On the sampling distribution of the ML estimators in Network Autocorrelation Models

This work investigates the finite sample properties of the maximum likelihood (ML) estimators for network autocorrelation models (NAMs), a class of auto-regressive models used to study the effect of networks on dependent variables of interest when the data points are interdependent. It is known that the estimated autocorrelation parameter has a finite sample negative bias, the amount of which is positively related with the network density (Mizruchi, Neuman, 2008, 2010). A recent study on the statistical power of a test on the same parameter is also available (Wang et al. 2014). We examine the whole finite sample distribution of both the ML estimator of the autocorrelation parameter and the regressor parameters. More specifically, through an extensive simulation study, this work investigates whether – and the conditions under which – the ML estimators are normally distributed. The finite sample distributions are evaluated with respect to the network density and topology, the distribution of error terms, and the strength of the autocorrelation parameter. It turns out that the ML estimators of the autocorrelation parameter and of the intercept are not normally distributed in case of small sample size, even in presence of normally distributed errors. Furthermore, the network density has some effect on the variability of the estimators. On the other hand, it seems that other features of the network topologies, in the main, have little effects on the estimator distributions. Also, proper methods to deal with the bias of autocorrelation parameter are introduced and studied. Particularly, a residual-based bootstrap is proposed, in line with a related literature (Lin et al., 2011; Yang, 2013). A further simulation study shows that the bootstrap based distributions are more accurate and should be preferred in case of low density and moderate network effects.