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Abstract
In the analysis of survey data, it is of interest to estimate and quantify uncertainty about means or totals for each of several nonoverlapping subpopulations or areas. When the sample size for a given area is small, standard confidence intervals based on data only from that area can be unacceptably wide. In order to reduce interval width, practitioners often utilize multilevel models in order to borrow information across areas, resulting in intervals centered around shrinkage estimators. However, such intervals only have the nominal coverage rate on average across areas under the assumed model for across-area heterogeneity. The coverage rate for a given area depends on the actual value of the area mean and can be nearly zero for areas with means that are far from the across-group average. As such, the use of uncertainty intervals centered around shrinkage estimators are inappropriate when area-specific coverage rates are desired. In this article, we propose an alternative confidence interval procedure for area means and totals under normally distributed sampling errors. This procedure not only has constant 1−α frequentist coverage for all values of the target quantity but also uses auxiliary information to borrow information across areas. Because of this, the corresponding intervals have shorter expected lengths than standard confidence intervals centered on the unbiased direct estimator. Importantly, the coverage of the procedure does not depend on the assumed model for across-area heterogeneity. Rather, improvements to the model for across-area heterogeneity result in reduced expected interval width.

The authors examine a standard gravity model of international commerce augmented to include political as well as institutional influences on bilateral trade. Using annual data from 1980-2001, they estimate regression coefficients and residual dependencies using a hierarchy of models in each year. Rather than gauge the generalizability of these patterns via traditional measures of statistical significance such as p-values, this article develops and employs a strategy to evaluate the out-of-sample predictive strength of various models. The analysis of recent international commerce shows that in addition to a typical gravity-model specification, political and institutional variables are important. The article also demonstrates that the often-reported link between international conflict and bilateral trade is elusive, and that inclusion of conflict in a trade model can sometimes lead to reduced out-of-sample predictive performance. Further, this article illustrates that there are substantial, persistent residual exporter- and importer-specific effects, and that ignoring such patterns in relational trade data results in an incomplete picture of international commerce, even in the context of a well-established framework such as the gravity model.

Despite the desire to focus on the interconnected nature of politics and economics at the global scale, most empirical studies in the field of international relations assume not only that the major actors are sovereign, but also that their relationships are portrayed in data that are modeled as independent phenomena. In contrast, this article illustrates the use of linear and bilinear random—effects models to represent statistical dependencies that often characterize dyadic data such as international relations. In particular, we show how to estimate models for dyadic data that simultaneously take into account: (a) regressor variables, (b) correlation of actions having the same actor, (c) correlation of actions having the same target, (d) correlation of actions between a pair of actors (i.e., reciprocity of actions), and (e) third-order dependencies, such as transitivity, clustering, and balance. We apply this new approach to the political relations among a wide range of political actors in Central Asia over the period 1989–1999, illustrating the presence and strength of second- and third-order statistical dependencies in these data.

We introduce a Bayesian approach to conduct inferential analyses on dyadic data while accounting for interdependencies between observations through a set of additive and multiplicative effects (AME). The AME model is built on a generalized linear modeling framework and is thus flexible enough to be applied to a variety of contexts. We contrast the AME model to two prominent approaches in the literature: the latent space model (LSM) and the exponential random graph model (ERGM). Relative to these approaches, we show that the AME approach is (a) to be easy to implement; (b) interpretable in a general linear model framework; (c) computationally straightforward; (d) not prone to degeneracy; (e) captures first-, second-, and third-order network dependencies; and (f) notably outperforms ERGMs and LSMs on a variety of metrics and in an out-of-sample context. In summary, AME offers a straightforward way to undertake nuanced, principled inferential network analysis for a wide range of social science questions.

Previous models of international conflict have suffered two shortfalls. They tend not to embody dynamic changes, focusing rather on static slices of behavior over time across a single relational dimension. These models have also been empirically evaluated in ways that assumed the independence of each country, when in reality they are searching for the interdependence among all countries. A number of approaches are available now for analyzing relational data such as international conflict in a network context and a number of these can even handle longitudinal relational data, but none are developed to the point of exploring how networks can coevolve over time. We illustrate a solution to the limitations of existing approaches and apply this novel, dynamic, network based approach to study the dependencies among the ebb and flow of daily international interactions using a newly developed, and openly available, database of events among nations.