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Goodness of fit tests for random multigraph models
[journal article]
Abstract
Goodness of fit tests for two probabilistic multigraph models are presented. The first model is random stub matching given fixed degrees (RSM) so that edge assignments to vertex pair sites are dependent, and the second is independent edge assignments (IEA) according to a common probability distribut... view more
Goodness of fit tests for two probabilistic multigraph models are presented. The first model is random stub matching given fixed degrees (RSM) so that edge assignments to vertex pair sites are dependent, and the second is independent edge assignments (IEA) according to a common probability distribution. Tests are performed using goodness of fit measures between the edge multiplicity sequence of an observed multigraph, and the expected one according to a simple or composite hypothesis. Test statistics of Pearson type and of likelihood ratio type are used, and the expected values of the Pearson statistic under the different models are derived. Test performances based on simulations indicate that even for small number of edges, the null distributions of both statistics are well approximated by their asymptotic χ2-distribution. The non-null distributions of the test statistics can be well approximated by proposed adjusted χ2-distributions used for power approximations. The influence of RSM on both test statistics is substantial for small number of edges and implies a shift of their distributions towards smaller values compared to what holds true for the null distributions under IEA. Two applications on social networks are included to illustrate how the tests can guide in the analysis of social structure.... view less
Keywords
network; aggregation; model; data; social network; statistical test; statistics
Classification
Methods and Techniques of Data Collection and Data Analysis, Statistical Methods, Computer Methods
General Sociology, Basic Research, General Concepts and History of Sociology, Sociological Theories
Free Keywords
Network model; multivariate networks; data aggregation; random multigraphs; goodness of fit; random stub matching
Document language
English
Publication Year
2022
Page/Pages
p. 1-26
Journal
Journal of Applied Statistics (2022)
DOI
https://doi.org/10.1080/02664763.2022.2099816
ISSN
1360-0532
Status
Published Version; peer reviewed
Licence
Creative Commons - Attribution 4.0
FundingGefördert durch die Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 491156185 / Funded by the German Research Foundation (DFG) - Project number 491156185