Can we improve multilevel regression and poststratification (MRP) through new ways to leverage information?

Multilevel regression and poststratification (MRP) has become a popular and important small area estimation method in social sciences. The method enables researchers to reliably estimate public opinion in small areas such as constituencies, states, and districts. Since it was first developed, numerous studies have extended and advanced the method. This thesis asks whether we can further improve MRP estimates with alternative methodological approaches. Each chapter explores how these methodologies could be applied with MRP, and whether each improves MRP estimate accuracy. As a preface to the introduction of these alternative methods, in chapter two, the thesis asks: what is standard practice for the application of MRP in social science? I address this question through a systematic review of 86 studies which use MRP. Drawing on the collective wisdom of researchers to date, the chapter details how each of the main MRP characteristics are typically applied in practice. In chapter three, I explore whether using cross-validation lasso regression can improve variable selection for MRP applications. I explore how the method should be applied, and whether this method is an improvement on what might be considered current standard practice for variable selection. The results are somewhat mixed but show that lasso could be a useful tool. I argue that incorporating lasso into the model building process, alongside standard variable selection approaches, would represent an improvement over current MRP variable selection practice. In chapter four, I explore whether an unevenly distributed sample among small areas might be a useful strategy when applying MRP to electoral forecasting. The chapter set outs how this method could be applied and explores whether it improves MRP. Overall, the results show the method can improve estimate accuracy in important small areas, and in turn, can improve the probability of correctly forecasting an electoral outcome. In the final chapter, I explore how we can use informative priors with MRP. I employ a two-stage prior elicitation method with MRP and apply to estimating vote choice at numerous elections. The results indicate the method can improve estimate accuracy and precision. The results also give some indication that this method could be useful for improving sub-group inference and computational efficiency. However, improvements are inconsistent across different elections, and often improvements are only significant for the smallest sample sizes.