Sparse network asymptotics for logistic regression

Arbeitspapier

Consider a bipartite network where N consumers choose to buy or not to buy M different products. This paper considers the properties of the logistic regression of the N ×M array of "i-buys-j" purchase decisions, [Yij ] 1ÈiÈN,1ÈjÈM, onto known functions of consumer and product attributes under asymptotic sequences where (i) both N and M grow large and (ii) the average number of products purchased per consumer is finite in the limit. This latter assumption implies that the network of purchases is sparse: only a (very) small fraction of all possible purchases are actually made (concordant with many realworld settings). Under sparse network asymptotics, the first and last terms in an extended Hoeffding-type variance decomposition of the score of the logit composite log-likelihood are of equal order. In contrast, under dense network asymptotics, the last term is asymptotically negligible. Asymptotic normality of the logistic regression coefficients is shown using a martingale central limit theorem (CLT) for triangular arrays. Unlike in the dense case, the normality result derived here also holds under degeneracy of the network graphon. Relatedly, when there "happens to be" no dyadic dependence in the dataset in hand, it specializes to recently derived results on the behavior of logistic regression with rare events and iid data. Sparse network asymptotics may lead to better inference in practice since they suggest variance estimators which (i) incorporate additional sources of sampling variation and (ii) are valid under varying degrees of dyadic dependence.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: cemmap working paper ; No. CWP51/20

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Multiple or Simultaneous Equation Models: Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models ; Multiple or Simultaneous Equation Models: Panel Data Models; Spatio-temporal Models ; Multiple or Simultaneous Equation Models: Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
• Thema: Networks ; Exchangeable Random Arrays ; Dyadic Clustering ; Sparse Networks ; Logistic Regression ; Rare Events ; Marginal Effects

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Graham, Bryan S.
• Ereignis: Veröffentlichung
• (wer): Centre for Microdata Methods and Practice (cemmap)
• (wo): London
• (wann): 2020

Weitere Informationen

• DOI: doi:10.47004/wp.cem.2020.5120
• Handle: http://hdl.handle.net/10419/241926
• Letzte Aktualisierung: 10.03.2025, 11:43 MEZ