arXiv subjects

Rayleigh Lei

Publications and source records attributed to Rayleigh Lei.

12 recordsLinked to original sources

arXiv2026

Modeling Ordinal Survey Data with Unfolding Models

Surveys that rely on ordinal polychotomous (Likert-like) items are widely employed to capture individual preferences because they allow respondents to express both the direction and strength of their preferences. Latent factor models traditionally used in this context implicitly assume that the response functions (the cumulative distribution of the ordinal outcome) are monotonic on the latent trait. This assumption can be too restrictive in several application areas, including in political science and marketing. In this work, we propose a novel ordinal probit unfolding model that can accommodate both monotonic and non-monotonic response functions. The advantages of the model are illustrated by analyzing an immigration attitude survey conducted in the United States.

stat.ME↗

arXiv2025

Calibrating hierarchical Bayesian domain inference for a proportion

Small area estimation (SAE) improves estimates for local communities or groups, such as counties, neighborhoods, or demographic subgroups, when data are insufficient for each area. This is important for targeting local resources and policies, especially when national-level or large-area data mask variation at a more granular level. Researchers often fit hierarchical Bayesian models to stabilize SAE when data are sparse. Ideally, Bayesian procedures also exhibit good frequentist properties, as demonstrated by calibrated Bayes metrics. However, hierarchical Bayesian models tend to shrink domain estimates toward the overall mean and may produce credible intervals that do not maintain nominal coverage. Hoff et al. developed the Frequentist, but Assisted by Bayes (FAB) intervals for subgroup estimates with normally distributed outcomes. However, non-normally distributed data present new challenges, and multiple types of intervals have been proposed for estimating proportions. We examine domain inference with binary outcomes and extend FAB intervals to improve nominal coverage. We describe how to numerically compute FAB intervals for a proportion and evaluate their performance through repeated simulation studies. Leveraging multilevel regression and poststratification (MRP), we further refine SAE to correct for sample selection bias, construct the FAB intervals for MRP estimates and assess their repeated sampling properties. Finally, we apply the proposed inference methods to estimate COVID-19 infection rates across geographic and demographic subgroups. We find that the FAB intervals improve nominal coverage, at the cost of wider intervals.

stat.ME↗

arXiv2025

pumBayes: Bayesian Estimation of Probit Unfolding Models for Binary Preference Data in R

Probit unfolding models (PUMs) are a novel class of scaling models that allow for items with both monotonic and non-monotonic response functions and have shown great promise in the estimation of preferences from voting data in various deliberative bodies. This paper presents the R package pumBayes, which enables Bayesian inference for both static and dynamic PUMs using Markov chain Monte Carlo algorithms that require minimal or no tuning. In addition to functions that carry out the sampling from the posterior distribution of the models, the package also includes various support functions that can be used to pre-process data, select hyperparameters, summarize output, and compute metrics of model fit. We demonstrate the use of the package through an analysis of two datasets, one corresponding to roll-call voting data from the 116th U.S. House of Representatives, and a second one corresponding to voting records in the U.S. Supreme Court between 1937 and 2021.

stat.CO↗

arXiv2024

Learning Topic Hierarchies by Tree-Directed Latent Variable Models

We study a parametric family of latent variable models, namely topic models, equipped with a hierarchical structure among the topic variables. Such models may be viewed as a finite mixture of the latent Dirichlet allocation (LDA) induced distributions, but the LDA components are constrained by a latent hierarchy, specifically a rooted and directed tree structure, which enables the learning of interpretable and latent topic hierarchies of interest. A mathematical framework is developed in order to establish identifiability of the latent topic hierarchy under suitable regularity conditions, and to derive bounds for posterior contraction rates of the model and its parameters. We demonstrate the usefulness of such models and validate its theoretical properties through a careful simulation study and a real data example using the New York Times articles.

math.ST↗

arXiv2024

Logit unfolding choice models for binary data

Discrete choice models with non-monotonic response functions are important in many areas of application, especially political sciences and marketing. This paper describes a novel unfolding model for binary data that allows for heavy-tailed shocks to the underlying utilities. One of our key contributions is a Markov chain Monte Carlo algorithm that requires little or no parameter tuning, fully explores the support of the posterior distribution, and can be used to fit various extensions of our core model that involve (Bayesian) hypothesis testing on the latent construct. Our empirical evaluations of the model and the associated algorithm suggest that they provide better complexity-adjusted fit to voting data from the United States House of Representatives.

stat.ME↗

arXiv2023

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.

stat.ME↗

arXiv2023

A Novel Class of Unfolding Models for Binary Preference Data

We develop a new class of spatial voting models for binary preference data that can accommodate both monotonic and non-monotonic response functions, and are more flexible than alternative "unfolding" models previously introduced in the literature. We then use these models to estimate revealed preferences for legislators in the U.S. House of Representatives and justices on the U.S. Supreme Court. The results from these applications indicate that the new models provide superior complexity-adjusted performance to various alternatives and also that the additional flexibility leads to preferences' estimates that are closer matches to the perceived ideological positions of legislators and justices.

stat.AP↗

arXiv2023

Dynamic Factor Models for Binary Data in Circular Spaces: An Application to the U.S. Supreme Court

Latent factor models are widely used in the social and behavioral science as scaling tools to map discrete multivariate outcomes into low dimensional, continuous scales. In political science, dynamic versions of classical factor models have been widely used to study the evolution of justices' preferences in multi-judge courts. In this paper, we discuss a new dynamic factor model that relies on a latent circular space that can accommodate voting behaviors in which justices commonly understood to be on opposite ends of the ideological spectrum vote together on a substantial number of otherwise closely-divided opinions. We apply this model to data on non-unanimous decisions made by the U.S. Supreme Court between 1937 and 2021, and show that, for most of this period, voting patterns can be better described by a circular latent space.

stat.AP↗

arXiv2022

Modeling Random Directions in 2D Simplex Data

We propose models and algorithms for learning about random directions in two-dimensional simplex data, and apply our methods 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 while allowing for possible heterogeneous behaviors. To that end, we propose Bayesian models that rely on and expand upon building blocks in circular and spatial statistics by exploiting suitable transformation based on the polar coordinates for circular 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 illustrated via a thorough simulation study, and applied to an analysis of movements and trends of income categories using the Home Mortgage Disclosure Act data.

stat.ME↗

arXiv2021

Scalable nonparametric Bayesian learning for heterogeneous and dynamic velocity fields

Analysis of heterogeneous patterns in complex spatio-temporal data finds usage across various domains in applied science and engineering, including training autonomous vehicles to navigate in complex traffic scenarios. Motivated by applications arising in the transportation domain, in this paper we develop a model for learning heterogeneous and dynamic patterns of velocity field data. We draw from basic nonparameric Bayesian modeling elements such as hierarchical Dirichlet process and infinite hidden Markov model, while the smoothness of each homogeneous velocity field element is captured with a Gaussian process prior. Of particular focus is a scalable approximate inference method for the proposed model; this is achieved by employing sequential MAP estimates from the infinite HMM model and an efficient sequential GP posterior computation technique, which is shown to work effectively on simulated data sets. Finally, we demonstrate the effectiveness of our techniques to the NGSIM dataset of complex multi-vehicle interactions.

stat.ML↗

arXiv2020

Robust Unsupervised Learning of Temporal Dynamic Interactions

Robust representation learning of temporal dynamic interactions is an important problem in robotic learning in general and automated unsupervised learning in particular. Temporal dynamic interactions can be described by (multiple) geometric trajectories in a suitable space over which unsupervised learning techniques may be applied to extract useful features from raw and high-dimensional data measurements. Taking a geometric approach to robust representation learning for temporal dynamic interactions, it is necessary to develop suitable metrics and a systematic methodology for comparison and for assessing the stability of an unsupervised learning method with respect to its tuning parameters. Such metrics must account for the (geometric) constraints in the physical world as well as the uncertainty associated with the learned patterns. In this paper we introduce a model-free metric based on the Procrustes distance for robust representation learning of interactions, and an optimal transport based distance metric for comparing between distributions of interaction primitives. These distance metrics can serve as an objective for assessing the stability of an interaction learning algorithm. They are also used for comparing the outcomes produced by different algorithms. Moreover, they may also be adopted as an objective function to obtain clusters and representative interaction primitives. These concepts and techniques will be introduced, along with mathematical properties, while their usefulness will be demonstrated in unsupervised learning of vehicle-to-vechicle interactions extracted from the Safety Pilot database, the world's largest database for connected vehicles.

cs.LG↗

arXiv2016

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).

stat.AP↗