A statistical model for the analysis of mobility tables as weighted networks with an application to faculty hiring networks

Mobility of individuals between a wide variety of geographic locations, social positions, or roles is frequently analysed in the social sciences. In recent research, mobility has increasingly been conceptualised as a network. For example, residential mobility, when individuals move between neighbourhoods of a city, can be understood as a network in which neighbourhoods are nodes that are tied by counts of mobile individuals that move from one neighbourhood to another. Understanding mobility as a network allows to apply concepts and methods from the network analyst's toolbox. However, the statistical modelling of such weighted networks in which ties can have individual attributes remains difficult. In this article we propose a statistical model for the analysis of mobility tables conceptualised as networks, combining properties from log-linear models and exponential random graph models (ERGMs). When no endogenous patterns are modelled, it reduces to a classic log-linear model for mobility tables. When modelling endogenous patterns but ignoring individual attributes, the model can be understood as an ERGM for weighted networks in which tie weights denote counts. Making use of special constraints of mobility networks, the model offers a parsimonious way to deal with weighted ties. Going beyond classical ERG modelling, the proposed approach can additionally incorporate tie characteristics that represent individual attributes of mobile people. The model is applied to two cases of faculty hiring networks-linking current departments of faculty members with their PhD granting institution-in history and computer science in the US.