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On the question of effective sample size in network modeling: an asymptotic inquiry

Journal Article


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Abstract


  • The modeling and analysis of networks and network data has seen an

    explosion of interest in recent years and represents an exciting direction for

    potential growth in statistics. Despite the already substantial amount of work

    done in this area to date by researchers from various disciplines, however,

    there remain many questions of a decidedly foundational nature — natural

    analogues of standard questions already posed and addressed in more

    classical areas of statistics — that have yet to even be posed, much less addressed.

    Here we raise and consider one such question in connection with

    network modeling. Specifically, we ask, “Given an observed network, what

    is the sample size?” Using simple, illustrative examples from the class of

    exponential random graph models, we show that the answer to this question

    can very much depend on basic properties of the networks expected under

    the model, as the number of vertices nV in the network grows. In particular,

    adopting the (asymptotic) scaling of the variance of the maximum likelihood

    parameter estimates as a notion of effective sample size, say neff, we show

    that whether the networks are sparse or not under our model (i.e., having

    relatively few or many edges between vertices, respectively) is sufficient to yield an order of magnitude difference in neff, from O(nV) to O(n2V). We

    then explore some practical implications of this result, using both simulation

    and data on food-sharing from Lamalera, Indonesia.

Publication Date


  • 2015

Citation


  • Krivitsky, P. N.. & Kolaczyk, E. D. (2015). On the question of effective sample size in network modeling: an asymptotic inquiry. Statistical Science: a review journal, 30 (2), 184-198.

Scopus Eid


  • 2-s2.0-84930889619

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=5527&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4506

Has Global Citation Frequency


Number Of Pages


  • 14

Start Page


  • 184

End Page


  • 198

Volume


  • 30

Issue


  • 2

Place Of Publication


  • United States

Abstract


  • The modeling and analysis of networks and network data has seen an

    explosion of interest in recent years and represents an exciting direction for

    potential growth in statistics. Despite the already substantial amount of work

    done in this area to date by researchers from various disciplines, however,

    there remain many questions of a decidedly foundational nature — natural

    analogues of standard questions already posed and addressed in more

    classical areas of statistics — that have yet to even be posed, much less addressed.

    Here we raise and consider one such question in connection with

    network modeling. Specifically, we ask, “Given an observed network, what

    is the sample size?” Using simple, illustrative examples from the class of

    exponential random graph models, we show that the answer to this question

    can very much depend on basic properties of the networks expected under

    the model, as the number of vertices nV in the network grows. In particular,

    adopting the (asymptotic) scaling of the variance of the maximum likelihood

    parameter estimates as a notion of effective sample size, say neff, we show

    that whether the networks are sparse or not under our model (i.e., having

    relatively few or many edges between vertices, respectively) is sufficient to yield an order of magnitude difference in neff, from O(nV) to O(n2V). We

    then explore some practical implications of this result, using both simulation

    and data on food-sharing from Lamalera, Indonesia.

Publication Date


  • 2015

Citation


  • Krivitsky, P. N.. & Kolaczyk, E. D. (2015). On the question of effective sample size in network modeling: an asymptotic inquiry. Statistical Science: a review journal, 30 (2), 184-198.

Scopus Eid


  • 2-s2.0-84930889619

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=5527&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4506

Has Global Citation Frequency


Number Of Pages


  • 14

Start Page


  • 184

End Page


  • 198

Volume


  • 30

Issue


  • 2

Place Of Publication


  • United States