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| 2. |
- Hagberg, Jan, 1958-
(författare)
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On Degree Variance in Random Graphs
- 2004
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is concerned with degree moments and degree variance in random graphs. The degree of vertex i in a graph is the number of edges incident to vertex i.In the first paper, degree moments and functions of degree moments are investigated for three random graph models. In statistical applications of random graph models the degree moments, and functions of the degree moments, have been found useful both as summary statistics and for inference on particular random graph models. Exact and asymptotic formulas are given for various degree statistics, in particular the degree variance.The second paper focus on the degree variance. Exact and asymptotic distributions of the degree variance are investigated for Bernoulli graphs and uniform random graphs. For graphs of large order, we show that the degree variance is approximately gamma distributed with parameters obtained from the first two moments of the degree variance. The usefulness of the results is illustrated by a graph centrality test with a critical value obtained from the gamma distribution.The third and last paper is concerned with extreme values and other attained values of the degree variance among graphs of fixed order and size, and among graphs of fixed order. The structure of the extreme graphs is investegated and it is shown that the maximum value of the degree variance can be obtained from integer sequences associated to the triangular numbers. Explicite formulas for the number of possible values and recurrence relations for the attained values of the degree variance are developed.
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| 3. |
- Karlberg, Martin, 1970-
(författare)
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Triad count estimation and transitivity testing in graphs and digraphs
- 1997
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Triads and transitivity are two concepts within the field of social network analysis that are closely related to each other. We study some estimation and testing problems related to those concepts, using the tools of graph theory; the results obtained could be applied to graphs representing other kinds of data than social relations. Throughout this thesis, we focus on the role of local networks. A local network for an individual in a friendship network may be regarded as the network between the friends of this person. Two local network attributes that we pay special attention to are the size and the density. The local size of a vertex is defined so that it counts the number of transitive relationships in which that vertex is involved; this definition is not undisputable in the digraph situation, since not all edges in the local network are counted using that definition. We define the local density of a vertex in such a way, that its expected value is equal to the expected overall density of the network under some commonly used simple random graph and random digraph models. When dealing with triad count estimation, we consider the situation when we have observed information about a probability sample of vertices in a graph or digraph; we let the amount of information observed for each vertex range from the vertex degree to the entire local network of that vertex. Horvitz-Thompson estimators (and variance estimators for those estimators) for the triad counts are given. A main result is that when local networks without information on the identities of the vertices in that network are observed, the triad counts may be expressed as sums of vertex attributes; this greatly facilitates the estimation based on vertex sampling designs more complex than simple random sampling. Transitivity testing is considered for graphs and digraphs that are observed in their entirety. We study two different kinds of transitivity tests; tests based on the counts of transitive and intransitive triads and triples, and tests based on the mean local density over all vertices. The null hypothesis used is that the graphs and digraphs observed have been generated according to some conditional uniform random graph model that does not imply a high degree of transitivity. The powers of the tests against random graph distributions that generate highly transitive graphs are examined in simulation studies. In other simulation studies, the tests are applied to a large set of school class sociograms. When (undirected) graphs are considered, the test based on the proportion of transitive triads out of the non-vacuously transitive ones is found to be best at detecting transitivity; for digraphs, the test based on the difference between the mean local density and the overall network density is the best transitivity detector.
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| 4. |
- Koskinen, Johan, 1974-, et al.
(författare)
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Multilevel longitudinal analysis of social networks
- 2023
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Ingår i: Journal of the Royal Statistical Society. - : Oxford University Press (OUP). - 0964-1998 .- 1467-985X. ; 186:3, s. 376-400
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Tidskriftsartikel (refereegranskat)abstract
- Stochastic actor-oriented models (SAOMs) are a modelling framework for analysing network dynamics using network panel data. This paper extends the SAOM to the analysis of multilevel network panels through a random coefficient model, estimated with a Bayesian approach. The proposed model allows testing theories about network dynamics, social influence, and interdependence of multiple networks. It is illustrated by a study of the dynamic interdependence of friendship networks and minor delinquency. Data were available for 126 classrooms in the first year of secondary school, of which 82 were used, containing relatively few missing data points and having not too much network turnover.
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| 5. |
- Krause, Robert, et al.
(författare)
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Missing data in cross-sectional networks - An extensive comparison of missing data treatment methods
- 2020
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Ingår i: Social Networks. - : ELSEVIER. - 0378-8733 .- 1879-2111. ; 62, s. 99-112
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Tidskriftsartikel (refereegranskat)abstract
- This paper compares several missing data treatment methods for missing network data on a diverse set of simulated networks under several missing data mechanisms. We focus the comparison on three different outcomes: descriptive statistics, link reconstruction, and model parameters. The results indicate that the often used methods (analysis of available cases and null-tie imputation) lead to considerable bias on descriptive statistics with moderate or large proportions of missing data. Multiple imputation using sophisticated imputation models based on exponential random graph models (ERGMs) lead to acceptable biases in descriptive statistics and model parameters even under large amounts of missing data. For link reconstruction multiple imputation by simple ERGM performed well on small data sets, while missing data was more accurately imputed in larger data sets with multiple imputation by complex Bayesian ERGMs (BERGMs).
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| 6. |
- Krause, Robert W., et al.
(författare)
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Missing Network Data A Comparison of Different Imputation Methods
- 2018
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Ingår i: 2018 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM). - : Institute of Electrical and Electronics Engineers (IEEE). - 9781538660515 - 9781538660522 ; , s. 159-163
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Konferensbidrag (refereegranskat)abstract
- This paper compares several imputation methods for missing data in network analysis on a diverse set of simulated networks under several missing data mechanisms. Previous work has highlighted the biases in descriptive statistics of networks introduced by missing data. The results of the current study indicate that the default methods (analysis of available cases and null-tie imputation) do not perform well with moderate or large amounts of missing data. The results further indicate that multiple imputation using sophisticated imputation models based on exponential random graph models (ERGMs) lead to acceptable biases even under large amounts of missing data.
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| 7. |
- Nowicki, Krzysztof, et al.
(författare)
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Estimation and prediction for stochastic blockstructures
- 2001
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Ingår i: Journal of the American Statistical Association. - : Informa UK Limited. - 0162-1459 .- 1537-274X. ; 96:455, s. 1077-1087
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Tidskriftsartikel (refereegranskat)abstract
- A statistical approach to a posteriori blockmodeling for digraphs and valued digraphs is proposed. The probability model assumes that the vertices of the digraph are partitioned into several unobserved (latent) classes and that the probability distribution of the relation between two vertices depends only on the classes to which they belong. A Bayesian estimator based on Gibbs sampling is proposed. The basic model is not identified, because class labels are arbitrary. The resulting identifiability problems are solved by restricting inference to the posterior distributions of invariant functions of the parameters and the vertex class membership. In addition, models are considered where class labels are identified by prior distributions for the class membership of some of the vertices. The model is illustrated by an example from the social networks literature (Kapferer's tailor shop).
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| 8. |
- Preciado, Paulina, et al.
(författare)
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Does proximity matter? : Distance dependence of adolescent friendships
- 2012
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Ingår i: Social Networks. - : Elsevier. - 0378-8733 .- 1879-2111. ; 34:1, s. 18-31
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Tidskriftsartikel (refereegranskat)abstract
- Geographic proximity is a determinant factor of friendship. Friendship datasets that include detailed geographic information are scarce, and when this information is available, the dependence of friendship on distance is often modelled by pre-specified parametric functions or derived from theory without further empirical assessment. This paper aims to give a detailed representation of the association between distance and the likelihood of friendship existence and friendship dynamics, and how this is modified by a few basic social and individual factors. The data employed is a three-wave network of 336 adolescents living in a small Swedish town, for whom information has been collected on their household locations. The analysis is a three-step process that combines (1) nonparametric logistic regressions to unravel the overall functional form of the dependence of friendship on distance, without assuming it has a particular strength or shape; (2) parametric logistic regressions to construct suitable transformations of distance that can be employed in (3) stochastic models for longitudinal network data, to assess how distance, individual covariates, and network structure shape adolescent friendship dynamics. It was found that the log-odds of friendship existence and friendship dynamics decrease smoothly with the logarithm of distance. For adolescents in different schools the dependence is linear, and stronger than for adolescents in the same school. Living nearby accounts, in this dataset, for an aspect of friendship dynamics that is not explicitly modelled by network structure or by individual covariates. In particular, the estimated distance effect is not correlated with reciprocity or transitivity effects. (C) 2011 Elsevier B.V. All rights reserved.
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| 9. |
- Snijders, Tom A. B., et al.
(författare)
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Estimation and Prediction for Stochastic Blockmodels for Graphs with Latent Block Structure
- 1997
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Ingår i: Journal of Classification. - : Springer Science and Business Media LLC. - 1432-1343 .- 0176-4268. ; 14, s. 75-100
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Tidskriftsartikel (refereegranskat)abstract
- A statistical approach to a posteriori blockmodeling for graphs is proposed. The model assumes that the vertices of the graph are partitioned into two unknown blocks and that the probability of an edge between two vertices depends only on the blocks to which they belong. Statistical procedures are derived for estimating the probabilities of edges and for predicting the block structure from observations of the edge pattern only. ML estimators can be computed using the EM algorithm, but this strategy is practical only for small graphs. A Bayesian estimator, based on Gibbs sampling, is proposed. This estimator is practical also for large graphs. When ML estimators are used, the block structure can be predicted based on predictive likelihood. When Gibbs sampling is used, the block structure can be predicted from posterior predictive probabilities. A side result is that when the number of vertices tends to infinity while the probabilities remain constant, the block structure can be recovered correctly with probability tending to 1.
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| 10. |
- Snijders, Tom, et al.
(författare)
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Network Dynamics
- 2023. - 2nd
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Ingår i: The SAGE Handbook of Social Network Analysis. - Thousand Oaks : Sage Publications.
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Bokkapitel (refereegranskat)abstract
- This chapter gives a critical overview of the models available for analyzing longitudinal social network data, and sketches the two most important model families, the stochastic actor-oriented models and the longitudinal exponential random graph models.
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| 11. |
- Stadtfeld, Christoph, et al.
(författare)
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Statistical Power in Longitudinal Network Studies
- 2020
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Ingår i: Sociological Methods & Research. - : Sage Publications. - 0049-1241 .- 1552-8294. ; 49:4, s. 1103-1132
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Tidskriftsartikel (refereegranskat)abstract
- Longitudinal social network studies can easily suffer from insufficient statistical power. Studies that simultaneously investigate change of network ties and change of nodal attributes (selection and influence studies) are particularly at risk because the number of nodal observations is typically much lower than the number of observed tie variables. This article presents a simulation-based procedure to evaluate statistical power of longitudinal social network studies in which stochastic actor-oriented models are to be applied. Two detailed case studies illustrate how statistical power is strongly affected by network size, number of data collection waves, effect sizes, missing data, and participant turnover. These issues should thus be explored in the design phase of longitudinal social network studies.
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| 12. |
- Steglich, Christian, Dr, 1968-, et al.
(författare)
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Stochastic network modelling as generative social science
- 2022
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Ingår i: Handbook of sociological science. - Cheltenham : Edward Elgar Publishing. - 9781789909425 - 9781789909432 ; , s. 73-99
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Bokkapitel (refereegranskat)abstract
- Stochastic models of sociocentric networks were originally developed for testing hypotheses about micro-level dependencies on the basis of empirical network data. Such dependencies lead to phenomena like clustering, hub formation, or network autocorrelation. Due to the complex nature of sociocentric networks, parameter estimates of these models are typically obtained by simulation-based inference. This opens the possibility of re-purposing these models as simulation tools for the study of emergent macro-level phenomena. The combination of fitting micro-level models to empirical data sets and explanation of macro-level outcomes renders these models powerful tools for sociological inquiry into interdependent social systems. In this chapter, the use of stochastic actor-oriented models as generative models for such networked social systems is discussed. This is illustrated with an investigation of the emergence of subgroups in adolescents' friendship networks.
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| 13. |
- van Rijsewijk, Loes, et al.
(författare)
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The Interplay between Adolescents’ Friendships and the Exchange of Help : A Longitudinal Multiplex Social Network Study
- 2019
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Ingår i: Journal of research on adolescence. - : Wiley-Blackwell Publishing Inc.. - 1050-8392 .- 1532-7795.
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this study was to unravel the interrelatedness of friendship and help, and to examine the characteristics of friendship and help networks. The effects of mutual versus one‐sided help relations on friendship initiation and maintenance, and vice versa, were examined. Friendship and help networks were analyzed (N = 953 students; 41 classrooms; Mage = 12.7). The results illustrate that friendship and help networks show some similarities, but only partly overlap and have distinct characteristics. Longitudinal multiplex social network analyses showed that mutual help was important for the maintenance of friendship, but not for the initiation of friendship. Further, particularly mutual friendships provided a context in which help took place. Implications of these findings are discussed.
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