Bradford S. Jones

Modeling Multilevel Data Structures

data are becoming quite common in political science and provide numerous opportunities for theory testing and development. Unfortunately this type of data typically generates a number of statistical problems, of which clustering is particularly impor? tant. To exploit the opportunities of? fered by multilevel data, and to solve the statistical problems inherent in them, special statistical techniques are required. In this article, we focus on a technique that has become popular in educational statistics and sociology?multilevel analysis. In multilevel analysis, researchers build models that capture the layered structure of multilevel data, and determine how layers interact and impact a dependent variable of interest. Our objective in this article is to introduce the logic and statistical theory behind multilevel models, to illustrate how such models can be applied fruitfully in political science, and to call atten? tion to some of the pitfalls in multilevel analysis.

Vote-Seeking Incentives and Legislative Representation in Six Presidential Democracies

Through the use of an original data set of bill initiation activity in six presidential democracies, we advance scholarly understanding of how the institutional incentives faced by legislative candidates influence representation. We extend and adapt theory, derived primarily from the experience of the U.S. Congress, demonstrating its viability, once assumed constants from the U.S. case are explicitly modeled, in quite distinct institutional contexts. In particular, we find the focus of individual legislators on national versus parochial concerns responds to the incentives provided by the candidate selection process, general election rules, legislator career patterns, and interbranch relations.

Beyond Logit and Probit: Cox Duration Models of Single, Repeating, and Competing Events for State Policy Adoption:

Since 1990, the standard statistical approach for studying state policy adoption has been an event history analysis using binary link models, such as logit or probit. In this article, we evaluate this logit-probit approach and consider some alternative strategies for state policy adoption research. In particular, we discuss the Cox model, which avoids the need to parameterize the baseline hazard function and, therefore, is often preferable to the logit-probit approach. Furthermore, we demonstrate how the Cox model can be modified to deal effectively with repeatable and competing events, events that the logit-probit approach cannot be used to model.

Maintenance Processes in International Rivalries

This article asks a new question: what are the processes that maintain rivalries? The authors argue that rivalries are maintained through the failure of realist strategies and conflict management ones. They focus on stalemate outcomes as both a signal that militarized strategies for dealing with conflict have not succeeded and as reasons for the countries to continue the rivalry. They explore the process of rivalry maintenance, largely from the perspective of the punctuated equilibrium model of rivalries, and examine 1,166 rivalries across the period from 1816 to 1992. They contrast their approach with that of the “repeated conflicts” literature, which only examines the impact of the previous dispute on recurring conflict. The authors find that the most recent conflict does matter, and the longer term history of the rivalry is more important. They also find that the impacts of various factors (e.g., democracy) change over the course of the rivalry.

Diagnostic Methods for the Event History Model

In this chapter, we consider some important issues regarding model selection, assessment, and diagnostic methods through the use of residuals. The issues discussed in this chapter have a direct analog to methods of model selection and to model diagnostics in the context of the traditional linear model. For example, issues pertaining to functional form, influential observations, and similar other topics are directly relevant to the duration model. Because most of the methods of specification analysis discussed in this chapter make use of residuals, in the next section, we consider the different kinds of residuals that are retrievable from a typical duration model. Following this, we present several illustrations using residual analysis to assess various facets of the duration model. Most of the discussion in this chapter is presented in terms of the Cox model; however, diagnostic methods for parametric models are considered at the end of the chapter. Residuals in Event History Models The basic idea of a residual is to compare predicted and observed durations. In OLS regression, residuals are deviations of the observed values of the dependent variable from the values estimated or predicted value under the regression model, that is y i – ŷ i . In event history analysis, defining a residual is more difficult because of censoring and because of issues relevant to estimation methods like maximum likelihood (in the case of parametric models) or maximum partial likelihood (in the case of the Cox model).

Issues in Model Selection

A wide variety of models for duration data have been discussed. Each of the approaches has certain advantages and disadvantages. The principal argument we have made is that in most social science settings, the Cox model should generally be preferred over its alternatives, for example the parametric models or some of the discrete models discussed in the last chapter. In this chapter, we revisit some of the models proposed and discuss some of the desirable and undesirable features inherent in the implementation of them. Following this discussion, we consider another class of models that create, in a sense, a “middle ground” between the Cox and parametric alternatives. The basic models discussed in this section are proposed by Royston (2001) and Royston and Parmar (2002). Advantages and Disadvantages of Modeling Strategies In this section, we discuss some of the advantages and disadvantages of the parametric models, discrete-time models, and the Cox models. We consider the standard parametric models first. Parametric Models Revisited The principal advantage of parametric duration models is the ability of the model to provide parameter estimates while simultaneously producing a relatively simple and easy-to-interpret characterization of the baseline hazard rate. Further, the parametric approach is flexible insofar as one simply needs to specify one of any number of suitable distribution functions. Commonly (and often by default), the Weibull distribution function is the distribution of choice in many applications; but there are numerous other functions that can be applied to duration data (each having concomitant assumptions regarding h 0 ( t )).