions: dyad level
Cross-dependencies between networks changethe representation of the internal dynamics:Observed reciprocation and homophily for networksare partly accounted for by multiplex entrainmentand reciprocation & homophily in the other networks;this is the case especially for advice;
homophily in friendship mediated by communication;
performance homophily remains only for communication;
homophily in advice remains only for nationality.
Communicate with those having similar performance,
and they will advise you.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 37 / 63
Levels in One Network Example: Vanina’s MBA study
Conclusions: dyad level
Cross-dependencies between networks changethe representation of the internal dynamics:Observed reciprocation and homophily for networksare partly accounted for by multiplex entrainmentand reciprocation & homophily in the other networks;this is the case especially for advice;
homophily in friendship mediated by communication;
performance homophily remains only for communication;
homophily in advice remains only for nationality.
Communicate with those having similar performance,
and they will advise you.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 37 / 63
Levels in One Network Example: Vanina’s MBA study
Conclusions: triad level
Most cross-network triadic effects disappearwhen controlling for actor-level dependencies.
This illustrates/generalizes Feld’s (ASR 1982) remarkthat unmodeled degree heterogeneitymay lead to spurious conclusions of transitivity.
The only remaining cross-network triadic effect is thenegative mixed closure Friendship ; Communication,
counteracting the positive dyadic dependency F⇔ C;
they communicate relatively less with friends of friends
who are not also direct friends.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 38 / 63
Levels in One Network Example: Vanina’s MBA study
Conclusions: triad level
Most cross-network triadic effects disappearwhen controlling for actor-level dependencies.
This illustrates/generalizes Feld’s (ASR 1982) remarkthat unmodeled degree heterogeneitymay lead to spurious conclusions of transitivity.
The only remaining cross-network triadic effect is thenegative mixed closure Friendship ; Communication,counteracting the positive dyadic dependency F⇔ C;
they communicate relatively less with friends of friends
who are not also direct friends.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 38 / 63
Levels in One Network Network Theory
Network Theory Pattern ???There are two main networks (friendship and advice),representing interactions that are connected totwo distinct goals: social well-being and academic success.
The two goals are not contradictory but pursuing themdemands time – a limited resource.
At the dyadic level multiplexity is dominant,leading to positive association between the networks,related to multi-functionality of personal contacts;
at the actor level, specialization is dominant(depending on preferences and comparative advantage),leading to negative association between the networks.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 39 / 63
Levels in One Network Network Theory
Network Theory Pattern ???There are two main networks (friendship and advice),representing interactions that are connected totwo distinct goals: social well-being and academic success.
The two goals are not contradictory but pursuing themdemands time – a limited resource.
At the dyadic level multiplexity is dominant,leading to positive association between the networks,related to multi-functionality of personal contacts;
at the actor level, specialization is dominant(depending on preferences and comparative advantage),leading to negative association between the networks.
.Tom A.B. Snijders Multilevel Flavours Manchester Keynote 39 / 63
Levels in One Network Network Theory
Here only networks are considered;it would be interesting to combine thiswith individual goal achievement results.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 40 / 63
Multiple Parallel Networks
2Multiple Parallel Networks
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 41 / 63
Multiple Parallel Networks Sample from a population of networks
Multilevel network analysis in the sense of analyzingmultiple similar networks, mutually independent,permits research to transcend the level ofnetwork as case studies,and to generalize to a population of networks.
This was proposed by Snijders & Baerveldt(J. Math. Soc. 2003).
Also see Entwisle, Faust, Rindfuss, & Kaneda (AJS, 2007).
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 42 / 63
Multiple Parallel Networks Sample from a population of networks
Sample from Population of Networks
Suppose we have a sample indexed by j = 1, . . . ,Nfrom a population of networks,where the networks are similar in some sense;stochastic replicates of each other;
they all are regarded as realizations ofprocesses obeying the same model,but having different parameters θ1, . . . , θj, . . . , θN .
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 43 / 63
Multiple Parallel Networks Sample from a population of networks
Sample from Population of Networks
Suppose we have a sample indexed by j = 1, . . . ,Nfrom a population of networks,where the networks are similar in some sense;stochastic replicates of each other;they all are regarded as realizations ofprocesses obeying the same model,but having different parameters θ1, . . . , θj, . . . , θN .
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 43 / 63
Multiple Parallel Networks Fixed effects
Meta-Analysis ∼ Fixed Effects Model:
θ1, . . . , θj, . . . , θN are arbitrary values,no assumption about a population is made.
two-stage procedure:
estimate each θj separately, combine the results byFisher’s procedure for combining independent tests:‘is there any evidence for a hypothesized effect?’
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 44 / 63
Multiple Parallel Networks Fixed effects
Meta-Analysis ∼ Fixed Effects Model:
θ1, . . . , θj, . . . , θN are arbitrary values,no assumption about a population is made.
two-stage procedure:
estimate each θj separately, combine the results byFisher’s procedure for combining independent tests:‘is there any evidence for a hypothesized effect?’
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 44 / 63
Multiple Parallel Networks Fixed effects
Meta-Analysis ∼ Fixed Effects Model (contd.):
For coordinate k of the parameter, test null hypothesis
H0 : θkj = 0 for all j
against alternative hypothesis
H1 : θkj = 0 for at least one j .
(Two-sided variants also are possible.)
Procedure: see, e.g., Snijders & Bosker Section 3.7.
Mercken, Snijders, Steglich, & de Vries (2009)applied this in a study of smoking initiation:7704 adolescents in 70 schools in 6 countries.
.Tom A.B. Snijders Multilevel Flavours Manchester Keynote 45 / 63
Multiple Parallel Networks Random effects: two-stage procedure
Meta-Analysis ∼ Random Effects Model:θ1, . . . , θj, . . . , θN are drawn randomlyfrom a population P[net] of networks,no further distributional assumptions are made.
Two-stage procedure:
estimate each θj separately,combine the results in a meta-analysis (Cochran 1954),(‘V-known problem in multilevel analysis)which allows testing hypotheses about P[net]
such as, for a coordinate k ,
Htotal0 : all θkj = 0;
Hmean0 : E{θkj} = 0;
Hspread0 : var{θkj} = 0.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 46 / 63
Multiple Parallel Networks Random effects: two-stage procedure
Meta-Analysis ∼ Random Effects Model:θ1, . . . , θj, . . . , θN are drawn randomlyfrom a population P[net] of networks,no further distributional assumptions are made.
Two-stage procedure:
estimate each θj separately,combine the results in a meta-analysis (Cochran 1954),(‘V-known problem in multilevel analysis)which allows testing hypotheses about P[net]
such as, for a coordinate k ,
Htotal0 : all θkj = 0;
Hmean0 : E{θkj} = 0;
Hspread0 : var{θkj} = 0.
.Tom A.B. Snijders Multilevel Flavours Manchester Keynote 46 / 63
Multiple Parallel Networks Random effects: two-stage procedure
The input for the meta-analysis consists ofestimates θ̂j and their standard errors s.e.j.
The meta analysis is constructed based on the model
θ̂j = μ + Uj + Ej ,
where μ is the population mean,Uj is the true effect of group j,and Ej is the statistical error of estimation.
Uj and Ej are independent residuals with mean 0,the Uj are i.i.d. with unknown variance,and var(Ej) = s.e.2
j(‘V–known’).
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 47 / 63
Multiple Parallel Networks Random effects: two-stage procedure
The input for the meta-analysis consists ofestimates θ̂j and their standard errors s.e.j.
The meta analysis is constructed based on the model
θ̂j = μ + Uj + Ej ,
where μ is the population mean,Uj is the true effect of group j,and Ej is the statistical error of estimation.
Uj and Ej are independent residuals with mean 0,the Uj are i.i.d. with unknown variance,and var(Ej) = s.e.2
j(‘V–known’).
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 47 / 63
Multiple Parallel Networks Random effects: two-stage procedure
Meta-Analysis ∼ Random Effects Model (contd.)
This has been applied in quite many studies: e.g.,
Lubbers (2003):homophily in 57 classrooms with 1466 students (also withintegrated random coefficient p∗ approach);
Baerveldt, van Duijn, Vermeij, van Hemert (2004):ethnic homophily in 20 schools, 1317 students;
Valente, Fujimoto, Chou, and Spruit-Metz (2009):friendship & obesity, 17 classrooms with 617 students;
Mercken, Snijders, Steglich, & de Vries (2009):fr. & smoking, 7704 adolescents, 70 schools, 6 countries;also other studies by Liesbeth Mercken.
.Tom A.B. Snijders Multilevel Flavours Manchester Keynote 48 / 63
Multiple Parallel Networks Random effects: integrated procedure
Meta-Analysis ∼ Integrated Random Effects Model:θ1, . . . , θj, . . . , θN are drawn randomlyfrom a population P[net] of networks,and are assumed to havea common multivariate normal N (μ,Σ) distribution,perhaps conditionally on network-level covariates.
Integrated procedure:
Estimate μ and Σ and consider the‘posterior’ distribution of θj given the data.
Advantage:The analysis of the separate networks draws strength fromthe total sample of networks by regression to the mean.
Useful especially for many small networks.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 49 / 63
Multiple Parallel Networks Random effects: integrated procedure
Meta-Analysis ∼ Integrated Random Effects Model:θ1, . . . , θj, . . . , θN are drawn randomlyfrom a population P[net] of networks,and are assumed to havea common multivariate normal N (μ,Σ) distribution,perhaps conditionally on network-level covariates.
Integrated procedure:
Estimate μ and Σ and consider the‘posterior’ distribution of θj given the data.
Advantage:The analysis of the separate networks draws strength fromthe total sample of networks by regression to the mean.
Useful especially for many small networks.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 49 / 63
Multiple Parallel Networks Random effects: integrated procedure
Meta-Analysis ∼ Integrated Random Effects Model:θ1, . . . , θj, . . . , θN are drawn randomlyfrom a population P[net] of networks,and are assumed to havea common multivariate normal N (μ,Σ) distribution,perhaps conditionally on network-level covariates.
Integrated procedure:
Estimate μ and Σ and consider the‘posterior’ distribution of θj given the data.
Advantage:The analysis of the separate networks draws strength fromthe total sample of networks by regression to the mean.
Useful especially for many small networks.
.Tom A.B. Snijders Multilevel Flavours Manchester Keynote 49 / 63
Multiple Parallel Networks Random effects: integrated procedure
Meta-Analysis ∼ Integrated Random Effects Model (contd.)
New developmentsin collaboration between Johan Koskinen and T.S.,for the stochastic actor-oriented model for network dynamics.
Recall that this is a model for network dynamics,where the dynamics isan unobserved sequence of ‘micro steps’and the parameters are estimated from network panel data.
This is elaborated following a likelihood-based approach;see Koskinen & Snijders (JSPI 2007),Snijders, Koskinen & Schweinberger (AAS 2010),Schweinberger (PhD thesis 2007, Chapters 4 and 5).
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 50 / 63
Multiple Parallel Networks Random effects: integrated procedure
Meta-Analysis ∼ Integrated Random Effects Model (contd.)
New developmentsin collaboration between Johan Koskinen and T.S.,for the stochastic actor-oriented model for network dynamics.
Recall that this is a model for network dynamics,where the dynamics isan unobserved sequence of ‘micro steps’and the parameters are estimated from network panel data.
This is elaborated following a likelihood-based approach;see Koskinen & Snijders (JSPI 2007),Snijders, Koskinen & Schweinberger (AAS 2010),Schweinberger (PhD thesis 2007, Chapters 4 and 5).
.Tom A.B. Snijders Multilevel Flavours Manchester Keynote 50 / 63
Multiple Parallel Networks Random effects: integrated procedure
Here we discuss a Bayesian approach, where the parametersμ,Σ have a prior distribution. We assume the conjugate prior,
Σ−1 swishartp(Λ−10 , ν0), and conditionally on Σ
μ | Σ s Np(μ0,Σ/κ0) .
Thus, the parameters of the prior are Λ0, ν0, κ0.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 51 / 63
Multiple Parallel Networks Random effects: integrated procedure
The joint p.d.f., for data y1, . . . ,yj, . . . ,yN, is
fInvWish�
Σ | Λ−10 , ν0�
ϕp�
μ | (μ0,Σ/κ0)�
prior
×∏N
j=1 ϕp(θj | μ,Σ) hierarchical model
×∏N
j=1 pSAOM(yj | θj) network model
Since pSAOM(yj | θj) cannot be calculated directly,we employ data augmentation (Tanner & Wong, 1987):augment the network panel data by the sequence vjof all microsteps connecting the consecutive observations.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 52 / 63
Multiple Parallel Networks Random effects: integrated procedure
The joint p.d.f., for data y1, . . . ,yj, . . . ,yN, is
fInvWish�
Σ | Λ−10 , ν0�
ϕp�
μ | (μ0,Σ/κ0)�
prior
×∏N
j=1 ϕp(θj | μ,Σ) hierarchical model
×∏N
j=1 pSAOM(yj | θj) network model
Since pSAOM(yj | θj) cannot be calculated directly,we employ data augmentation (Tanner & Wong, 1987):augment the network panel data by the sequence vjof all microsteps connecting the consecutive observations.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 52 / 63
Multiple Parallel Networks Random effects: integrated procedure
The joint p.d.f., for data y1, . . . ,yj, . . . ,yN, is
fInvWish�
Σ | Λ−10 , ν0�
ϕp�
μ | (μ0,Σ/κ0)�
prior
×∏N
j=1 ϕp(θj | μ,Σ) hierarchical model
×∏N
j=1 pSAOM(yj | θj) network model
Since pSAOM(yj | θj) cannot be calculated directly,we employ data augmentation (Tanner & Wong, 1987):augment the network panel data by the sequence vjof all microsteps connecting the consecutive observations.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 52 / 63
Multiple Parallel Networks Random effects: integrated procedure
The joint p.d.f., for data y1, . . . ,yj, . . . ,yN, is
fInvWish�
Σ | Λ−10 , ν0�
ϕp�
μ | (μ0,Σ/κ0)�
prior
×∏N
j=1 ϕp(θj | μ,Σ) hierarchical model
×∏N
j=1 pSAOM(yj | θj) network model
Since pSAOM(yj | θj) cannot be calculated directly,we employ data augmentation (Tanner & Wong, 1987):augment the network panel data by the sequence vjof all microsteps connecting the consecutive observations.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 52 / 63
Multiple Parallel Networks Random effects: integrated procedure
The joint p.d.f., for data y1, . . . ,yj, . . . ,yN,using data augmentation, is the sum over vj of
fInvWish�
Σ | Λ−10 , ν0�
ϕp�
μ | (μ0,Σ/κ0)�
prior
×∏N
j=1 ϕp(θj | μ,Σ) hierarchical model
×∏N
j=1 pSAOM(vj | θj,yj) . network model
The posterior distribution can be sampledby Markov chain Monte Carlo (MCMC).The unknown random variables are
μ,Σ; θ1, . . . , θN; v1, . . . ,vN
and these are sampled in turn, as follows.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 53 / 63
Multiple Parallel Networks Random effects: integrated procedure
The joint p.d.f., for data y1, . . . ,yj, . . . ,yN,using data augmentation, is the sum over vj of
fInvWish�
Σ | Λ−10 , ν0�
ϕp�
μ | (μ0,Σ/κ0)�
prior
×∏N
j=1 ϕp(θj | μ,Σ) hierarchical model
×∏N
j=1 pSAOM(vj | θj,yj) . network model
The posterior distribution can be sampledby Markov chain Monte Carlo (MCMC).The unknown random variables are
μ,Σ; θ1, . . . , θN; v1, . . . ,vN
and these are sampled in turn, as follows.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 53 / 63
Multiple Parallel Networks Random effects: integrated procedure
The joint p.d.f., for data y1, . . . ,yj, . . . ,yN,using data augmentation, is the sum over vj of
fInvWish�
Σ | Λ−10 , ν0�
ϕp�
μ | (μ0,Σ/κ0)�
prior
×∏N
j=1 ϕp(θj | μ,Σ) hierarchical model
×∏N
j=1 pSAOM(vj | θj,yj) . network model
The posterior distribution can be sampledby Markov chain Monte Carlo (MCMC).The unknown random variables are
μ,Σ; θ1, . . . , θN; v1, . . . ,vN
and these are sampled in turn, as follows.
.Tom A.B. Snijders Multilevel Flavours Manchester Keynote 53 / 63
Multiple Parallel Networks Random effects: integrated procedure
1 For all j make some Metropolis Hastings stepssampling vj | yj, θj,as in Snijders, Koskinen & Schweinberger (2010).
2 For all j make one or more Metropolis Hastings stepssampling θj | vj, μ,Σ,using a random walk proposal distribution(Schweinberger 2007, Ch. 5.4;Koskinen & Snijders 2007, Sect. 4.4).
3 Sample (μ,Σ) | θ1, . . . , θN,Λ0, ν0, κ0
from the full conditional distribution.
This requires tuning to obtain good mixing – as usual.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 54 / 63
Multiple Parallel Networks Random effects: integrated procedure
1 For all j make some Metropolis Hastings stepssampling vj | yj, θj,as in Snijders, Koskinen & Schweinberger (2010).
2 For all j make one or more Metropolis Hastings stepssampling θj | vj, μ,Σ,using a random walk proposal distribution(Schweinberger 2007, Ch. 5.4;Koskinen & Snijders 2007, Sect. 4.4).
3 Sample (μ,Σ) | θ1, . . . , θN,Λ0, ν0, κ0
from the full conditional distribution.
This requires tuning to obtain good mixing – as usual.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 54 / 63
Multiple Parallel Networks Random effects: integrated procedure
1 For all j make some Metropolis Hastings stepssampling vj | yj, θj,as in Snijders, Koskinen & Schweinberger (2010).
2 For all j make one or more Metropolis Hastings stepssampling θj | vj, μ,Σ,using a random walk proposal distribution(Schweinberger 2007, Ch. 5.4;Koskinen & Snijders 2007, Sect. 4.4).
3 Sample (μ,Σ) | θ1, . . . , θN,Λ0, ν0, κ0
from the full conditional distribution.
This requires tuning to obtain good mixing – as usual.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 54 / 63
Multiple Parallel Networks Random effects: integrated procedure
1 For all j make some Metropolis Hastings stepssampling vj | yj, θj,as in Snijders, Koskinen & Schweinberger (2010).
2 For all j make one or more Metropolis Hastings stepssampling θj | vj, μ,Σ,using a random walk proposal distribution(Schweinberger 2007, Ch. 5.4;Koskinen & Snijders 2007, Sect. 4.4).
3 Sample (μ,Σ) | θ1, . . . , θN,Λ0, ν0, κ0
from the full conditional distribution.
This requires tuning to obtain good mixing – as usual.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 54 / 63
Multiple Actor Types
3Multiple Actor Sets
andMultiple Relations
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 55 / 63
Multiple Actor Types
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 56 / 63
Multiple Actor Types
Multilevel network analysis with multiple actor typeswas pioneered by Breiger (Soc. Forces, 1974),Hedstrøm, Sandell & Stern (AJS, 2000) andLazega, Jourda, Mounier & Stofer (Social Networks, 2008).
The 2012 Sunbelt Conference saw an avalanche of new work,with contributions by Alessandro Lomi, Peng Wang,and Johan Koskinen.
At this conference we see many further developments.
what can I add???
Longitudinal data of linked networks with multiple actor typesalso can be analyzed using RSiena, thanks tothe flexible design by Krists Boitmanis and Ruth Ripley.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 57 / 63
Multiple Actor Types
Multilevel network analysis with multiple actor typeswas pioneered by Breiger (Soc. Forces, 1974),Hedstrøm, Sandell & Stern (AJS, 2000) andLazega, Jourda, Mounier & Stofer (Social Networks, 2008).
The 2012 Sunbelt Conference saw an avalanche of new work,with contributions by Alessandro Lomi, Peng Wang,and Johan Koskinen.
At this conference we see many further developments.
what can I add???
Longitudinal data of linked networks with multiple actor typesalso can be analyzed using RSiena, thanks tothe flexible design by Krists Boitmanis and Ruth Ripley.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 57 / 63
Multiple Actor Types
Multilevel network analysis with multiple actor typeswas pioneered by Breiger (Soc. Forces, 1974),Hedstrøm, Sandell & Stern (AJS, 2000) andLazega, Jourda, Mounier & Stofer (Social Networks, 2008).
The 2012 Sunbelt Conference saw an avalanche of new work,with contributions by Alessandro Lomi, Peng Wang,and Johan Koskinen.
At this conference we see many further developments.
what can I add???
Longitudinal data of linked networks with multiple actor typesalso can be analyzed using RSiena, thanks tothe flexible design by Krists Boitmanis and Ruth Ripley.
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 57 / 63
Multiple Actor Types
Multilevel network analysis with multiple actor typeswas pioneered by Breiger (Soc. Forces, 1974),Hedstrøm, Sandell & Stern (AJS, 2000) andLazega, Jourda, Mounier & Stofer (Social Networks, 2008).
The 2012 Sunbelt Conference saw an avalanche of new work,with contributions by Alessandro Lomi, Peng Wang,and Johan Koskinen.
At this conference we see many further developments.
what can I add???
Longitudinal data of linked networks with multiple actor typesalso can be analyzed using RSiena, thanks tothe flexible design by Krists Boitmanis and Ruth Ripley.
.Tom A.B. Snijders Multilevel Flavours Manchester Keynote 57 / 63
Large Networks
4Large Networks
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 58 / 63
Large Networks
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 59 / 63
Large Networks
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 60 / 63
Large Networks
A collection of many groups ∼ many ‘parallel’ networksis really a case of a large networkwhere between-group ties are ignored.
The applicability of our usual network models to large groups(hundreds of actors and more) seems limited by the factthat we still do not know a lot about howthe large-scale structure of networks differs from thesmall-scale and medium-scale structures;
and large networks must be full of heterogeneitywhere, e.g., ERGM parameters will not be constantin all ‘regions’ of the network– but how to define such ‘regions’?
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 61 / 63
Large Networks
Models for large networks should incorporatelatent heterogeneity – at which level?
actors / subgroups ?
Work by Johan Koskinen – Michael Schweinberger – ....
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 62 / 63
Large Networks
Models for large networks should incorporatelatent heterogeneity – at which level?
actors / subgroups ?
Work by Johan Koskinen – Michael Schweinberger – ....
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 62 / 63
Large Networks
Models for large networks should incorporatelatent heterogeneity – at which level?
actors / subgroups ?
Work by Johan Koskinen – Michael Schweinberger – ....
.
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 62 / 63
the road on and on
Tom A.B. Snijders Multilevel Flavours Manchester Keynote 63 / 63