Replication data for: Location, Location, Location: An MCMC Approach to Modeling the Spatial Context of War & Peace

This article demonstrates how spatially dependent data with a categorical response variable can be addressed in a statistical model. We introduce the idea of an autologistic model where the response for one observation is dependent on the value of the response among adjacent observations. The autologistic model has likelihood function that is mathematically intractable, since the observations are conditionally dependent upon one another. We review alternative techniques for estimating this model, with special emphasis on recent advances using Markov chain Monte Carlo (MCMC) techniques. We evaluate a highly simplified autologistic model of conflict where the likelihood of war involvement for each nation is conditional on the war involvement of proximate states. We estimate this autologistic model for a single year (1988) via maximum pseudolikelihood and MCMC maximum likelihood methods. Our results indicate that the autologistic model fits the data much better than an unconditional model and that the MCMC estimates generally dominate the pseudolikelihood estimates. The autologistic model generates predicted probabilities greater than 0.5 and has relatively good predictive abilities in an out-of-sample forecast for the subsequent decade (1989 to 1998), correctly identifying not only ongoing conflicts, but also new ones.

本文阐述了如何在统计模型中处理带有类别响应变量的空间依赖数据。本文提出了自逻辑斯蒂模型（autologistic model）的概念，该模型中单个观测的响应值依赖于相邻观测的响应值。由于观测值之间存在条件依赖关系，自逻辑斯蒂模型的似然函数在数学上难以求解。本文综述了该模型的各类估计替代方法，重点探讨了基于马尔可夫链蒙特卡洛（Markov chain Monte Carlo, MCMC）方法的最新研究进展。本文评估了一个高度简化的冲突场景自逻辑斯蒂模型：每个国家卷入战争的概率，取决于其邻近国家的战争卷入状态。本文采用伪似然极大估计法与马尔可夫链蒙特卡洛极大似然法，针对1988年这单个年份拟合了该自逻辑斯蒂模型。研究结果表明，自逻辑斯蒂模型对数据的拟合效果远优于无条件模型，且马尔可夫链蒙特卡洛估计的整体表现优于伪似然估计。该自逻辑斯蒂模型生成的预测概率均大于0.5，且在1989至1998年这十年的样本外预测中展现出较为优异的预测性能：不仅能准确识别持续发生的冲突，还能正确预判新冲突的出现。