Bayesian fused lasso modeling for binary data

In this study, we have considered the modeling and analyses of binary data. We modeled binary data with categorical predictors, using logistic regression to develop a statistical method. We found that ANOVA-type analyses often performed unsatisfactory, even when using arcsine-square-root trans-formations. We concluded that such methods are not appropriate, especially in cases where the fractions were close to 0 or 1. The logistic transformation of fraction data could be a promising alternative, but it is not desirable in the statistical sense. The major purpose of this paper is to demonstrate that logistic regression with an ANOVA-model like parameterization aids our understanding and provides a somewhat different, but sound, statistical background. We examined a simple real world example to show that we can efficiently test the significance of regression parameters, look for interactions, estimate related confidence intervals, and calculate the difference between the mean values of the referent and experimental subgroups. This paper demonstrates that precise confidence interval estimates can be obtained using the proposed ANOVA-model like approach. The method discussed here can be extended to any type of experimental fraction data analysis, particularly for experimental design.

In this chapter we consider dependent data but move from the linear models of Chap.8 to general regression models. As in Chap.6, we consider generalized linear models (GLMs) and, more briefly, nonlinear models. We first give an outline of this chapter. In Sect.9.2 we describe three motivating datasets to which we return throughout the chapter. The GLMs discussed in Sect.6.3 can be extended to incorporate dependences in observations on the same unit; as with the linear model, an obvious way to carry out modeling in this case is to introduce unit-specific random effects. Within a GLM a natural approach is for these random effects to be included on the linear predictor scale. The resultant conditional models are known as generalized linear mixed models (GLMMs), and these are introduced in Sect.9.3. In Sects.9.4 and9.5 we describe likelihood and conditional likelihood methods of estimation, with Sect.9.6 devoted to a Bayesian treatment. Section9.7 illustrates some of the flexibility of GLMMs by describing and applying a particular model for spatial dependence. An alternative random effects specification, based on conjugacy, is described in Sect.9.8. An important approach to the modeling and analysis of dependent data that is philosophically different from the random effects formulation is via marginal models and generalized estimating equations (GEE), and these are the subject of Sect.9.9. In Sect.9.10, a second GEE approach is described in which the estimating equations for the mean are supplemented with a second set for the variances/covariances. For GLMMs, extra care must be taken with parameter interpretation, and Sect.9.11 discusses this issue, emphasizing how interpretation differs between conditional and marginal models. In PartII of the book, which focused on independent data, Chap.7 was devoted to models for binary data. For dependent data, models binary data are less well developed, and so we do not devote a complete chapter to their description. However, Sect.9.12 introduces the modeling of dependent binary data, and, subsequently, Sects.9.13 and 9.14 describe conditional (mixed) and marginal models for binary data. Section 9.15 considers how nonlinear models, as defined in Sect.6.10, can be extended to the dependent data case. For such models, many applications concentrate on inference for units, and so the introduction of random effects is again suggested. We refer to the resultant class of models as nonlinear mixed models (NLMMs). Section9.16 considers issues related to the parameterization of the nonlinear model. Inference for nonlinear mixed models via likelihood and Bayes approaches is covered in Sects.9.17 and9.18, while GEE is briefly considered in Sect.9.19. The assessment of assumptions for general regression models is described in Sect.9.20, with concluding comments contained in Sect.9.21. Additional references appear in Sect.9.22.

In 2023 and 2024 and in partnership with Sage on Earth Consulting, BGC Engineering undertook a province-wide hazard exposure assessment for the provincial government of British Columbia, Canada. British Columbia spans approximately 940,000 square kilometers, stretching from the Pacific Ocean in the west to the Rocky Mountains in the east and from the Yukon border in the north to Washington State in the south. This expansive region faces a wide array of natural hazards, including flooding from mountain streams, tsunamis and shoreline erosion in coastal communities; earthquakes; landslides; debris flows; wildfires; drought; extreme heat and, increasingly, cascading hazards intensified by climate change. The goal of this project was to design and implement a geospatial workflow for assessing exposure of valued assets to hazards, delivered to a government agency in a standardized format that facilitated future updates and public governance over data sharing.  To accomplish this, BGC designed a data model and analysis pipeline that had sufficient performance for the iterative processing of large multi-hazard and asset datasets and that could be packaged for government agency development of a data portal. Within the data model, hazards were defined as areas which exceed hazard-specific intensity thresholds and/or annual probability of occurrence; these binary hazard data were the primary input to the analysis pipeline for each hazard type. The list of assets to be included in the analysis was determined through a series of consultations with project stakeholders aimed at identifying which assets are most important and what data was available consistently for the entire province. The result of the analysis was a set of exposure metrics representing population counts, monetary values of property exposed to hazards, and the lengths of transportation and utility networks within hazard zones summarized using a uniform 1.5 km x 1.5 km grid. These metrics were delivered along with documentation of the data model, the data, and the codebase for the analysis pipeline.The resulting analysis revealed spatial patterns of hazard exposure and provided actionable insights to support provincial-scale risk management. This work represents a foundational step in risk assessment and mitigation planning. It offers a means of prioritizing local-scale risk assessments within a jurisdiction as vast as British Columbia, enabling focused resource allocation and informed decision-making. Collaboration was central to the project's success. In association with Sage on Earth Consulting , BGC engaged with multiple stakeholders to refine inputs and validate assumptions, and ensure the outputs were accessible and meaningful. The results are designed for government-managed web access to both data inputs and analysis outputs, promoting transparency and usability for diverse audiences.This provincial hazard exposure assessment highlights the importance of integrating data,  geospatial analysis, stakeholder collaboration, and practical tools to address the complex challenges posed by natural hazards in British Columbia. The findings not only advance the understanding of hazard exposure but also lay the groundwork for more detailed, localized risk assessments and targeted mitigation efforts. 

Latent variable models for the topographic organisation of discrete and strictly positive data

A comparison of machine learning surrogate models for net present value prediction from well placement binary data

Evaluation of stochastic global optimization methods for modeling vapor–liquid equilibrium data

The collection of continuous data on transects is a common practice in habitat and fishery stock assessments; however, the application of standard regression models that assume independence to serially correlated data is problematic. We show that generalized linear mixed models (GLMMs), i.e. generalized linear models for longitudinal data, that are normally used for studies performed over time can also be applied to other types of clustered or serially correlated data. We apply a specific GLMM for longitudinal data, a hierarchical Bayesian logistic mixed-effects model (BLMM), to a marine ecology dataset obtained from submersible video recordings of the seabed on transects at two sites in the Gulf of Alaska. The BLMM was effective in relating the presence of red tree corals (Primnoa pacifica; i.e. binary data) to habitat characteristics: the presence of red tree corals is highly associated with bedrock as the primary substrate (estimated odds ratio 9–19), high to very high seabed roughness (estimated odds ratio 3–5), and medium to high slope (estimated odds ratio 2–3). The covariate depth was less important at the sites. We also demonstrate and compare two methods of model checking: full and mixed posterior predictive assessments, the latter of which provided a more realistic assessment, and we calculate the variance partition coefficient for reporting the variation explained by multiple levels of the hierarchical model.

Missing data are frequently encountered in longitudinal clinical trials. To better monitor and understand the progress over time, one must handle the missing data appropriately and examine whether the missing data mechanism is ignorable or nonignorable. In this article, we develop a new probit model for longitudinal binary response data. It resolves a challenging issue for estimating the variance of the random effects, and substantially improves the convergence and mixing of the Gibbs sampling algorithm. We show that when improper uniform priors are specified for the regression coefficients of the joint multinomial model via a sequence of one-dimensional conditional distributions for the missing data indicators under nonignorable missingness, the joint posterior distribution is improper. A variation of Jeffreys prior is thus established as a remedy for the improper posterior distribution. In addition, an efficient Gibbs sampling algorithm is developed using a collapsing technique. Two model assessment criteria, the deviance information criterion (DIC) and the logarithm of the pseudomarginal likelihood (LPML), are used to guide the choices of prior specifications and to compare the models under different missing data mechanisms. We report on extensive simulations conducted to investigate the empirical performance of the proposed methods. The proposed methodology is further illustrated using data from an HIV prevention clinical trial.

This book on multivariate models, statistical inference, and data analysis contains deep coverage of multivariate non-normal distributions for modeling of binary, count, ordinal, and extreme value response data. It is virtually self-contained, and includes many exercises and unsolved problems.

Bayesian Approaches to Copula Modelling

A model is proposed for multivariate binary data that incorporates positive dependence among components in a natural way. The model is derived from reliability-theoretic concepts, but is regarded as appropriate for analysis of multivariate binary data in any field when positive dependence is an appropriate assumption. Maximum likelihood estimation by iterative solution of likelihood equations is discussed for the general model, and asymptotically efficient estimates are obtained in closed form for the fully parameterized (saturated) model. The estimation procedures are illustrated on a data set from Martin and Bradley (1972). Key Words: Multivariate binary dataPositive dependenceShock modelsEstimationAsymptotic efficiency

Several hierarchical classes models can be considered for the modeling of three-way three-mode binary data, including the INDCLAS model (Leenen, Van Mechelen, De Boeck, and Rosenberg, 1999), the Tucker3-HICLAS model (Ceulemans, Van Mechelen, and Leenen, 2003), the Tucker2-HICLAS model (Ceulemans and Van Mechelen, 2004), and the Tucker1-HICLAS model that is introduced in this paper. Two questions then may be raised: (1) how are these models interrelated, and (2) given a specific data set, which of these models should be selected, and in which rank? In the present paper, we deal with these questions by (1) showing that the distinct hierarchical classes models for three-way three-mode binary data can be organized into a partially ordered hierarchy, and (2) by presenting model selection strategies based on extensions of the well-known scree test and on the Akaike information criterion. The latter strategies are evaluated by means of an extensive simulation study and are illustrated with an application to interpersonal emotion data. Finally, the presented hierarchy and model selection strategies are related to corresponding work by Kiers (1991) for principal component models for three-way three-mode real-valued data.

1. Introduction 2. Binary regression: the logit model 3. Generalized linear models 4. Modeling of binary data 5. Alternative binary regression models 6. Regularization and variable selection for parametric models 7. Regression analysis of count data 8. Multinomial response models 9. Ordinal response models 10. Semi- and nonparametric generalized regression 11. Tree-based methods 12. The analysis of contingency tables: log-linear and graphical models 13. Multivariate response models 14. Random effects models 15. Prediction and classification Appendix A. Distributions Appendix B. Some basic tools Appendix C. Constrained estimation Appendix D. Kullback-Leibler distance and information-based criteria of model fit Appendix E. Numerical integration and tools for random effects modeling.

Longitudinal models of binary or ordered categorical data are often evaluated for adequacy by the ability of these to characterize the transition frequency and type between response states. Drug development decisions are often concerned with accurate prediction and inference of the probability of response by time and dose. A question arises on whether the transition probabilities need to be characterized adequately to ensure accurate response prediction probabilities unconditional on the previous response state. To address this, a simulation study was conducted to assess bias in estimation, prediction and inferences of autocorrelated latent variable models (ALVMs) when the transition probabilities are misspecified due to ill-posed random effects structures, inadequate likelihood approximation or omission of the autocorrelation component. The results may be surprising in that these suggest that characterizing autocorrelation in ALVMs is not as important as specifying a suitably rich random effects structure.

SummaryWe consider estimating binary response models on an unbalanced panel, where the outcome of the dependent variable may be missing due to nonrandom selection, or there is self‐selection into a treatment. In the present paper, we first consider estimation of sample selection models and treatment effects using a fully parametric approach, where the error distribution is assumed to be normal in both primary and selection equations. Arbitrary time dependence in errors is permitted. Estimation of both coefficients and partial effects, as well as tests for selection bias, are discussed. Furthermore, we consider a semiparametric estimator of binary response panel data models with sample selection that is robust to a variety of error distributions. The estimator employs a control function approach to account for endogenous selection and permits consistent estimation of scaled coefficients and relative effects.