arXiv subjects

Elena A. Erosheva

Publications and source records attributed to Elena A. Erosheva.

15 recordsLinked to original sources

arXiv2026

Statistical Inference for Bivariate Functional Causal Discovery

Causal discovery methods aim to determine the causal direction between variables using observational data. Functional causal discovery methods rely on structural and distributional assumptions to determine directionality but typically lack statistical inference. This paper reviews the statistical guarantees of existing functional causal discovery methods in theory, software, and applied use, highlighting a key gap: the absence of a unified inferential framework that applies broadly across model classes. As a first step toward addressing this gap, we formalize a test-based approach for bivariate causal discovery by repurposing goodness-of-fit and independence tests within a hypothesis-testing framework. Because directionality is determined through two disjoint hypothesis tests, corresponding to four causal discovery outcomes, the approach provides explicit uncertainty quantification and diagnostic insight into assumption violations. Resampling is further used to estimate the rates of causal discovery outcomes, offering an additional layer of inference. We demonstrate the use and behavior of our inferential framework through simulations that vary the degree of assumption violation, as well as through real-data applications. We conclude with practical lessons and recommendations for advancing statistical guarantees in functional causal discovery.

stat.ME↗

arXiv2026

Can statistical models capture Mamdani's success? Social choice, ranked-choice voting, and model fit, with an application to the 2025 New York City Democratic Primary

Ranked-choice voting is increasingly prevalent in elections. An extensive literature in social choice theory -- the study of collective decision-making with the goal of making compromises among disparate opinions -- considers theoretical and empirical properties of various election procedures. Recently, a sub-literature on rationalizability, led by social choice theorists and computer scientists, makes explicit connections between social choice rules and maximum likelihood estimation. This paper further illuminates connections between social choice and statistical summaries of data. We begin by studying rationalizability from a statistical perspective, expanding existing results to realistic voting contexts and deriving statistical details necessary for model estimation and assessment. We then apply our work to ranked-choice votes from the 2025 New York City Democratic mayoral primary election. We demonstrate how rationalizing models impose unrealistic distributional assumptions and thus exhibit poor fit to voting data. Additionally, we show that non-rationalizing models meaningfully elucidate heterogeneous voter preferences. Our work demonstrates the inability of rationalizing models to capture key features of distributions of preferences in political elections, depriving analysts of fundamental uses, such as inference, typically associated with statistical modeling. Conversely, we show that statistical modeling can capture nuanced voter preferences by paying careful attention to plausible data-generating mechanisms.

stat.AP↗

arXiv2026

Causal Discovery via Statistical Power (CDSP)

Causal discovery methods aim to infer causal direction from observational data. Functional causal discovery approaches use structural asymmetries to identify causal directionality but rely on strong modeling assumptions and provide limited tools for uncertainty quantification. We introduce Causal Discovery via Statistical Power (CDSP), a statistical inference framework that connects causal direction estimation with statistical power and enables uncertainty quantification. Considering the foundational setting of bivariate observational data, we show how quantities analogous to statistical power and effect size can be used in causal discovery to determine when data contain sufficient information to favor one direction over the other. We introduce the effect-size asymmetry assumption that characterizes when the probability of correctly detecting the causal direction (i.e., the power of causal discovery) exceeds that of incorrectly favoring the reverse direction. We show that the effect-size asymmetry assumption can be used for causal direction estimation with uncertainty quantification. Simulations show that CDSP direction estimation is robust to mild and moderate model misspecifications. Real data analyses on 100 cause-effect benchmark pairs further demonstrate that CDSP reduces false discovery rates by approximately 18% relative to a commonly used existing method.

stat.ME↗

arXiv2024

Bayesian Rank-Clustering

Traditional statistical inference on ordinal comparison data results in an overall ranking of objects, e.g., from best to worst, with each object having a unique rank. However, ranks of some objects may not be statistically distinguishable. This could happen due to insufficient data or to the true underlying object qualities being equal. Because uncertainty communication in estimates of overall rankings is notoriously difficult, we take a different approach and allow groups of objects to have equal ranks or be $\textit{rank-clustered}$ in our model. Existing models related to rank-clustering are limited by their inability to handle a variety of ordinal data types, to quantify uncertainty, or by the need to pre-specify the number and size of potential rank-clusters. We solve these limitations through our proposed Bayesian $\textit{Rank-Clustered Bradley-Terry-Luce}$ model. We accommodate rank-clustering via parameter fusion by imposing a novel spike-and-slab prior on object-specific worth parameters in Bradley-Terry-Luce family of distributions for ordinal comparisons. We demonstrate rank-clustering on simulated and real datasets in surveys, elections, and sports analytics.

stat.ME↗

arXiv2023

Dimension-Grouped Mixed Membership Models for Multivariate Categorical Data

Mixed Membership Models (MMMs) are a popular family of latent structure models for complex multivariate data. Instead of forcing each subject to belong to a single cluster, MMMs incorporate a vector of subject-specific weights characterizing partial membership across clusters. With this flexibility come challenges in uniquely identifying, estimating, and interpreting the parameters. In this article, we propose a new class of Dimension-Grouped MMMs (Gro-M$^3$s) for multivariate categorical data, which improve parsimony and interpretability. In Gro-M$^3$s, observed variables are partitioned into groups such that the latent membership is constant for variables within a group but can differ across groups. Traditional latent class models are obtained when all variables are in one group, while traditional MMMs are obtained when each variable is in its own group. The new model corresponds to a novel decomposition of probability tensors. Theoretically, we derive transparent identifiability conditions for both the unknown grouping structure and model parameters in general settings. Methodologically, we propose a Bayesian approach for Dirichlet Gro-M$^3$s to inferring the variable grouping structure and estimating model parameters. Simulation results demonstrate good computational performance and empirically confirm the identifiability results. We illustrate the new methodology through applications to a functional disability survey dataset and a personality test dataset.

stat.ME↗

arXiv2023

Modeling Preferences: A Bayesian Mixture of Finite Mixtures for Rankings and Ratings

Rankings and ratings are commonly used to express preferences but provide distinct and complementary information. Rankings give ordinal and scale-free comparisons but lack granularity; ratings provide cardinal and granular assessments but may be highly subjective or inconsistent. Collecting and analyzing rankings and ratings jointly has not been performed until recently due to a lack of principled methods. In this work, we propose a flexible, joint statistical model for rankings and ratings under heterogeneous preferences: the Bradley-Terry-Luce-Binomial (BTL-Binomial). We employ a Bayesian mixture of finite mixtures (MFM) approach to estimate heterogeneous preferences, understand their inherent uncertainty, and make accurate decisions based on ranking and ratings jointly. We demonstrate the efficiency and practicality of the BTL-Binomial MFM approach on real and simulated datasets of ranking and rating preferences in peer review and survey data contexts.

stat.ME↗

arXiv2022

Partial-Mastery Cognitive Diagnosis Models

Cognitive diagnosis models (CDMs) are a family of discrete latent attribute models that serve as statistical basis in educational and psychological cognitive diagnosis assessments. CDMs aim to achieve fine-grained inference on individuals' latent attributes, based on their observed responses to a set of designed diagnostic items. In the literature, CDMs usually assume that items require mastery of specific latent attributes and that each attribute is either fully mastered or not mastered by a given subject. We propose a new class of models, partial mastery CDMs (PM-CDMs), that generalizes CDMs by allowing for partial mastery levels for each attribute of interest. We demonstrate that PM-CDMs can be represented as restricted latent class models. Relying on the latent class representation, we propose a Bayesian approach for estimation. We present simulation studies to demonstrate parameter recovery, to investigate the impact of model misspecification with respect to partial mastery, and to develop diagnostic tools that could be used by practitioners to decide between CDMs and PM-CDMs. We use two examples of real test data -- the fraction subtraction and the English tests -- to demonstrate that employing PM-CDMs not only improves model fit, compared to CDMs, but also can make substantial difference in conclusions about attribute mastery. We conclude that PM-CDMs can lead to more effective remediation programs by providing detailed individual-level information about skills learned and skills that need to study.

stat.ME↗

arXiv2022

On the validity of bootstrap uncertainty estimates in the Mallows-Binomial model

The Mallows-Binomial distribution is the first joint statistical model for rankings and ratings (Pearce and Erosheva, 2022). Because frequentist estimation of the model parameters and their uncertainty is challenging, it is natural to consider the nonparametric bootstrap. However, it is not clear that the nonparametric bootstrap is asymptotically valid in this setting. This is because the Mallows-Binomial model is parameterized by continuous quantities whose discrete order affects the likelihood. In this note, we demonstrate that bootstrap uncertainty of the maximum likelihood estimates in the Mallows-Binomial model are asymptotically valid.

math.ST↗

arXiv2022

A Unified Statistical Learning Model for Rankings and Scores with Application to Grant Panel Review

Rankings and scores are two common data types used by judges to express preferences and/or perceptions of quality in a collection of objects. Numerous models exist to study data of each type separately, but no unified statistical model captures both data types simultaneously without first performing data conversion. We propose the Mallows-Binomial model to close this gap, which combines a Mallows' $ϕ$ ranking model with Binomial score models through shared parameters that quantify object quality, a consensus ranking, and the level of consensus between judges. We propose an efficient tree-search algorithm to calculate the exact MLE of model parameters, study statistical properties of the model both analytically and through simulation, and apply our model to real data from an instance of grant panel review that collected both scores and partial rankings. Furthermore, we demonstrate how model outputs can be used to rank objects with confidence. The proposed model is shown to sensibly combine information from both scores and rankings to quantify object quality and measure consensus with appropriate levels of statistical uncertainty.

stat.ME↗

arXiv2022

Gender-based homophily in collaborations across a heterogeneous scholarly landscape

In this article, we investigate the role of gender in collaboration patterns by analyzing gender-based homophily -- the tendency for researchers to co-author with individuals of the same gender. We develop and apply novel methodology to the corpus of JSTOR articles, a broad scholarly landscape, which we analyze at various levels of granularity. Most notably, for a precise analysis of gender homophily, we develop methodology which explicitly accounts for the fact that the data comprises heterogeneous intellectual communities and that not all authorships are exchangeable. In particular, we distinguish three phenomena which may affect the distribution of observed gender homophily in collaborations: a structural component that is due to demographics and non-gendered authorship norms of a scholarly community, a compositional component which is driven by varying gender representation across sub-disciplines and time, and a behavioral component which we define as the remainder of observed gender homophily after its structural and compositional components have been taken into account. Using minimal modeling assumptions, the methodology we develop allows us to test for behavioral homophily. We find that statistically significant behavioral homophily can be detected across the JSTOR corpus and show that this finding is robust to missing gender indicators in our data. In a secondary analysis, we show that the proportion of women representation in a field is positively associated with the probability of finding statistically significant behavioral homophily.

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arXiv2018

On the use of bootstrap with variational inference: Theory, interpretation, and a two-sample test example

Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and to carry out Bayesian inference, however, quantification of uncertainty with variational inference remains challenging from both theoretical and practical perspectives. This paper is concerned with developing uncertainty measures for variational inference by using bootstrap procedures. We first develop two general bootstrap approaches for assessing the uncertainty of a variational estimate and the study the underlying bootstrap theory in both fixed- and increasing-dimension settings. We then use the bootstrap approach and our theoretical results in the context of mixed membership modeling with multivariate binary data on functional disability from the National Long Term Care Survey. We carry out a two-sample approach to test for changes in the repeated measures of functional disability for the subset of individuals present in 1989 and 1994 waves.

stat.ME↗

arXiv2017

A Variational EM Method for Mixed Membership Models with Multivariate Rank Data: an Analysis of Public Policy Preferences

In this article, we consider modeling ranked responses from a heterogeneous population. Specifically, we analyze data from the Eurobarometer 34.1 survey regarding public policy preferences towards drugs, alcohol and AIDS. Such policy preferences are likely to exhibit substantial differences within as well as across European nations reflecting a wide variety of cultures, political affiliations, ideological perspectives and common practices. We use a mixed membership model to account for multiple subgroups with differing preferences and to allow each individual to possess partial membership in more than one subgroup. Previous methods for fitting mixed membership models to rank data in a univariate setting have utilized an MCMC approach and do not estimate the relative frequency of each subgroup. We propose a variational EM approach for fitting mixed membership models with multivariate rank data. Our method allows for fast approximate inference and explicitly estimates the subgroup sizes. Analyzing the Eurobarometer 34.1 data, we find interpretable subgroups which generally agree with the "left vs right" classification of political ideologies.

stat.ME↗

arXiv2016

On the relationship between set-based and network-based measures of gender homophily in scholarly publications

There is an increased interest in the scientific community in the problem of measuring gender homophily in co-authorship on scholarly publications (Eisen, 2016). For a given set of publications and co-authorships, we assume that author identities have not been disambiguated in that we do not know when one person is an author on more than one paper. In this case, one way to think about measuring gender homophily is to consider all observed co-authorship pairs and obtain a set-based gender homophily coefficient (e.g., Bergstrom et al., 2016). Another way is to consider papers as observed disjoint networks of co-authors and use a network-based assortativity coefficient (e.g., Newman, 2003). In this note, we review both metrics and show that the gender homophily set-based index is equivalent to the gender assortativity network-based coefficient with properly weighted edges.

cs.DL↗

arXiv2014

A semiparametric approach to mixed outcome latent variable models: Estimating the association between cognition and regional brain volumes

Multivariate data that combine binary, categorical, count and continuous outcomes are common in the social and health sciences. We propose a semiparametric Bayesian latent variable model for multivariate data of arbitrary type that does not require specification of conditional distributions. Drawing on the extended rank likelihood method by Hoff [Ann. Appl. Stat. 1 (2007) 265-283], we develop a semiparametric approach for latent variable modeling with mixed outcomes and propose associated Markov chain Monte Carlo estimation methods. Motivated by cognitive testing data, we focus on bifactor models, a special case of factor analysis. We employ our semiparametric Bayesian latent variable model to investigate the association between cognitive outcomes and MRI-measured regional brain volumes.

stat.AP↗

arXiv2007

Describing disability through individual-level mixture models for multivariate binary data

Data on functional disability are of widespread policy interest in the United States, especially with respect to planning for Medicare and Social Security for a growing population of elderly adults. We consider an extract of functional disability data from the National Long Term Care Survey (NLTCS) and attempt to develop disability profiles using variations of the Grade of Membership (GoM) model. We first describe GoM as an individual-level mixture model that allows individuals to have partial membership in several mixture components simultaneously. We then prove the equivalence between individual-level and population-level mixture models, and use this property to develop a Markov Chain Monte Carlo algorithm for Bayesian estimation of the model. We use our approach to analyze functional disability data from the NLTCS.

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