network analysis using stata...introduction nwcommands contribution application conclusion...
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Introduction nwcommands Contribution Application Conclusion References
Network Analysis using StataNwcommands, extensions and applications.
Charlie JoyezUniversité Cote d’Azur (UCA), GREDEG, Université de Nice
Sept 2018, KU Leuven, BrusselStata User Group Meeting
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Introduction nwcommands Contribution Application Conclusion References
MotivationNetworks are everywhere. flexible mathematical object
I Complex systems, interactions, interdependence’s.I Two type of use in (Social) Sciences
I Theoretical modeling with complex micro-foundationsI Empirical analysis of existing networks.
I Booming in several fields with data availability and computingcapabilities.
I Increasing interest (See Stata news january 2018 (33-1))ObjectiveHow to easily proceed to network analysis using Stata?
I Node level and network wide analysis
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Introduction nwcommands Contribution Application Conclusion References
Outline
I- Introduction
II - nwcommands
III - Contribution
IV - Application
V - Conclusion and discussion
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nwcommands - Presentation
I Developed (maintained) by Thomas Grund - Univ. College Dublin
I http://nwcommands.orgI install nwcommands-ado, from(http://www.nwcommands.org)
I Entire suite of commands, close to Stata commands (nw prefix)I declare, use, save network dataI Manipulate (keep, drop, permute, etc.) nodes or entire networksI Compute network metrics
I At the node level (centrality, etc)I At the entire network level (density, overall clustering coeff ).
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Declare DataI From a Mata Matrix (Adjacency matrix)
I mata A=(0,10,1 \5,0,0 \0,2,0)mata A
nwset, mat(A) name(netA)
I From an edge list
I nwfromedge _fromid _toid link, name(Net1) undirected
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Introduction nwcommands Contribution Application Conclusion References
Node-level metrics
I nwdegreeI _degree: Number of direct neighborsI di =
∑j
mi,j , M = A : /A Unweighted adjacency matrixI returns Freeman (1979) index
Cx =∑N
i=1 Cx(p∗) − Cx(pi)max
∑N
i=1 Cx(p∗) − Cx(pi)I nwdegree, valued
I _strength: Sum of edges weightsI si =
∑j
aij
I Other node centrality metrics : Betweeness & closeness, Katz,Eigenvector.
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Network-wide information
I tnwsummarize
I nwgeodesicI Longest past, diameter, avg shortest path (unweighted)
I nwclustering Overall clustering coefficient (nb triads / nb possibletriads)
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Introduction nwcommands Contribution Application Conclusion References
Outline
I- Introduction
II - nwcommands
III - Contribution
IV - Application
V - Conclusion and discussion
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Introduction nwcommands Contribution Application Conclusion References
Node-level metrics 1/2
I Average Nearest Neighbors Degree (Strength)I nwannd : Average nearest neighbor degree.
I mataneighbor = mymat:>0Z=st_data(.,"_degree")mata: totdegreemat = neighbor*Zmata: ANNDmat=totdegreemat:/Zend mata
I nwdisparity (Barthélemy et al., 2005) : distribution of edge’s weight(concentration)disparityi =
∑j(wij/si)2
I nw_harmonic centrality (suited for disconnected graphs)I H(x) =
∑y 6=x
1d(y,x)
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Introduction nwcommands Contribution Application Conclusion References
Node-level metrics 2/2
Weighted / directed extension of existing commandsI nwcluster : directions and/or weighted generalization (Onnela
et al., 2005)
I nw_wcc : Weighted Clustering Coefficients (Fagiolo, 2006)
I nw_geodesic (weights as distance)
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Introduction nwcommands Contribution Application Conclusion References
Network level
I nwreciprocity (Barrat et al., 2004)I mata
s=sum(W)Z = W :* (W :< W’) + W’ :* (W’ :< W) /*min of symmetricselements = reciprocated ties*/E=sum(Z)r=E/send mata
I Compares reciprocity with N random draws (same size, density).I nwstrengthcent : (Freeman, 1979) index based on Strength.
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Introduction nwcommands Contribution Application Conclusion References
Declaration
I From neigbor lists (only existing ties). A variable may indicate thesequence.
I nw_fromneighbor nw_fromlist test,node(NODE) id(ID)direction(year)
Initial data
Final data
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Introduction nwcommands Contribution Application Conclusion References
Outline
I- Introduction
II - nwcommands
III - Contribution
IV - Application
V - Conclusion and discussion
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Introduction nwcommands Contribution Application Conclusion References
Application to international economics
I World Trade Web on 2016
I Declare to be weighted directed network : 192*192 tablemkmat flow_*, matrix(M)mata A=st_matrix("M")nwset , mat(A) name(TradeNet‘v’)
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Application - 2
I Most central nodes?I Eigenvector centrality
Degree centralization Strength Centralization0.364 0.176
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Application - 3
Econometrics of networksI Use of network metrics (e.g. centrality indexes of nodes) into
traditional analysis. (Hidalgo et al., 2007)I Regress network structure (dyadic data)
I Individuals in networks not iidI OLS biased unless FE or clusteringI QAP : unit = dyadic value + random permutations of rows and columns.
I nwqap MNEnet_2011 GVCnet_2010 , mode(dist) type(reg)permutation(500)
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Introduction nwcommands Contribution Application Conclusion References
Outline
I- Introduction
II - nwcommands
III - Contribution
IV - Application
V - Conclusion and discussion
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Introduction nwcommands Contribution Application Conclusion References
Conclusion
I Network analysis made easy through StataI easy to learn and contributeI suited to a wide range of issues
Next stepsI generalize metrics to weighted, directed, unconnected graphs.
I Fit to complex networks.I improve network graphs & plots vizualizationI Incorporate nwcommands into Stata 16?I Promote network analysis to colleague/students already familiar with
Stata.
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Introduction nwcommands Contribution Application Conclusion References
Thank [email protected]
Many thanks to Thomas Grund for its nwcommands: Network Analysis with StataAdditional Stata commands used for this paper are available on my RePEc Ideas page or
directy from SSC (e.g. ssc install nwannd)
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References
Barrat, A., Barthelemy, M., Pastor-Satorras, R., and Vespignani, A. The architecture ofcomplex weighted networks. Proceedings of the National Academy of Sciences of the UnitedStates of America, 101(11):3747–3752, 2004.
Barthélemy, M., Barrat, A., Pastor-Satorras, R., and Vespignani, A. Characterization andmodeling of weighted networks. Physica a: Statistical mechanics and its applications, 346(1):34–43, 2005.
Fagiolo, G. Directed or undirected? a new index to check for directionality of relations insocio-economic networks. Economics Bulletin, 3(34):1–12, 2006.
Freeman, L. C. Centrality in social networks conceptual clarification. Social networks, 1(3):215–239, 1979.
Hidalgo, C. A., Klinger, B., Barabasi, A.-L., and Hausmann, R. The product spaceconditions the development of nations. Paper 0708.2090, arXiv.org, 2007. 00468.
Joyez, C. On the topological structure of multinationals network. Physica A: StatisticalMechanics and its Applications, 473:578 – 588, 2017.
Onnela, J.-P., Saramäki, J., Kertész, J., and Kaski, K. Intensity and coherence of motifs inweighted complex networks. Physical Review E, 71(6):065103, 2005.