Estimating Binary Spatial Autoregressive Models for Rare Events

This paper proposes a new statistical estimator, to be applied to the prediction of state failures. State failures are typically conceptualised in a binary fashion---a state fails or it does not---and are rare events (King & Zeng 2001). Furthermore, state failures are not geographically independent events. The failure of one state can be expected to have an impact on the stability and peace in neighboring states, increasing the probability of state failures in geographical contiguous regions. Currently there is mixed evidence of such diffusion of state failure taking place (Iqbal & Starr 2008). This paper proposes a new estimator to be used for estimates of the spatial interdependence among state failures and focuses on the ability to predict state failures in an international context. The most used spatial regression models for binary dependent variable consider a symmetric link function. When the dependent variable represents a rare event, a symmetric link function is not coherent. Following (Calabrese & Osmetti 2013), we suggest the quantile function of the Generalized Extreme Value (GEV) distribution as link function in a spatial generalised linear model and we call this model the Spatial GEV (SGEV) regression model. To estimate the parameters of such model, a Gibbs sampler based on work by Le Sage (2000) and Wang & Dey (2010) is proposed. We analyse the performance of our model by Monte Carlo simulations and comparison on state failure data.