Goodness of fit for log-linear network models: dynamic Markov bases using hypergraphs

Elizabeth Gross (), Sonja Petrović () and Despina Stasi ()
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Elizabeth Gross: San José State University
Sonja Petrović: Illinois Institute of Technology
Despina Stasi: Illinois Institute of Technology

Annals of the Institute of Statistical Mathematics, 2017, vol. 69, issue 3, No 8, 673-704

Abstract: Abstract Social networks and other sparse data sets pose significant challenges for statistical inference, since many standard statistical methods for testing model/data fit are not applicable in such settings. Algebraic statistics offers a theoretically justified approach to goodness-of-fit testing that relies on the theory of Markov bases. Most current practices require the computation of the entire basis, which is infeasible in many practical settings. We present a dynamic approach to explore the fiber of a model, which bypasses this issue, and is based on the combinatorics of hypergraphs arising from the toric algebra structure of log-linear models. We demonstrate the approach on the Holland–Leinhardt $$p_1$$ p 1 model for random directed graphs that allows for reciprocation effects.

Keywords: Algebraic statistics; Markov basis; Hypergraph; Toric ideal; Contingency table; Network model; Random graph; Sampling algorithm (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10463-016-0560-2

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