Structure and bias in the network autocorrelation model

In a recent paper (Mizruchi and Neuman, 2008), we showed that estimates of ρ in the network autocorrelation model exhibited a systematic negative bias and that the magnitude of this bias increased monotonically with increases in network density. We showed that this bias held regardless of the size of the network, the number of exogenous variables in the model, and whether the matrix W was normalized or in raw form. The networks in our simulations were random, however, which raises the question of the extent to which the negative bias holds in various structured networks. In this paper, we reproduce the simulations from our earlier paper on a series of networks drawn to represent well-known structures, including star, caveman, and small-world structures. Results from these simulations indicate that the pattern of negative bias in ρ continues to hold in all of these structures and that the negative bias continues to increase at increasing levels of density. Interestingly, the negative bias in ρ is especially pronounced at extremely low-density levels in the star network. We conclude by discussing the implications of these findings.