title: Testing the hypothesis of preferential attachment in social network formation.
abstract: The hypothesis of preferential attachment (PA) - whereby better connected individuals make more connections - is hotly debated, particularly in the context of epidemiological networks. The simplest models of PA, for example, are incompatible with the eradication of any disease through population-level control measures such as random vaccination. Typically, evidence has been sought for the presence or absence of preferential attachment via asymptotic power-law behaviour. Here, we present a general statistical method to test directly for evidence of PA in count data and apply this to data for contacts relevant to the spread of respiratory diseases. We find that while standard methods for model selection prefer a form of PA, careful analysis of the best fitting PA models allows for a level of contact heterogeneity that in fact allows control of respiratory diseases. Our approach is based on a flexible but numerically cheap likelihood-based model that could in principle be applied to other integer data where the hypothesis of PA is of interest.
authors.affiliation: School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL UK ; Warwick Infectious Disease Epidemiology Research (WIDER), University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL UK.
authors.forename: Thomas
authors.identifier: 0000-0001-5835-8062
authors.initials: T
authors.lastname: House
authors.affiliation: CHICAS, Faculty of Health and Medicine, Lancaster University, Lancaster, Lancashire LA1 4YG UK.
authors.forename: Jonathan M
authors.initials: JM
authors.lastname: Read
authors.affiliation: School of Social and Community Medicine, University of Bristol, Oakfield Grove, Clifton, BS8 2BN UK.
authors.forename: Leon
authors.initials: L
authors.lastname: Danon
authors.affiliation: Warwick Infectious Disease Epidemiology Research (WIDER), University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL UK.
authors.forename: Matthew J
authors.initials: MJ
authors.lastname: Keeling
keywords: MLE; Phase-type distribution; model selection; spectral methods