Dyadic (state-pair) data is completely inappropriate for analyzing multilateral events (such as large alliances and major wars). Scholars, particularly in international relations, often divide the actors in a multilateral event into a series of dyadic relations. Though this practice can dramatically increase the size of data sets, using dyadic data to analyze what are, in reality, k-adic events leads to model misspecification and, inevitably, statistical bias. In short, one cannot recover a k-adic data generating process using dy-adic data. In this paper, I accomplish three tasks. First, I use Monte Carlo simulations to confirm that analyzing k-adic events with dyadic data produces substantial bias. Second, I show that choice-based sampling, as popularized by King and Zeng (2001a, Explaining rare events in international relations. International Organization 55:693–715, and 2001b, Logistic regression in rare events data. Political Analysis 9:137–63), can be used to create feasibly sized k-adic data sets. Finally, I use the study of alliance formation by Gibler and Wolford (2006, Alliances, then democracy: An examination of the relationship between regime type and alliance formation. The Journal of Conflict Resolution 50:1–25) to illustrate how to apply this choice-based sampling solution and explain how to code independent variables in a k-adic context.

Using a Bayesian latent variable approach, we synthesize a new measure of democracy, the Unified Democracy Scores (UDS), from 10 extant scales. Our measure eschews the difficult—and often arbitrary—decision to use one existing democracy scale over another in favor of a cumulative approach that allows us to simultaneously leverage the measurement efforts of numerous scholars. The result of this cumulative approach is a measure of democracy that, for every country-year, is at least as reliable as the most reliable component measure and is accompanied by quantitative estimates of uncertainty in the level of democracy. Moreover, for those who wish to continue using previously existing scales or to evaluate research performed using those scales, we extract information from the new measure to perform heretofore impossible direct comparisons between component scales. Specifically, we estimate the relative reliability of the constituent indicators, compare the specific ordinal levels of each of the existing measures in relationship to one another and assess overall levels of disagreement across raters. We make the UDS and associated parameter estimates freely available online and provide a detailed tutorial that demonstrates how to best use the UDS in applied work.

Researchers using latent class (LC) analysis often proceed using the following three steps: (1) an LC model is built for a set of response variables, (2) subjects are assigned to LCs based on their posterior class membership probabilities, and (3) the association between the assigned class membership and external variables is investigated using simple cross-tabulations or multinomial logistic regression analysis. Bolck, Croon, and Hagenaars (2004) demonstrated that such a three-step approach underestimates the associations between covariates and class membership. They proposed resolving this problem by means of a specific correction method that involves modifying the third step. In this article, I extend the correction method of Bolck, Croon, and Hagenaars by showing that it involves maximizing a weighted log-likelihood function for clustered data. This conceptualization makes it possible to apply the method not only with categorical but also with continuous explanatory variables, to obtain correct tests using complex sampling variance estimation methods, and to implement it in standard software for logistic regression analysis. In addition, a new maximum likelihood (ML)—based correction method is proposed, which is more direct in the sense that it does not require analyzing weighted data. This new three-step ML method can be easily implemented in software for LC analysis. The reported simulation study shows that both correction methods perform very well in the sense that their parameter estimates and their SEs can be trusted, except for situations with very poorly separated classes. The main advantage of the ML method compared with the Bolck, Croon, and Hagenaars approach is that it is much more efficient and almost as efficient as one-step ML estimation.

This paper proposes a Bayesian generalized linear multilevel model with a pth-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, its pth-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.

The issue of how qualitative and quantitative information can be used together is critical. Brady, Collier, and Seawright (BCS) have argued that “causal process observations” can be adjoined to “data set observations.” This implies that qualitative methods can be used to add information to quantitative data sets. In a symposium in Political Analysis, I argued that such qualitative information cannot be adjoined in any meaningful way to quantitative data sets. In that symposium, the original authors offered several defenses, but, in the end, BCS can be seen as recommending good, but hopefully standard, research design practices that are normally thought of as central in the quantitative arena. It is good that BCS remind us that no amount of fancy statistics can save a bad research design.

Both qualitative and quantitative research routinely fall short, producing misleading causal inferences. Because these weaknesses are in part different, we are convinced that multimethod strategies are productive. Each approach can provide additional leverage that helps address shortcomings of the other. This position is quite distinct from that of Beck, who believes that the two types of analysis cannot be adjoined. We review examples of adjoining that Beck dismisses, based on what we see as his outdated view of qualitative methods. By contrast, we show that these examples demonstrate how qualitative and quantitative analysis can work together.