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COMPOSITE MIXTURE OF log-linear models WITH APPLICATION TO PSYCHIATRIC STUDIES

ANNALS OF APPLIED STATISTICS 2022年第2期16卷 765-790页

作者： Aliverti, Emanuele Dunson, David B. Univ Ca Foscari Venezia Dept Econ Venice Italy Duke Univ Dept Stat Sci Durham NC 27706 USA

Psychiatric studies of suicide provide fundamental insights on the evolution of severe psychopathologies, and contribute to the development of early treatment interventions. Our focus is on modelling different traits of psychosis and their interconnections, focusing on a case study on suicide attempt survivors. Such aspects are recorded via multivariate categorical data, involving a large numbers of items for multiple subjects. Current methods for multivariate categorical data-such as penalized log-linear models and latent structure analysis-are either limited to low-dimensional settings or include parameters with difficult interpretation. Motivated by this application, this article proposes a new class of approaches, which we refer to as Mixture of log linear models (MILLS). Combining latent class analysis and log-linear models, MILLS defines a novel Bayesian approach to model complex multivariate categorical data with flexibility and interpretability, providing interesting insights on the relationship between psychotic diseases and psychological aspects in suicide attempt survivors.

关键词： Psychiatric profiles Bayesian modelling categorical data contingency table log-linear models mixture model

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Classical iterative proportional scaling of log-linear models with rational maximum likelihood estimator

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2024年 164卷

作者： Coons, Jane Ivy Langer, Carlotta Ruddy, Michael Univ Oxford St Johns Coll Oxford England Univ Oxford Math Inst Oxford England Hamburg Univ Technol Hamburg Germany Qventus Blountstown FL USA

In this work we investigate multipartition models, the subset of log-linear models for which one can perform the classical iterative proportional scaling (IPS) algorithm to numerically compute the maximum likelihood estimate (MLE). Multipartition models include families of models such as hierarchical models and balanced, stratified staged trees. We define a sufficient condition, called the Generalized Running Intersection Property (GRIP), on the matrix representation of a multipartition model under which the classical IPS algorithm produces the exact MLE in one cycle. In this case, the MLE is a rational function of the data. Additionally we connect the GRIP to the toric fiber product and to previous results for hierarchical models and balanced, stratified staged trees. This leads to a characterization of balanced, stratified staged trees in terms of the GRIP.

关键词： Maximum likelihood estimation Iterative proportional scaling log-linear models Hierarchical models Staged tree models Toric fiber product

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Lasso Regularization for Selection of log-linear models: An Application to Educational Assortative Mating

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SOCIOlogICAL METHODS & RESEARCH 2021年第4期50卷 1763-1800页

作者： Bucca, Mauricio Urbina, Daniela R. European Univ Inst Florence Italy Princeton Univ 104 Wallace Hall Princeton NJ 08544 USA

log-linear models for contingency tables are a key tool for the study of categorical inequalities in sociology. However, the conventional approach to model selection and specification suffers from at least two limitations: reliance on oftentimes equivocal diagnostics yielded by fit statistics, and the inability to identify patterns of association not covered by model candidates. In this article, we propose an application of Lasso regularization that addresses the aforementioned limitations. We evaluate our method through a Monte Carlo experiment and an empirical study of educational assortative mating in Chile, 1990-2015. Results demonstrate that our approach has the virtue, relative to ad hoc specification searches, of offering a principled statistical criterion to inductively select a model. Importantly, we show that in situations where conventional fit statistics provide conflicting diagnostics, our Lasso-based approach is consistent in its model choice, yielding solutions that are both predictive and parsimonious.

关键词： log-linear models Lasso regularization assortative mating stratification

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Toric invariant theory for maximum likelihood estimation in log-linear models

Algebraic Statistics

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Algebraic Statistics 2021年第2期12卷 187-211页

作者： Carlos Améndola Kathlén Kohn Philipp Reichenbach Anna Seigal Department of Mathematics Technical University of Munich Germany Department of Mathematics KTH Royal Institute of Technology Stockholm Sweden Institut für Mathematik Technische Universität Berlin Germany Mathematical Institute University of Oxford United Kingdom Department of Mathematics Harvard University Cambridge MA United States

We establish connections between invariant theory and maximum likelihood estimation for discrete statistical models. We show that norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We use notions of stability under a torus action to characterize the existence of the maximum likelihood estimate, and discuss connections to scaling algorithms.

关键词： maximum likelihood estimation log-linear models graphical models torus actions null cone scaling algorithms

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Heatmaps for Patterns of Association in log-linear models

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SOCIUS 2020年第6期6卷

作者： Bucca, Mauricio European Univ Inst Florence Italy

log-linear models offer a detailed characterization of the association between categorical variables, but the breadth of their outputs is difficult to grasp because of the large number of parameters these models entail. Revisiting seminal findings and data from sociological work on social mobility, the author illustrates the use of heatmaps as a visualization technique to convey the complex patterns of association captured by log-linear models. In particular, turning log odds ratios derived from a model's predicted counts into heatmaps makes it possible to summarize large amounts of information and facilitates comparison across models' outcomes.

关键词： log-linear models heatmaps social mobility

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Assessing agreement between raters from the point of coefficients and log-linear models

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Journal of Data Science 2017年第1期15卷 1-24页

作者： Ayfer Ezgi Yilmaz Tulay Saracbasi Department of Statistics Hacettepe University

In square contingency tables, analysis of agreement between row and column classifications is of interest. For nominal categories, kappa co- efficient is used to summarize the degree of agreement between two raters. Numerous extensions and generalizations of kappa statistics have been pro- posed in the literature. In addition to the kappa coefficient, several authors use agreement in terms of log-linear models. This paper focuses on the approaches to study of inter-rater agreement for contingency tables with nominal or ordinal categories for multi-raters. In this article, we present a detailed overview of agreement studies and illustrate use of the approaches in the evaluation agreement over three numerical examples.

关键词： Agreement kappa log-linear models multi-raters nominal or-dinal weights

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BAYESIAN NONPARAMETRIC DISCLOSURE RISK ESTIMATION VIA MIXED EFFECTS log-linear models

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ANNALS OF APPLIED STATISTICS 2015年第1期9卷 525-546页

作者： Carota, Cinzia Filippone, Maurizio Leombruni, Roberto Polettini, Silvia Univ Turin Dipartimento Econ & Stat I-10153 Turin Italy Univ Glasgow Sch Comp Sci Glasgow G12 8QQ Lanark Scotland Univ Roma La Sapienza Dipartimento Metodi & Modelli Econ Terr & Finanza I-00161 Rome Italy

Statistical agencies and other institutions collect data under the promise to protect the confidentiality of respondents. When releasing microdata samples, the risk that records can be identified must be assessed. To this aim, a widely adopted approach is to isolate categorical variables key to the identification and analyze multi-way contingency tables of such variables. Common disclosure risk measures focus on sample unique cells in these tables and adopt parametric log-linear models as the standard statistical tools for the problem. Such models often have to deal with large and extremely sparse tables that pose a number of challenges to risk estimation. This paper proposes to overcome these problems by studying nonparametric alternatives based on Dirichlet process random effects. The main finding is that the inclusion of such random effects allows us to reduce considerably the number of fixed effects required to achieve reliable risk estimates. This is studied on applications to real data, suggesting, in particular, that our mixed models with main effects only produce roughly equivalent estimates compared to the all two-way interactions models, and are effective in defusing potential shortcomings of traditional log-linear models. This paper adopts a fully Bayesian approach that accounts for all sources of uncertainty, including that about the population frequencies, and supplies unconditional (posterior) variances and credible intervals.

关键词： Bayesian nonparametric models confidentiality disclosure risk Dirichlet process log-linear models mixed effects models

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Exploring temporal interactions of crash counts in California using distinct log-linear contingency table models

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INTERNATIONAL JOURNAL OF INJURY CONTROL AND SAFETY PROMOTION 2021年第3期28卷 360-375页

作者： Cheng, Wen Singh, Mankirat Clay, Edward Kwong, Jerry Cao, Menglu Li, Yihua Truong, Aaron Calif State Polytech Univ Pomona Dept Civil Engn Pomona CA 91768 USA Calif Dept Transportat Div Res Innovat & Syst Informat Sacramento CA USA Cent South Univ Forestry & Technol Logist & Traff Coll Dept Logist Engn Changsha Hunan Peoples R China

Temporal trait of crashes has huge impact on road crash occurrence and a large proportion of research have considered different time periods to determine the causes and features of crash occurrence or frequency. Compared with other safety studies based on a single time interval, considerably less research has relied on the use of multiple time units, especially for the time intervals of less than one year. The research aims to fill the gap by investigating the temporal distribution of crash counts using multiple time spans including hour, weekday and month. To illustrate the most accurate results possible, both the Chi-square test and Cochran-Mantel-Haenzel tests were employed to explore the independence of various time units based on two-way and three-way contingency tables. Eight contingency table models were developed which can be classified into four groups including Complete Independence, Joint Independence, Conditional Independence and Homogeneous Association. Finally, a set of evaluation criteria were utilized for evaluation of the model performance. The results revealed the significant association existence in all time variables (hour, weekday, month) and the model with both main and all interactive effects of time variables provides best prediction performance. Also, the findings showed that Hour 18, weekdays 1, 6, 7 (Friday and Weekends), and month 8 (August) have the largest number of crash occurrences. It is suggested that both main and interactive effects of time variables should be included for model development, which otherwise might yield misleading information. It is anticipated that research results will benefit the safety professionals with better understanding of the temporal patterns of crashes with different time periods and allow the safety administrators to allocate the safety resources.

关键词： Multiple time units main and interactive effects contingency table homogeneous association log-linear models

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Generating Independent Replicates Directly from the Posterior Distribution for a Class of Spatial Hierarchical models

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2025年第1期34卷 123-139页

作者： Bradley, Jonathan R. Clinch, Madelyn Florida State Univ Dept Stat 117 N Woodward Ave Tallahassee FL 32306 USA

Markov chain Monte Carlo (MCMC) allows one to generate dependent replicates from a posterior distribution for effectively any Bayesian hierarchical model. However, MCMC can produce a significant computational burden. This motivates us to consider finding expressions of the posterior distribution that are computationally straightforward to obtain independent replicates from directly. We focus on a broad class of Bayesian hierarchical models for spatially dependent data, which are often modeled via a latent Gaussian process (LGP). First, we derive a new class of distributions referred to as the generalized conjugate multivariate (GCM) distribution. The GCM distribution's theoretical development follows that of the conjugate multivariate (CM) distribution with two main differences: the GCM allows for latent Gaussian process assumptions, and the GCM explicitly accounts for hyperparameters through marginalization. The development of GCM is needed to obtain independent replicates directly from the exact posterior distribution, which has an efficient regression form. Hence, we refer to our method as Exact Posterior Regression (EPR). Simulation studies with weakly stationary spatial processes and spatial basis function expansions are provided. We provide an analysis of poverty incidence from the U.S. Census Bureau, and an analysis of high-dimensional remote sensing data. Supplementary materials for this article are available online.

关键词： Bayesian hierarchical model Big data Gibbs sampler log-linear models Markov chain Monte Carlo Non-Gaussian

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Efficient Posterior Sampling for Bayesian Poisson Regression

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2023年第3期32卷 917-926页

作者： D'Angelo, Laura Canale, Antonio Univ Milano Bicocca Dept Econ Management & Stat Milan Italy Univ Padua Dept Stat Sci Padua Italy

Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In the Bayesian context, however, there are no sufficient specific computational tools for efficient sampling from the posterior distribution of parameters, and standard algorithms, such as random walk Metropolis-Hastings or Hamiltonian Monte Carlo algorithms, are typically used. Herein, we developed an efficient Metropolis-Hastings algorithm and importance sampler to simulate from the posterior distribution of the parameters of Poisson log-linear models under conditional Gaussian priors with superior performance with respect to the state-of-the-art alternatives. The key for both algorithms is the introduction of a proposal density based on a Gaussian approximation of the posterior distribution of parameters. Specifically, our result leverages the negative binomial approximation of the Poisson likelihood and the successful Polya-gamma data augmentation scheme. Via simulation, we obtained that the time per independent sample of the proposed samplers is competitive with that obtained using the successful Hamiltonian Monte Carlo sampling, with the Metropolis-Hastings showing superior performance in all scenarios considered. Supplementary materials for this article are available online.

关键词： Count data Horseshoe prior Importance sampling log-linear models Metropolis-Hastings Polya-gamma

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