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Multifactor error structures utilize factor analysis to deal with complex cross-sectional dependence in Time-Series Cross-Sectional data caused by cross-level interactions. The multifactor error structure specification is a generalization of the fixed-effects model. This article extends the existing multifactor error models from panel econometrics to multilevel modeling, from linear setups to generalized linear models with the probit and logistic links, and from assuming serial independence to modeling the error dynamics with an autoregressive process. I develop Markov Chain Monte Carlo algorithms mixed with a rejection sampling scheme to estimate the multilevel multifactor error structure model with apth-order autoregressive process in linear, probit, and logistic specifications. I conduct several Monte Carlo studies to compare the performance of alternative specifications and approaches with varying degrees of data complication and different sample sizes. The Monte Carlo studies provide guidance on when and how to apply the proposed model. An empirical application sovereign default demonstrates how the proposed approach can accommodate a complex pattern of cross-sectional dependence and helps answer research questions related to units' sensitivity or vulnerability to systemic shocks.

This paper proposes a Bayesian generalized linear multilevel model with apth-order autoregressive error process to analyze unbalanced binary time-series cross-sectional (TSCS) data. The model specification is motivated by the generic TSCS data structure and is intended to handle the associated inefficiency and endogeneity problems. It accommodates heterogeneity across units and between time periods in the form of random intercepts and random-effect coefficients. At the same time, itspth-order autoregressive error process, employed either by itself or in concert with other dynamic methods, adequately corrects serial correlation and improves statistical inference and forecasting. With a stationarity restriction on the error process, the model can also be used as a residual-based cointegration test on discrete TSCS data. This is especially valuable because cointegration testing on discrete TSCS data is methodologically challenging and rarely conducted in practice. To handle the estimation difficulties, I developed an efficient Markov chain Monte Carlo (MCMC) algorithm by orthogonalizing the error term with the Cholesky decomposition and adding an auxiliary variable. The parameter expansion method, that is, partial group move—multigrid Monte Carlo updating (PGM-MGMC), is employed to further improve MCMC mixing and speed up convergence. The paper also provides a computational scheme to approximate the Bayes's factor for the purposes of serial correlation diagnostics, lag order determination, and variable selection. Simulated and empirical examples are used to assess the model and techniques.

AbstractThis paper proposes a Bayesian multilevel spatio-temporal model with a time-varying spatial autoregressive coefficient to estimate temporally heterogeneous network interdependence. To tackle the classic reflection problem, we use multiple factors to control for confounding caused by latent homophily and common exposures. We develop a Markov Chain Monte Carlo algorithm to estimate parameters and adopt Bayesian shrinkage to determine the number of factors. Tests on simulated and empirical data show that the proposed model improves identification of network interdependence and is robust to misspecification. Our method is applicable to various types of networks and provides a simpler and more flexible alternative to coevolution models.

AbstractThis paper proposes a Bayesian alternative to the synthetic control method for comparative case studies with a single or multiple treated units. We adopt a Bayesian posterior predictive approach to Rubin's causal model, which allows researchers to make inferences about both individual and average treatment effects on treated observations based on the empirical posterior distributions of their counterfactuals. The prediction model we develop is a dynamic multilevel model with a latent factor term to correct biases induced by unit-specific time trends. It also considers heterogeneous and dynamic relationships between covariates and the outcome, thus improving precision of the causal estimates. To reduce model dependency, we adopt a Bayesian shrinkage method for model searching and factor selection. Monte Carlo exercises demonstrate that our method produces more precise causal estimates than existing approaches and achieves correct frequentist coverage rates even when sample sizes are small and rich heterogeneities are present in data. We illustrate the method with two empirical examples from political economy.

Following older debates in international relations literature concerning the relative importance of domestic versus systemic factors, newer debates emphasize interdependence among states and the complex interactions between systemic and domestic factors. As globalization and democratization advance, theories and empirical models of international politics have become more complicated. We present a systematic theoretical categorization of relationships between domestic and systemic variables. We use this categorization so that scholars can match their theory to the appropriate empirical model and assess the degree to which systemic factors affect their arguments. We also present two advances at the frontier of these empirical models. In one, we combine hierarchical models of moderating relationships with spatial models of interdependence among units within a system. In the other, we provide a model for analyzing spatial interdependence that varies over time. This enables us to examine how the level of interdependence among units has evolved. We illustrate our categorization and new models by revisiting the recent international political economy (IPE) debate over the relationship between trade policy and regime type in developing countries. Adapted from the source document.

AbstractFollowing older debates in international relations literature concerning the relative importance of domestic versus systemic factors, newer debates emphasize interdependence among states and the complex interactions between systemic and domestic factors. As globalization and democratization advance, theories and empirical models of international politics have become more complicated. We present a systematic theoretical categorization of relationships between domestic and systemic variables. We use this categorization so that scholars can match their theory to the appropriate empirical model and assess the degree to which systemic factors affect their arguments. We also present two advances at the frontier of these empirical models. In one, we combine hierarchical models of moderating relationships with spatial models of interdependence among units within a system. In the other, we provide a model for analyzing spatial interdependence that varies over time. This enables us to examine how the level of interdependence among units has evolved. We illustrate our categorization and new models by revisiting the recent international political economy (IPE) debate over the relationship between trade policy and regime type in developing countries.

Jurisprudential regime theory is a legal explanation of decision-making on the U.S. Supreme Court that asserts that a key precedent in an area of law fundamentally restructures the relationship between case characteristics and the outcomes of future cases. In this article, we offer a multivariate multiple change-point probit model that can be used to endogenously test for the existence of jurisprudential regimes. Unlike the previously employed methods, our model does so by estimating the locations of many possible change-points along with structural parameters. We estimate the model using Markov chain Monte Carlo methods, and use Bayesian model comparison to determine the number of change-points. Our findings are consistent with jurisprudential regimes in the Establishment Clause and administrative law contexts. We find little support for hypothesized regimes in the areas of free speech and search-and-seizure. The Bayesian multivariate change-point model we propose has broad potential applications to studying structural breaks in either regular or irregular time-series data about political institutions or processes.