The 2008 election: A preregistered replication analysis

We present an increasingly stringent set of replications of Ghitza & Gelman (2013), a multilevel regression and poststratification analysis of polls from the 2008 U.S. presidential election campaign, focusing on a set of plots showing the estimated Republican vote share for whites and for all voters, as a function of income level in each of the states. We start with a nearly-exact duplication that uses the posted code and changes only the model-fitting algorithm; we then replicate using already-analyzed data from 2004; and finally we set up preregistered replications using two surveys from 2008 that we had not previously looked at. We have already learned from our preliminary, non-preregistered replication, which has revealed a potential problem with the published analysis of Ghitza & Gelman (2013); it appears that our model may not sufficiently account for nonsampling error, and that some of the patterns presented in that earlier paper may simply reflect noise. In addition to the substantive interest in validating earlier findings about demographics, geography, and voting, the present project serves as a demonstration of preregistration in a setting where the subject matter is historical (and thus the replication data exist before the preregistration plan is written) and where the analysis is exploratory (and thus a replication cannot be simply deemed successful or unsuccessful based on the statistical significance of some particular comparison).Comment: This article is a review and preregistration plan. It will be published, along with a new Section 5 describing the results of the preregistered analysis, in Statistics and Public Polic

Modeling random directions of changes in simplex-valued data

We propose models and algorithms for learning about random directions in simplex-valued data. The models are applied to the study of income level proportions and their changes over time in a geostatistical area. There are several notable challenges in the analysis of simplex-valued data: the measurements must respect the simplex constraint and the changes exhibit spatiotemporal smoothness and may be heterogeneous. To that end, we propose Bayesian models that draw from and expand upon building blocks in circular and spatial statistics by exploiting a suitable transformation for the simplex-valued data. Our models also account for spatial correlation across locations in the simplex and the heterogeneous patterns via mixture modeling. We describe some properties of the models and model fitting via MCMC techniques. Our models and methods are applied to an analysis of movements and trends of income categories using the Home Mortgage Disclosure Act data.Comment: arXiv admin note: text overlap with arXiv:2103.1221

Modal Rayleigh-like streaming in layered acoustofluidic devices

Classical Rayleigh streaming is well known and can be modelled using Nyborg’s limiting velocity method as driven by fluid velocities adjacent to the walls parallel to the axis of the main acoustic resonance. We have demonstrated previously the existence and the mechanism of four-quadrant transducer plane streaming patterns in thin-layered acoustofluidic devices which are driven by the limiting velocities on the walls perpendicular to the axis of the main acoustic propagation. We have recently found experimentally that there is a third case which resembles Rayleigh streaming but is a more complex pattern related to three-dimensional cavity modes of an enclosure. This streaming has vortex sizes related to the effective wavelength in each cavity axis of the modes which can be much larger than those found in the one-dimensional case with Rayleigh streaming. We will call this here modal Rayleigh-like streaming and show that it can be important in layered acoustofluidic manipulation devices. This paper seeks to establish the conditions under which each of these is dominant and shows how the limiting velocity field for each relates to different parts of the complex acoustic intensity patterns at the driving boundaries

Modeling Simplex-valued Data and Latent Structures

Examples of data that lie in a simplex abound in a variety of fields. The chemical, mineral, and/or fossil percentages of a collection of rocks is of interest to geologists. Demographers and policy makers might examine the income proportions or racial compositions of neighborhoods or other political units. However, it can be challenging to model this type of data, particularly because each observation must sum up to one. If not handled correctly, this might induce what Karl Pearson called "spurious correlation". As a trivial example of this, take an observation that has two values and sums up to one. Then, the values must be negatively correlated with each other. While traditional approaches for these type of data involve analyzing the log ratio transforms, this might be problematic if any of the observations have a zero as one of their values or for interpretation. Additional challenges arise if this data changes over time. The first two chapters lay the framework for how such data may be modeled. The second chapter proposes doing so using a general affine transformation for the overall change and a sufficiently rich error model for the difference between the overall transformation and the observation at the next time point. Of the three models explored, the rotational geodesic error model is most promising. However, it might not be appropriate to assume that the direction observations moved in is uniformly distributed. Using ideas from directional statistics, we discuss in the third chapter how to model directions that appear to be similar for observations with similar values. In both chapters, we run simulation studies and analyze the income proportions from Los Angeles County. In each case, our analysis is able to discover trends consistent with larger macroeconomic ones and provide further details about these trends. The last chapter discusses tree-based mixtures of probability simplices. In other words, the simplices share vertices in a way that can be represented by a tree with the root node corresponding to a vertex shared by all simplices and the leaf nodes corresponding to vertices present in one simplex. We show when such models have posterior consistency and demonstrate how to efficiently fit them using geometric methods. Indeed, we apply them to analyze a subset of articles from the New York Times, uncovering meaningful topics and interesting semantic relationships between these topics. While we leave it to future work, these methods might also be combined with the ones from previous chapters to model how sub-regions of data that lie in a simplex change over time.PHDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/174205/1/rayleigh_1.pd