In regional economics research, a problem of interest is to detect similarities between regions, and estimate their shared coefficients in economics models. In this article, we propose a mixture of finite mixtures (MFM) clustered regression model with auxiliary covariates that account for similarities in demographic or economic characteristics over a spatial domain. Our Bayesian construction provides both inference for number of clusters and clustering configurations, and estimation for parameters for each cluster. Empirical performance of the proposed model is illustrated through simulation experiments, and further applied to a study of influential factors for monthly housing cost in Georgia.
We introduce a Bayesian nonparametric regression model for data with multiway (tensor) structure, motivated by an application to periodontal disease (PD) data. Our outcome is the number of diseased sites measured over four different tooth types for each subject, with subject-specific covariates available as predictors. The outcomes are not well-characterized by simple parametric models, so we use a nonparametric approach with a binomial likelihood wherein the latent probabilities are drawn from a mixture with an arbitrary number of components, analogous to a Dirichlet Process (DP). We use a fl…
Motivated by the problem of accurately predicting gap times between successive blood donations, we present here a general class of Bayesian nonparametric models for clustering. These models allow for prediction of new recurrences, accommodating covariate information that describes the personal characteristics of the sample individuals. We introduce a prior for the random partition of the sample individuals which encourages two individuals to be co-clustered if they have similar covariate values. Our prior generalizes PPMx models in the literature, which are defined in terms of cohesion and sim…
Popular parametric and semiparametric hazards regression models for clustered survival data are inappropriate and inadequate when the unknown effects of different covariates and clustering are complex. This calls for a flexible modeling framework to yield efficient survival prediction. Moreover, for some survival studies involving time to occurrence of some asymptomatic events, survival times are typically interval censored between consecutive clinical inspections. In this article, we propose a robust semiparametric model for clustered interval-censored survival data under a paradigm of Bayesi…
This article concerns a class of generalized linear mixed models for clustered data, where the random effects are mapped uniquely onto the grouping structure and are independent between groups. We derive necessary and sufficient conditions that enable the marginal likelihood of such class of models to be expressed in closed-form. Illustrations are provided using the Gaussian, Poisson, binomial and gamma distributions. These models are unified under a single umbrella of conjugate generalized linear mixed models, where "conjugate" refers to the fact that the marginal likelihood can be expressed …
In economic development, there are often regions that share similar economic characteristics, and economic models on such regions tend to have similar covariate effects. In this paper, we propose a Bayesian clustered regression for spatially dependent data in order to detect clusters in the covariate effects. Our proposed method is based on the Dirichlet process which provides a probabilistic framework for simultaneous inference of the number of clusters and the clustering configurations. The usage of our method is illustrated both in simulation studies and an application to a housing cost dat…
This paper is motivated by the panel surveys, called Statistics on Income and Living Conditions (SILC), conducted annually on (randomly selected) country-representative households to monitor EU 2020 aims on poverty reduction. We particularly consider the surveys conducted in Turkey, within the scope of integration to the EU, between 2010 and 2013. Our main interests are on health aspects of economic and living conditions. The outcome is {\it self-reported health} that is clustered longitudinal ordinal, since repeated measures of it are nested within individuals and individuals are nested withi…
Statistical power is often a concern for clustered RCTs due to variance inflation from design effects and the high cost of adding study clusters (such as hospitals, schools, or communities). While covariate pre-specification is the preferred approach for improving power to estimate regression-adjusted average treatment effects (ATEs), further precision gains can be achieved through covariate selection once primary outcomes have been collected. This article uses design-based methods underlying clustered RCTs to develop a Lasso-OLS hybrid procedure for the post-hoc selection of covariates and AT…
This study is concerned with the analysis of three-level ordinal outcome data with polytomous logistic regression in the presence of random-effects. It is assumed that the random-effects follow a Bridge distribution for the logit link, which allows one to obtain marginal interpretations of the regression coefficients. The data are obtained from the Turkish Income and Living Conditions Study, where the outcome variable is self-rated health (SRH), which is ordinal in nature. The analysis of these data is to compare covariate sub-groups and draw region- and family-level inferences in terms of SRH…
In medical studies, the collected covariates usually contain underlying outliers. For clustered /longitudinal data with censored observations, the traditional Gehan-type estimator is robust to outliers existing in response but sensitive to outliers in the covariate domain, and it also ignores the within-cluster correlations. To take account of within-cluster correlations, varying cluster sizes, and outliers in covariates, we propose weighted Gehan-type estimating functions for parameter estimation in the accelerated failure time model for clustered data. We provide the asymptotic properties of…
In randomized experiments, treatment and control groups should be roughly the same--balanced--in their distributions of pretreatment variables. But how nearly so? Can descriptive comparisons meaningfully be paired with significance tests? If so, should there be several such tests, one for each pretreatment variable, or should there be a single, omnibus test? Could such a test be engineered to give easily computed $p$-values that are reliable in samples of moderate size, or would simulation be needed for reliable calibration? What new concerns are introduced by random assignment of clusters? Wh…
Estimating the average treatment causal effect in clustered data often involves dealing with unmeasured cluster-specific confounding variables. Such variables may be correlated with the measured unit covariates and outcome. When the correlations are ignored, the causal effect estimation can be biased. By utilizing sufficient statistics, we propose an inverse conditional probability weighting (ICPW) method, which is robust to both (i) the correlation between the unmeasured cluster-specific confounding variable and the covariates and (ii) the correlation between the unmeasured cluster-specific c…
Multi-species distribution modeling, which relates the occurrence of multiple species to environmental variables, is an important tool used by ecologists for both predicting the distribution of species in a community and identifying the important variables driving species co-occurrences. Recently, Dunstan, Foster and Darnell [Ecol. Model. 222 (2011) 955-963] proposed using finite mixture of regression (FMR) models for multi-species distribution modeling, where species are clustered based on their environmental response to form a small number of "archetypal responses." As an illustrative exampl…
This paper proposes a modelling strategy to infer the impact of a covariate on the dependence structure of right-censored clustered event time data. The joint survival function of the event times is modelled using a parametric conditional copula whose parameter depends on a cluster-level covariate in a functional way. We use a local likelihood approach to estimate the form of the copula parameter and outline a generalized likelihood ratio-type test strategy to formally test its constancy. A bootstrap procedure is employed to obtain an approximate $p$-value for the test. The performance of the …
Cluster-induced target shift and synthetic approximation for high-dimensional clustered data
Florida International University（佛罗里达国际大学）；University of Nottingham Ningbo China（诺丁汉大学宁波校区）；University of Pennsylvania（宾夕法尼亚大学）；Dartmouth College（达特茅斯学院）；Oklahoma State University（俄克拉荷马州立大学）
BPEC is an R package for Bayesian Phylogeographic and Ecological Clustering which allows geographical, environmental and phenotypic measurements to be combined with DNA sequences in order to reveal clustered structure resulting from migration events. DNA sequences are modelled using a collapsed version of a simplified coalescent model projected onto haplotype trees, which subsequently give rise to constrained clusterings as migrations occur. Within each cluster, a multivariate Gaussian distribution of the covariates (geographical, environmental, phenotypic) is used. Inference follows tailored …
Small Area Estimation under Spatial Regimes: Spatially Clustered Fay-Herriot Models for Agricultural Indicators
University of Milano-Bicocca（米兰比可卡大学）；Fondazione Eni Enrico Mattei (FEEM)（埃尼·恩里科·马泰伊基金会）；University of Campania "Luigi Vanvitelli"（坎帕尼亚路易吉·范维特利大学）；Keio University（庆应义塾大学）
We consider the inference problem for high-dimensional linear models, when covariates have an underlying spatial organization reflected in their correlation. A typical example of such a setting is high-resolution imaging, in which neighboring pixels are usually very similar. Accurate point and confidence intervals estimation is not possible in this context with many more covariates than samples, furthermore with high correlation between covariates. This calls for a reformulation of the statistical inference problem, that takes into account the underlying spatial structure: if covariates are lo…
Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured dependence--remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkag…
Informative cluster size (ICS) arises in situations with clustered data where a latent relationship exists between the number of participants in a cluster and the outcome measures. Although this phenomenon has been sporadically reported in statistical literature for nearly two decades now, further exploration is needed in certain statistical methodologies to avoid potentially misleading inferences. For inference about population quantities without covariates, inverse cluster size reweightings are often employed to adjust for ICS. Further, to study the effect of covariates on disease progressio…
A distinctive feature of a clustered observational study is its multilevel or nested data structure arising from the assignment of treatment, in a non-random manner, to groups or clusters of units or individuals. Examples are ubiquitous in the health and social sciences including patients in hospitals, employees in firms, and students in schools. What is the optimal matching strategy in a clustered observational study? At first thought, one might start by matching clusters of individuals and then, within matched clusters, continue by matching individuals. But as we discuss in this paper, the o…
With the advent of ubiquitous monitoring and measurement protocols, studies have started to focus more and more on complex, multivariate and heterogeneous datasets. In such studies, multivariate response variables are drawn from a heterogeneous population often in the presence of additional covariate information. In order to deal with this intrinsic heterogeneity, regression analyses have to be clustered for different groups of units. Up until now, mixture model approaches assigned units to distinct and non-overlapping groups. However, not rarely these units exhibit more complex organization a…
Marine conservation preserves fish biodiversity, protects marine and coastal ecosystems, and supports climate resilience and adaptation. Despite the importance of establishing marine protected areas (MPAs), research on the effectiveness of MPAs with different conservation policies is limited due to the lack of quantitative MPA information. In this paper, leveraging a global MPA database, we investigate the causal impact of MPA policies on fish biodiversity. To address challenges posed by this clustered and confounded observational study, we construct a matching estimator of the average treatme…
This article proposes a mixture modeling approach to estimating cluster-wise conditional distributions in clustered (grouped) data. We adapt the mixture-of-experts model to the latent distributions, and propose a model in which each cluster-wise density is represented as a mixture of latent experts with cluster-wise mixing proportions distributed as Dirichlet distribution. The model parameters are estimated by maximizing the marginal likelihood function using a newly developed Monte Carlo Expectation-Maximization algorithm. We also extend the model such that the distribution of cluster-wise mi…
In various applications with large spatial regions, the relationship between the response variable and the covariates is expected to exhibit complex spatial patterns. We propose a spatially clustered varying coefficient model, where the regression coefficients are allowed to vary smoothly within each cluster but change abruptly across the boundaries of adjacent clusters, and we develop a unified approach for simultaneous coefficient estimation and cluster identification. The varying coefficients are approximated by penalized splines, and the clusters are identified through a fused concave pena…
Clustered multistate process data are commonly encountered in multicenter observational studies and clinical trials. A clinically important estimand with such data is the marginal probability of being in a particular transient state as a function of time. However, there is currently no method for nonparametric marginal regression analysis of these probabilities with clustered multistate process data. To address this problem, we propose a weighted functional generalized estimating equations approach which does not impose Markov assumptions or assumptions regarding the structure of the within-cl…
Healthcare cost prediction is a challenging task due to the high-dimensionality and high correlation among covariates. Additionally, the skewed, heavy-tailed, and often multi-modal nature of cost data can complicate matters further due to unobserved heterogeneity. In this study, we propose a novel framework for finite mixture regression models that incorporates covariate clustering methods to better account for the effects of clustered covariates on subgroups of the outcome, which enables a more accurate characterization of the complex distribution of the data. The proposed framework can be fo…
When drawing causal inferences about the effects of multiple treatments on clustered survival outcomes using observational data, we need to address implications of the multilevel data structure, multiple treatments, censoring and unmeasured confounding for causal analyses. Few off-the-shelf causal inference tools are available to simultaneously tackle these issues. We develop a flexible random-intercept accelerated failure time model, in which we use Bayesian additive regression trees to capture arbitrarily complex relationships between censored survival times and pre-treatment covariates and …
In a regression analysis, suppose we suspect that there are several heterogeneous groups in the population that a sample represents. Mixture regression models have been applied to address such problems. By modeling the conditional distribution of the response given the covariate as a mixture, the sample can be clustered into groups and the individual regression models for the groups can be estimated simultaneously. This approach treats the covariate as deterministic so that the covariate carries no information as to which group the subject is likely to belong to. Although this assumption may b…
Propensity score weighting is a tool for causal inference to adjust for measured confounders. Survey data are often collected under complex sampling designs such as multistage cluster sampling, which presents challenges for propensity score modeling and estimation. In addition, for clustered data, there may also be unobserved cluster effects related to both the treatment and the outcome. When such unmeasured confounders exist and are omitted in the propensity score model, the subsequent propensity score adjustment will be biased. We propose a calibrated propensity score weighting adjustment fo…
Continuous response variables often need to be transformed to meet regression modeling assumptions; however, finding the optimal transformation is challenging and results may vary with the choice of transformation. When a continuous response variable is measured repeatedly for a subject or the continuous responses arise from clusters, it is more challenging to model the continuous response data due to correlation within clusters. We extend a widely used ordinal regression model, the cumulative probability model (CPM), to fit clustered continuous response variables based on generalized estimati…
Recently, applied sciences, including longitudinal and clustered studies in biomedicine require the analysis of ultra-high dimensional linear mixed effects models where we need to select important fixed effect variables from a vast pool of available candidates. However, all existing literature assume that all the available covariates and random effect components are independent of the model error which is often violated (endogeneity) in practice. In this paper, we first investigate this important issue in ultra-high dimensional linear mixed effects models with particular focus on the fixed eff…
We propose a novel semiparametric model for the joint distribution of a continuous longitudinal outcome and the baseline covariates using an enriched Dirichlet process (EDP) prior. This joint model decomposes into a linear mixed model for the outcome given the covariates and marginals for the covariates. The nonparametric EDP prior is placed on the regression and spline coefficients, the error variance, and the parameters governing the predictor space. We predict the outcome at unobserved time points for subjects with data at other time points as well as for new subjects with only baseline cov…
Finite Mixtures of Generalized Estimating Equations for Clustering Multivariate Correlated Outcomes
Faculty of Economics, Keio University（庆应义塾大学经济学部）；Research School of Finance, Actuarial Studies and Statistics, The Australian National University（澳大利亚国立大学金融、精算与统计研究学院）
Propensity score weighting is a tool for causal inference to adjust for measured confounders in observational studies. In practice, data often present complex structures, such as clustering, which make propensity score modeling and estimation challenging. In addition, for clustered data, there may be unmeasured cluster-specific variables that are related to both the treatment assignment and the outcome. When such unmeasured cluster-specific confounders exist and are omitted in the propensity score model, the subsequent propensity score adjustment may be biased. In this article, we propose a ca…
This work demonstrates the ability to produce readily interpretable statistical metrics for model fit, fixed effects covariance coefficients, and prediction confidence. Importantly, this work compares 4 suitable and commonly applied epistemic UQ approaches, BNN, SWAG, MC dropout, and ensemble approaches in their ability to calculate these statistical metrics for the ARMED MEDL models. In our experiment for AD prognosis, not only do the UQ methods provide these benefits, but several UQ methods maintain the high performance of the original ARMED method, some even provide a modest (but not statis…
