Moving Beyond the Collapsed Campaign: Tools and Techniques for Studying Non-Normal, Heterogeneous Dynamics.

Abstract

Studies of campaign effects tend to examine individual differences, or temporal dynamics, but not both. Methodologists typically recommend working with either pooled or aggregate data (e.g. Romer et al., 2004; Brady & Johnston, 2006), but this potentially throws valuable information about how response mechanisms are contingent on non-longitudinal features of the data. This dissertation regards joint specifications of cross-sectional and longitudinal dimensions as a basic extension of existing technologies for studying variance and covariance components in multi-level models. Features of dynamic specifications are regarded as potentially varying at the individual level, and non-normal innovations are introduced to represent the relative rarity of effectual events. The present work requires a few important assumptions—that models are block- wise conditionally-linear, mode-separable, and tail-bounded in the random effects. These requirements are satisfied by a wide-variety of substantive models, and lend themselves to an elliptical approximation to the mode of the likelihood, as well as importance samplers guaranteed to have finite variance. Chapter 2 presents a pilot study of heterogeneous campaign effects in the 2000 U.S. Presidential campaign using the author’s HetDyn package for R. Individual- differences in responsiveness and the persistence of responses by levels of political sophistication are interpreted in light of theories of information-processing and per- suasion (Zaller & Feldman, 1992; Lodge & Taber, 2000). As statistical inference remains difficult in such models, the author’s QuasiModal package for R is used to explore the possibility of relatively automated, efficient algorithms for Bayesian computation. A new family of MCMC sampling updates, the Pseudo-Marginal Metropolis algorithm (e.g. Andrieu & Roberts, 2009) is intro- duced in Chapter 3 and seems promising due to its targeting of the marginal model. This algorithm achieves relative computational efficiency due to avoiding extra com- putations usually required for detailed balance. In Chapter 4, a simulation study reveals fast convergence of a simple Importance Sampling version of Pseudo-Marginal Metropolis, relative to a more conventional Blockwise Metropolis-Hastings sampler. In order to improve mixing, an alternative Pseudo Marginal Metropolis algorithm using Annealed Importance Sampling (Neal, 2001) is proposed.