625
Views
5
CrossRef citations to date
0
Altmetric
Theory and Methods

Testing for Nodal Dependence in Relational Data Matrices

Pages 1037-1046 | Received 01 Jun 2013, Published online: 07 Nov 2015

REFERENCES

  • Airoldi, E., Blei, D., Fienberg, S., and Xing, E. (2008), “Mixed Membership Stochastic Blockmodels,” The Journal of Machine Learning Research, 9, 1981–2014.
  • Allen, G.I., and Tibshirani, R. (2010), “Transposable Regularized Covariance Models With an Application to Missing Data Imputation,” The Annals of Applied Statistics, 4, 764–790.
  • Anderson, T., Hsu, H., and Fang, K.-T. (1986), “Maximum-Likelihood Estimates and Likelihood-Ratio Criteria for Multivariate Elliptically Contoured Distributions,” Canadian Journal of Statistics, 14, 55–59.
  • Bergmann, S., Ihmels, J., and Barkai, N. (2003), “Similarities and Differences in Genome-Wide Expression Data of Six Organisms,” PLoS Biology, 2, e9.
  • Bergstrand, J. (1985), “The Gravity Equation in International Trade: Some Microeconomic Foundations and Empirical Evidence,” The Review of Economics and Statistics, 67, 474–481.
  • Butland, G., Peregrín-Alvarez, J.M., Li, J., Yang, W., Yang, X., Canadien, V., Starostine, A., Richards, D., Beattie, B., Krogan, N., Davey, M., Parkinson, J., Greenblatt, J., and Emili, A. (2005), “Interaction Network Containing Conserved and Essential Protein Complexes in Escherichia Coli,” Nature, 433, 531–537.
  • Dawid, A. (1981), “Some Matrix-Variate Distribution Theory: Notational Consi-derations and a Bayesian Application,” Biometrika, 68, 265–274.
  • Eaton, M. (1983), Multivariate Statistics: A Vector Space Approach, New York: Wiley.
  • Eriksen, P.S. (1987), “Proportionality of Covariance Matrices,” The Annals of Statistics, 15, 732–748.
  • Fletcher, A., Bonell, C., and Sorhaindo, A. (2011), “You are What Your Friends Eat: Systematic Review of Social Network Analyses of Young People’s Eating Behaviours and Bodyweight,” Journal of Epidemiology and Community Health, 65, 548–555.
  • Flury, B.K. (1986), “Proportionality of k Covariance Matrices,” Statistics & Probability Letters, 4, 29–33.
  • Gupta, A., and Varga, T. (1994), “A New Class of Matrix Variate Elliptically Contoured Distributions,” Statistical Methods & Applications, 3, 255–270.
  • Gupta, A. (1995), “Some Inference Problems for Matrix Variate Elliptically Contoured Distributions,” Statistics: A Journal of Theoretical and Applied Statistics, 26, 219–229.
  • Hoff, P. (2005), “Bilinear Mixed-Effects Models for Dyadic Data,” Journal of the American Statistical Association, 100, 286–295.
  • Hoff, P. (2008), “Modeling Homophily and Stochastic Equivalence in Symmetric Relational Data,” in Advances in Neural Information Processing Systems 20, eds. J. Platt, D. Koller, Y. Singer and S. Roweis, Cambridge, MA: MIT Press, pp. 657–664.
  • Hoff, P. (2011), “Separable Covariance Arrays via the Tucker Product, With Applications to Multivariate Relational Data,” Bayesian Analysis, 6, 179–196.
  • Hoff, P., Raftery, A., and Handcock, M. (2002), “Latent Space Approaches to Social Network Analysis,” Journal of the American Statistical Association, 97, 1090–1098.
  • Holland, P., Laskey, K., and Leinhardt, S. (1983), “Stochastic Blockmodels: First Steps,” Social Networks, 5, 109–137.
  • Jensen, S.T., and Johansen, S. (1987), “Estimation of Proportional Covariances,” Statistics & Probability Letters, 6, 83–85.
  • Jensen, S.T., and Madsen, J. (2004), “Estimation of Proportional Covariances in the Presene of Certain Linear Restrictions,” The Annals of Statistics, 32, 219–232.
  • Kenny, D., and Voie, L. (1984), “The Social Relations Model,” Advances in Experimental Social Psychology, 18, 142–182.
  • Lafosse, R., and Berge, J. (2006), “A Simultaneous Concor Algorithm for the Analysis of Two Partitioned Matrices,” Computational Statistics & Data Analysis, 50, 2529–2535.
  • Lazzarini, S., Chaddad, F., and Cook, M. (2001), “Integrating Supply Chain and Network Analyses: The Study of Netchains,” Journal on Chain and Network Science, 1, 7–22.
  • Leskovec, J., Lang, K., Dasgupta, A., and Mahoney, M. (2008), “Statistical Properties of Community Structure in Large Social and Information Networks,” in Proceeding of the 17th International Conference on World Wide Web, pp. 695–704. ACM.
  • Li, H. (2006), “The Covariance Structure and Likelihood Function for Multivariate Dyadic Data,” Journal of Multivariate Analysis, 97, 1263–1271.
  • Li, H., and Loken, E. (2002), “A Unified Theory of Statistical Analysis and Inference for Variance Component Models for Dyadic Data,” Statistica Sinica, 12, 519–535.
  • Lincoln, J., and Gerlach, M. (2004), Japan’s Network Economy: Structure, Persistence, and Change, Cambridge, UK: Cambridge University Press.
  • Lu, N., and Zimmerman, D. (2005), “The Likelihood Ratio Test for a Separable Covariance Matrix,” Statistics & Probability Letters, 73, 449–457.
  • McQuitty, L., and Clark, J. (1968), “Clusters From Iterative, Intercolumnar Correlational Analysis,” Educational and Psychological Measurement, 28, 211–238.
  • Mitchell, M., Genton, M., and Gumpertz, M. (2006), “A Likelihood Ratio Test for Separability of Covariances,” Journal of Multivariate Analysis, 97, 1025–1043.
  • Nowicki, K., and Snijders, T. (2001), “Estimation and Prediction for Stochastic Blockstructures,” Journal of the American Statistical Association, 96, 1077–1087.
  • Panning, W. (1982), “Fitting Blockmodels to Data,” Social Networks, 4, 81–101.
  • Potter, G., Handcock, M., Longini, I., and Halloran, M. (2012), “Estimating Within-School Contact Networks to Understand Influenza Transmission,” The Annals of Applied Statistics, 6, 1–26.
  • Roy, A., and Khattree, R. (2005), “On Implementation of a Test for Kronecker Product Covariance Structure for Multivariate Repeated Measures Data,” Statistical Methodology, 2, 297–306.
  • Sampson, S. (1968), “A Novitiate in a Period of Change: An Experimental and Case Study of Social Relationships,” PhD thesis, Cornell University.
  • Srivastava, M., von Rosen, T., and Rosen, D. (2008), “Models With a Kronecker Product Covariance Structure: Estimation and Testing,” Mathematical Methods of Statistics, 17, 357–370.
  • Stuart, J., Segal, E., Koller, D., and Kim, S. (2003), “A Gene-Coexpression Network for Global Discovery of Conserved Genetic Modules,” Science, 302, 249–255.
  • Thompson, E., and Geyer, C. (2007), “Fuzzy p-values in Latent Variable Problems,” Biometrika, 94, 49–60.
  • Tinbergen, J. (1962), Shaping the World Economy: Suggestions for an International Economic Policy, New York: Twentieth Century Fund.
  • Tseng, P. (2001), “Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization,” Journal of Optimization Theory and Applications, 109, 475–494.
  • Wang, Y., and Wong, G. (1987), “Stochastic Blockmodels for Directed Graphs,” Journal of the American Statistical Association, 82, 8–19.
  • Westveld, A., and Hoff, P. (2011a), “A Mixed Effects Model for Longitudinal Relational and Network Data, With Applications to International Trade and Conflict,” The Annals of Applied Statistics, 5, 843–872.
  • Westveld, A. (2011b), “A Mixed Effects Model for Longitudinal Relational and Network Data, With Applications to International Trade and Conflict,” The Annals of Applied Statistics, 5, 843–872.
  • White, H., Boorman, S., and Breiger, R. (1976), “Social Structure From Multiple Networks. I. Blockmodels of Roles and Positions,” American Journal of Sociology, 730–780.
  • Yu, K., Chu, W., Yu, S., Tresp, V., and Xu, Z. (2007), “Stochastic Relational Models for Discriminative Link Prediction,” Advances in Neural Information Processing Systems, 19, 1553.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.