Hierarchical Models (hierarchical + models)

Distribution by Scientific Domains

Kinds of Hierarchical Models

  • bayesian hierarchical models

  • Selected Abstracts

    Hierarchical Models in Environmental Science

    Christopher K. Wikle
    Summary Environmental systems are complicated. They include very intricate spatio-temporal processes, interacting on a wide variety of scales. There is increasingly vast amounts of data for such processes from geographical information systems, remote sensing platforms, monitoring networks, and computer models. In addition, often there is a great variety of scientific knowledge available for such systems, from partial differential equations based on first principles to panel surveys. It is argued that it is not generally adequate to consider such processes from a joint perspective. Instead, the processes often must be considered as a coherently linked system of conditional models. This paper provides a brief overview of hierarchical approaches applied to environmental processes. The key elements of such models can be considered in three general stages, the data stage, process stage, and parameter stage. In each stage, complicated dependence structure is mitigated by conditioning. For example, the data stage can incorporate measurement errors as well as multiple datasets with varying supports. The process and parameter stages can allow spatial and spatio-temporal processes as well as the direct inclusion of scientific knowledge. The paper concludes with a discussion of some outstanding problems in hierarchical modelling of environmental systems, including the need for new collaboration approaches. Résumé Les systèmes environnementaux sont complexes. Ils incluent des processus spatio-temporels trés complexes, interagissant sur une large variété d'échelles. II existe des quantités de plus en plus grandes de données sur de tels processus, provenant des systèmes d'information géographiques, des plateformes de télédétection, des réseaux de surveillance et des modèles informatiques. De plus, il y a souvent une grande variété de connaissance scientifique disponible sur de tels systémes, depuis les équations différentielles partielles jusqu'aux enquétes de panels. II est reconnu qu'il n'est généralement pas correct de considerer de tels processus d'une perspective commune. Au contraire, les processus doivent souvent étre examinés comme des systèmes de modèles conditionnels liés de manière cohérente. Cet article fournit un bref aperçu des approches hiérachiques appliquées aux processus environnementaux. Les éléments clés de tels modèles peuvent étre examinés à trois étapes principales: l'étape des donnèes, celle du traitement et celle des paramètres. A chaque étape, la structure complexe de dépendance est atténuée par le conditionnement. Par exemple, le stade des données peut incorporer des erreurs de mesure ainsi que de multiples ensembles de données sous divers supports. Les stades du traitement et des paramétres peuvent admettre des processus spatiaux et spatio-temporels ainsi que l'inclusion directe du savoir scientifique. L'article conclut par une discussion de quelques problèmes en suspens dans la modélisation hiérarchique des systèmes environnementaux, incluant le besoin de nouvelles approches de collaboration. [source]

    Functional Hierarchical Models for Identifying Genes with Different Time-Course Expression Profiles

    BIOMETRICS, Issue 2 2006
    F. Hong
    Summary Time-course studies of gene expression are essential in biomedical research to understand biological phenomena that evolve in a temporal fashion. We introduce a functional hierarchical model for detecting temporally differentially expressed (TDE) genes between two experimental conditions for cross-sectional designs, where the gene expression profiles are treated as functional data and modeled by basis function expansions. A Monte Carlo EM algorithm was developed for estimating both the gene-specific parameters and the hyperparameters in the second level of modeling. We use a direct posterior probability approach to bound the rate of false discovery at a pre-specified level and evaluate the methods by simulations and application to microarray time-course gene expression data on Caenorhabditis elegans developmental processes. Simulation results suggested that the procedure performs better than the two-way ANOVA in identifying TDE genes, resulting in both higher sensitivity and specificity. Genes identified from the C. elegans developmental data set show clear patterns of changes between the two experimental conditions. [source]


    CRIMINOLOGY, Issue 2 2006
    This study extends recent inquiries of contextual effects in sentencing by jointly examining the influence of judge and courtroom social contexts. It combines two recent years of individual sentencing data from the Pennsylvania Commission on Sentencing (PCS) with data on judicial background characteristics and county court social contexts. Three-level hierarchical models are estimated to investigate the influence of judge and county contexts on individual variations in sentencing. Results indicate that nontrivial sentencing variations are associated with both individual judge characteristics and county court contexts. Judicial background factors also condition the influence of individual offender characteristics in important ways. These and other findings are discussed in relation to contemporary theoretical perspectives on courtroom decision making that highlight the importance of both judge and court contexts in sentencing. The study concludes with suggestions for future research on contextual disparities in criminal sentencing. [source]

    Parsing the general and specific components of depression and anxiety with bifactor modeling,

    Leonard J. Simms Ph.D.
    Abstract Recent hierarchical models suggest that both general and specific components are needed to fully represent the variation observed among mood and anxiety disorders. However, little is known about the relative size, severity, and psychological meaning of these components. We studied these features through bifactor modeling of the symptoms from the Inventory of Depression and Anxiety Symptoms [IDAS; Watson et al., 2007] in 362 community adults, 353 psychiatric patients, and 673 undergraduates. Results revealed that although all IDAS symptom types loaded prominently both on a general factor as well as specific factors, some symptom groups,such as dysphoria, generalized anxiety, and irritability,were influenced more strongly by the general factor, whereas others,e.g., appetite gain, appetite loss, and low well-being,contained a larger specific component. Second, certain symptom groups,e.g., Suicidality, Panic, Appetite Loss, and Ill Temper,reflected higher severity than other symptom groups. Finally, general factor scores correlated strongly with markers of general distress and negative emotionality. These findings support a hierarchical structure among mood and anxiety symptoms and have important implications for how such disorders are described, assessed, and studied. Depression and Anxiety 0:1,13, 2007. Published 2007 Wiley-Liss, Inc. [source]

    Factorial validity of the center for epidemiologic studies-depression (CES-D) scale in military peacekeepers

    Jennifer A. Boisvert M.A.
    Abstract Despite widespread use of the Center for Epidemiologic Studies Depression Scale [CES-D], there are no investigations that examine its factor structure in a military sample. Separate confirmatory factor analyses were performed on responses to the CES-D obtained from 102 female and 102 male Canadian military peacekeepers in order to compare the fit of a four-factor intercorrelated (lower-order) model to a four-factor hierarchical (higher-order) model. The intercorrelated and hierarchical models fit the data well for both women and men, with hierarchical models fitting the data slightly better for women than men. These findings suggest that, for military women and men, the CES-D can be used to measure a set of distinct but interrelated depressive symptoms as well as a global construct of depression. Implications and future directions are discussed. Depression and Anxiety 17:19,25, 2003. © 2003 Wiley-Liss, Inc. [source]

    Scales of association: hierarchical linear models and the measurement of ecological systems

    ECOLOGY LETTERS, Issue 6 2007
    Sean M. McMahon
    Abstract A fundamental challenge to understanding patterns in ecological systems lies in employing methods that can analyse, test and draw inference from measured associations between variables across scales. Hierarchical linear models (HLM) use advanced estimation algorithms to measure regression relationships and variance,covariance parameters in hierarchically structured data. Although hierarchical models have occasionally been used in the analysis of ecological data, their full potential to describe scales of association, diagnose variance explained, and to partition uncertainty has not been employed. In this paper we argue that the use of the HLM framework can enable significantly improved inference about ecological processes across levels of organization. After briefly describing the principals behind HLM, we give two examples that demonstrate a protocol for building hierarchical models and answering questions about the relationships between variables at multiple scales. The first example employs maximum likelihood methods to construct a two-level linear model predicting herbivore damage to a perennial plant at the individual- and patch-scale; the second example uses Bayesian estimation techniques to develop a three-level logistic model of plant flowering probability across individual plants, microsites and populations. HLM model development and diagnostics illustrate the importance of incorporating scale when modelling associations in ecological systems and offer a sophisticated yet accessible method for studies of populations, communities and ecosystems. We suggest that a greater coupling of hierarchical study designs and hierarchical analysis will yield significant insights on how ecological processes operate across scales. [source]

    Evaluation of Bayesian models for focused clustering in health data

    ENVIRONMETRICS, Issue 8 2007
    Bo Ma
    Abstract This paper examines the ability of Bayesian hierarchical models to recover evidence of disease risk excess around a fixed location. This location can be a putative source of health hazard, such as an incinerator, mobile phone mast or dump site. While Bayesian models are convenient to use for modeling, it is useful to consider how well these models perform in the true risk scenarios. In what follows, we evaluate the ability of these models to recover the true risk under simulation. It is surprising that the resulting posterior parameters estimates are heavily biased. Using the credible intervals for distance decline parameter to assess ,coverage or power' of detecting distance effect, the ,power' decreases with increasing correlation in the background population effect. The inclusion of correlated heterogeneity in models does affect the ability of the models to detect the stronger distance decline scenarios. The uncorrelated heterogeneity seems little affect this ability however. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Analyzing weather effects on airborne particulate matter with HGLM

    ENVIRONMETRICS, Issue 7 2003
    Yoon Dong Lee
    Abstract Particulate matter is one of the six constituent air pollutants regulated by the United States Environmental Protection Agency. In analyzing such data, Bayesian hierarchical models have often been used. In this article we propose the use of hierarchical generalized linear models, which use likelihood inference and have well developed model-checking procedures. Comparisons are made between analyses from hierarchical generalized linear models and Daniels et al.'s (2001) Bayesian models. Model-checking procedure indicates that Daniels et al.'s model can be improved by use of the log-transformation of wind speed and precipitation covariates. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Bayesian hierarchical models in ecological studies of health,environment effects

    ENVIRONMETRICS, Issue 2 2003
    Sylvia Richardson
    Abstract We describe Bayesian hierarchical models and illustrate their use in epidemiological studies of the effects of environment on health. The framework of Bayesian hierarchical models refers to a generic model building strategy in which unobserved quantities (e.g. statistical parameters, missing or mismeasured data, random effects, etc.) are organized into a small number of discrete levels with logically distinct and scientifically interpretable functions, and probabilistic relationships between them that capture inherent features of the data. It has proved to be successful for analysing many types of complex epidemiological and biomedical data. The general applicability of Bayesian hierarchical models has been enhanced by advances in computational algorithms, notably those belonging to the family of stochastic algorithms based on Markov chain Monte Carlo techniques. In this article, we review different types of design commonly used in studies of environment and health, give details on how to incorporate the hierarchical structure into the different components of the model (baseline risk, exposure) and discuss the model specification at the different levels of the hierarchy with particular attention to the problem of aggregation (ecological) bias. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Assessing sources of variability in measurement of ambient particulate matter

    ENVIRONMETRICS, Issue 6 2001
    Michael J. Daniels
    Abstract Particulate matter (PM), a component of ambient air pollution, has been the subject of United States Environmental Protection Agency regulation in part due to many epidemiological studies examining its connection with health. Better understanding the PM measurement process and its dependence on location, time, and other factors is important for both modifying regulations and better understanding its effects on health. In light of this, in this paper, we will explore sources of variability in measuring PM including spatial, temporal and meteorological effects. In addition, we will assess the degree to which there is heterogeneity in the variability of the micro-scale processes, which may suggest important unmeasured processes, and the degree to which there is unexplained heterogeneity in space and time. We use Bayesian hierarchical models and restrict attention to the greater Pittsburgh (USA) area in 1996. The analyses indicated no spatial dependence after accounting for other sources of variability and also indicated heterogeneity in the variability of the micro-scale processes over time and space. Weather and temporal effects were very important and there was substantial heterogeneity in these effects across sites. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Identifiability of parameters and behaviour of MCMC chains: a case study using the reaction norm model

    M.M. Shariati
    Summary Markov chain Monte Carlo (MCMC) enables fitting complex hierarchical models that may adequately reflect the process of data generation. Some of these models may contain more parameters than can be uniquely inferred from the distribution of the data, causing non-identifiability. The reaction norm model with unknown covariates (RNUC) is a model in which unknown environmental effects can be inferred jointly with the remaining parameters. The problem of identifiability of parameters at the level of the likelihood and the associated behaviour of MCMC chains were discussed using the RNUC as an example. It was shown theoretically that when environmental effects (covariates) are considered as random effects, estimable functions of the fixed effects, (co)variance components and genetic effects are identifiable as well as the environmental effects. When the environmental effects are treated as fixed and there are other fixed factors in the model, the contrasts involving environmental effects, the variance of environmental sensitivities (genetic slopes) and the residual variance are the only identifiable parameters. These different identifiability scenarios were generated by changing the formulation of the model and the structure of the data and the models were then implemented via MCMC. The output of MCMC sampling schemes was interpreted in the light of the theoretical findings. The erratic behaviour of the MCMC chains was shown to be associated with identifiability problems in the likelihood, despite propriety of posterior distributions, achieved by arbitrarily chosen uniform (bounded) priors. In some cases, very long chains were needed before the pattern of behaviour of the chain may signal the existence of problems. The paper serves as a warning concerning the implementation of complex models where identifiability problems can be difficult to detect a priori. We conclude that it would be good practice to experiment with a proposed model and to understand its features before embarking on a full MCMC implementation. [source]

    Bone and Muscle Development During Puberty in Girls: A Seven-Year Longitudinal Study,,

    Leiting Xu
    Abstract The growth of lean mass precedes that of bone mass, suggesting that muscle plays an important role in the growth of bone. However, to date, no study has directly followed the growth of bone and muscle size through puberty and into adulthood. This study aimed to test the hypothesis that the growth of muscle size precedes that of bone size (width and length) and mass during puberty. Bone and muscle properties were measured using pQCT and DXA in 258 healthy girls at baseline (mean age, 11.2 yr) and 1-, 2-, 3,4- and 7-yr follow-up. Growth trends as a function of time relative to menarche were determined from prepuberty to early adulthood for tibial length (TL), total cross-sectional area (tCSA), cortical CSA (cCSA), total BMC (tBMC), cortical volumetric BMD (cBMD), and muscle CSA (mCSA) in hierarchical models. The timings of the peak growth velocities for these variables were calculated. Seventy premenopausal adults, comprising a subset of the girl's mothers (mean age, 41.5 yr), were included for comparative purposes. In contrast to our hypothesis, the growth velocity of mCSA peaked 1 yr later than that of tibial outer dimensions (TL and tCSA) and slightly earlier than tBMC. Whereas TL ceased to increase 2 yr after menarche, tCSA, cCSA, tBMC, and mCSA continued to increase and were still significantly lower than adult values at the age of 18 yr (all p < 0.01). The results do not support the view that muscle force drives the growth of bone size during puberty. [source]

    Bayesian measures of model complexity and fit

    David J. Spiegelhalter
    Summary. We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. Using an information theoretic argument we derive a measure pD for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest. In general pD approximately corresponds to the trace of the product of Fisher's information and the posterior covariance, which in normal models is the trace of the ,hat' matrix projecting observations onto fitted values. Its properties in exponential families are explored. The posterior mean deviance is suggested as a Bayesian measure of fit or adequacy, and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages. Adding pD to the posterior mean deviance gives a deviance information criterion for comparing models, which is related to other information criteria and has an approximate decision theoretic justification. The procedure is illustrated in some examples, and comparisons are drawn with alternative Bayesian and classical proposals. Throughout it is emphasized that the quantities required are trivial to compute in a Markov chain Monte Carlo analysis. [source]

    Does Racial Balance in Workforce Representation Yield Equal Justice?

    LAW & SOCIETY REVIEW, Issue 4 2009
    Race Relations of Sentencing in Federal Court Organizations
    Increasing racial and ethnic group representation in justice-related occupations is considered a potential remedy to racial inequality in justice administration, including sentencing disparity. Studies to date yield little evidence of such an effect; however, research limitations may account for the mixed and limited evidence of the significance of justice workforce racial diversity. Specifically, few studies consider group-level dynamics of race and representation, thus failing to contextualize racial group power relations in justice administration. To consider these contextual dynamics we combine court organizational and case-level data from 89 federal districts and use hierarchical models to assess whether variably "representative" work groups relate to district-level differences in sentencing. Using district-specific indexes of population and work group dissimilarity to define representation, we find no relationships between black judge representation and sentencing in general across districts, but that districts with more black representation among prosecutors are significantly less likely to sentence defendants to terms of imprisonment. We also find in districts with increased black representation among prosecutors, and to a lesser degree among judges, that black defendants are less likely to be imprisoned and white defendants are more likely to be imprisoned, with the effect of narrowing black-white disparities in sentencing. Consistent with the "power-threat" perspective, and perhaps "implicit racial bias" research, findings encourage modeling diversity to account for relative racial group power in processes of social control and suggest that racial justice may be moderately advanced by equal representation among authorities. [source]

    Does School Finance Litigation Cause Taxpayer Revolt?

    LAW & SOCIETY REVIEW, Issue 3 2006
    Proposition 1, Serrano
    An influential theory argues that court-ordered school finance equalization undermines support for public schools. Residents of wealthy school districts who cannot keep their tax revenues for their own school districts may vote to limit school funding altogether. Proponents of this theory point to Serrano v. Priest, a 1977 decision of the California Supreme Court that mandated equalization of school financing and was followed almost immediately by Proposition 13, a ballot initiative to limit the local property tax. I test the theory that these two events were causally related by using hierarchical models to analyze voters within school districts. I find no evidence that opposition to school finance equalization contributed to the tax revolt. Claims about the perverse consequences of school finance litigation should be greeted with skepticism. [source]

    Generating dark matter halo merger trees

    Hannah Parkinson
    ABSTRACT We present a new Monte Carlo algorithm to generate merger trees describing the formation history of dark matter haloes. The algorithm is a modification of the algorithm of Cole et al. used in the galform semi-analytic galaxy formation model. As such, it is based on the Extended Press,Schechter theory and so should be applicable to hierarchical models with a wide range of power spectra and cosmological models. It is tuned to be in accurate agreement with the conditional mass functions found in the analysis of merger trees extracted from the , cold dark matter Millennium N -body simulation. We present a comparison of its predictions not only with these conditional mass functions, but also with additional statistics of the Millennium Simulation halo merger histories. In all cases, we find it to be in good agreement with the Millennium Simulation and thus it should prove to be a very useful tool for semi-analytic models of galaxy formation and for modelling hierarchical structure formation in general. We have made our merger tree generation code and code to navigate the trees available at http://star-www.dur.ac.uk/~cole/merger_trees. [source]

    Quantitative morphological analysis of the Hubble Deep Field North and Hubble Deep Field South , I. Early- and late-type luminosity,size relations of galaxies out to z, 1

    I. Trujillo
    ABSTRACT Based on drizzled F606W and F814W images, we present quantitative structural parameters in the V -band rest-frame for all galaxies with z < 1 and I814(AB) < 24.5 mag in the Hubble Deep Fields North and South. Our structural parameters are based on a two-component surface brightness distribution using a Sérsic bulge and an exponential disc. Detailed simulations and comparisons with previous work are presented. The luminosity,size distribution of early-type galaxies is consistent with the hypothesis that their structural properties were already in place by z, 1 and have evolved passively since then; early-type galaxies were ,1.35(±0.1) mag brighter in rest-frame V -band luminosity at z, 0.7 than now. Compared with present-day late-type galaxies, those at z, 0.7 with LV > 0.2 × 1010 h,2 L, show a moderate decrease [,30(±10) per cent] in size [or interpreted differently, a decrease of ,0.77(±0.30) mag in the central surface brightness] at a given luminosity. Finally, we make a comparison of our results with the infall and hierarchical models. [source]

    From linear to non-linear scales: analytical and numerical predictions for weak-lensing convergence

    Andrew J. Barber
    ABSTRACT Weak-lensing convergence can be used directly to map and probe the dark-mass distribution in the Universe. Building on earlier studies, we recall how the statistics of the convergence field are related to the statistics of the underlying mass distribution, in particular to the many-body density correlations. We describe two model-independent approximations which provide two simple methods to compute the probability distribution function (pdf) of the convergence. We apply one of these to the case where the density field can be described by a lognormal pdf. Next, we discuss two hierarchical models for the high-order correlations which allow us to perform exact calculations and evaluate the previous approximations in such specific cases. Finally, we apply these methods to a very simple model for the evolution of the density field from linear to highly non-linear scales. Comparisons with the results obtained from numerical simulations, obtained from a number of different realizations, show excellent agreement with our theoretical predictions. We have probed various angular scales in the numerical work and considered sources at 14 different redshifts in each of two different cosmological scenarios, an open cosmology and a flat cosmology with non-zero cosmological constant. Our simulation technique employs computations of the full three-dimensional shear matrices along the line of sight from the source redshift to the observer and is complementary to more popular ray-tracing algorithms. Our results therefore provide a valuable cross-check for such complementary simulation techniques, as well as for our simple analytical model, from the linear to the highly non-linear regime. [source]

    A mathematical and statistical framework for modelling dispersal

    OIKOS, Issue 6 2007
    Tord Snäll
    Mechanistic and phenomenological dispersal modelling of organisms has long been an area of intensive research. Recently, there has been an increased interest in intermediate models between the two. Intermediate models include major mechanisms that affect dispersal, in addition to the dispersal curve of a phenomenological model. Here we review and describe the mathematical and statistical framework for phenomenological dispersal modelling. In the mathematical development we describe modelling of dispersal in two dimensions from a point source, and in one dimension from a line or area source. In the statistical development we describe applicable observation distributions, and the procedures of model fitting, comparison, checking, and prediction. The procedures are also demonstrated using data from dispersal experiments. The data are hierarchically structured, and hence, we fit hierarchical models. The Bayesian modelling approach is applied, which allows us to show the uncertainty in the parameter estimates and in predictions. Finally, we show how to account for the effect of wind speed on the estimates of the dispersal parameters. This serves as an example of how to strengthen the coupling in the modelling between the phenomenon observed in an experiment and the underlying process , something that should be striven for in the statistical modelling of dispersal. [source]

    Hierarchical modeling of genome-wide Short Tandem Repeat (STR) markers infers native American prehistory

    Cecil M. Lewis Jr.
    Abstract This study examines a genome-wide dataset of 678 Short Tandem Repeat loci characterized in 444 individuals representing 29 Native American populations as well as the Tundra Netsi and Yakut populations from Siberia. Using these data, the study tests four current hypotheses regarding the hierarchical distribution of neutral genetic variation in native South American populations: (1) the western region of South America harbors more variation than the eastern region of South America, (2) Central American and western South American populations cluster exclusively, (3) populations speaking the Chibchan-Paezan and Equatorial-Tucanoan language stock emerge as a group within an otherwise South American clade, (4) Chibchan-Paezan populations in Central America emerge together at the tips of the Chibchan-Paezan cluster. This study finds that hierarchical models with the best fit place Central American populations, and populations speaking the Chibchan-Paezan language stock, at a basal position or separated from the South American group, which is more consistent with a serial founder effect into South America than that previously described. Western (Andean) South America is found to harbor similar levels of variation as eastern (Equatorial-Tucanoan and Ge-Pano-Carib) South America, which is inconsistent with an initial west coast migration into South America. Moreover, in all relevant models, the estimates of genetic diversity within geographic regions suggest a major bottleneck or founder effect occurring within the North American subcontinent, before the peopling of Central and South America. Am J Phys Anthropol 2010. © 2009 Wiley-Liss, Inc. [source]

    Provider Utilization of High-Risk Donor Organs and Nucleic Acid Testing: Results of Two National Surveys

    L. M. Kucirka
    Fears of infectious transmission from CDC high-risk donors (HRDs) remain a significant disincentive, and the potential for human immunodeficiency virus/hepatitis C virus (HIV/HCV) nucleic acid testing (NAT) to allay these fears remains unstudied. We hypothesized that NAT, which narrows the window period between infection and detectability compared to the standard ELISA, might lead to increased provider willingness to use HRDs. Between January and April 2008, we performed two national surveys: one of current NAT practice among organ procurement organizations (OPOs); a second of HRD use among transplant surgeons. Surgeons who reported accepting 10% or more offers for a given HRD behavior and organ type were classified as ,high utilizers' of that subgroup. We built hierarchical models to examine associations between OPO NAT performance and provider utilization. Providers who ranked medical risks of HIV or HCV as important disincentives to HRD use had significantly lower odds of being high utilizers (HIV odds ratio 0.22, HCV odds ratio 0.41, p < 0.005). Furthermore, both HIV and HCV NAT performance were associated with significantly higher odds of being high utilizers (HIV odds ratio 1.58, HCV 2.69, p < 0.005). The demonstrated associations between OPO NAT performance and high provider utilization of HRDs should be considered in the ongoing debate about NAT in transplantation. [source]

    Bayesian nonparametric hierarchical modeling

    David B. Dunson
    Abstract In biomedical research, hierarchical models are very widely used to accommodate dependence in multivariate and longitudinal data and for borrowing of information across data from different sources. A primary concern in hierarchical modeling is sensitivity to parametric assumptions, such as linearity and normality of the random effects. Parametric assumptions on latent variable distributions can be challenging to check and are typically unwarranted, given available prior knowledge. This article reviews some recent developments in Bayesian nonparametric methods motivated by complex, multivariate and functional data collected in biomedical studies. The author provides a brief review of flexible parametric approaches relying on finite mixtures and latent class modeling. Dirichlet process mixture models are motivated by the need to generalize these approaches to avoid assuming a fixed finite number of classes. Focusing on an epidemiology application, the author illustrates the practical utility and potential of nonparametric Bayes methods. [source]

    Hierarchical and Joint Site-Edge Methods for Medicare Hospice Service Region Boundary Analysis

    BIOMETRICS, Issue 2 2010
    Haijun Ma
    Summary Hospice service offers a convenient and ethically preferable health-care option for terminally ill patients. However, this option is unavailable to patients in remote areas not served by any hospice system. In this article, we seek to determine the service areas of two particular cancer hospice systems in northeastern Minnesota based only on death counts abstracted from Medicare billing records. The problem is one of spatial boundary analysis, a field that appears statistically underdeveloped for irregular areal (lattice) data, even though most publicly available human health data are of this type. In this article, we suggest a variety of hierarchical models for areal boundary analysis that hierarchically or jointly parameterize,both,the areas and the edge segments. This leads to conceptually appealing solutions for our data that remain computationally feasible. While our approaches parallel similar developments in statistical image restoration using Markov random fields, important differences arise due to the irregular nature of our lattices, the sparseness and high variability of our data, the existence of important covariate information, and most importantly, our desire for full posterior inference on the boundary. Our results successfully delineate service areas for our two Minnesota hospice systems that sometimes conflict with the hospices' self-reported service areas. We also obtain boundaries for the spatial residuals from our fits, separating regions that differ for reasons yet unaccounted for by our model. [source]

    Comparison of Hierarchical Bayesian Models for Overdispersed Count Data using DIC and Bayes' Factors

    BIOMETRICS, Issue 3 2009
    Russell B. Millar
    Summary When replicate count data are overdispersed, it is common practice to incorporate this extra-Poisson variability by including latent parameters at the observation level. For example, the negative binomial and Poisson-lognormal (PLN) models are obtained by using gamma and lognormal latent parameters, respectively. Several recent publications have employed the deviance information criterion (DIC) to choose between these two models, with the deviance defined using the Poisson likelihood that is obtained from conditioning on these latent parameters. The results herein show that this use of DIC is inappropriate. Instead, DIC was seen to perform well if calculated using likelihood that was marginalized at the group level by integrating out the observation-level latent parameters. This group-level marginalization is explicit in the case of the negative binomial, but requires numerical integration for the PLN model. Similarly, DIC performed well to judge whether zero inflation was required when calculated using the group-marginalized form of the zero-inflated likelihood. In the context of comparing multilevel hierarchical models, the top-level DIC was obtained using likelihood that was further marginalized by additional integration over the group-level latent parameters, and the marginal densities of the models were calculated for the purpose of providing Bayes' factors. The computational viability and interpretability of these different measures is considered. [source]

    Hierarchical Spatial Modeling of Additive and Dominance Genetic Variance for Large Spatial Trial Datasets

    BIOMETRICS, Issue 2 2009
    Andrew O. Finley
    Summary This article expands upon recent interest in Bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets. Direct application of such models to large spatial datasets are, however, computationally infeasible because of cubic-order matrix algorithms involved in estimation. The situation is even worse in Markov chain Monte Carlo (MCMC) contexts where such computations are performed for several iterations. Here, we discuss approaches that help obviate these hurdles without sacrificing the richness in modeling. For genetic effects, we demonstrate how an initial spectral decomposition of the relationship matrices negate the expensive matrix inversions required in previously proposed MCMC methods. For spatial effects, we outline two approaches for circumventing the prohibitively expensive matrix decompositions: the first leverages analytical results from Ornstein,Uhlenbeck processes that yield computationally efficient tridiagonal structures, whereas the second derives a modified predictive process model from the original model by projecting its realizations to a lower-dimensional subspace, thereby reducing the computational burden. We illustrate the proposed methods using a synthetic dataset with additive, dominance, genetic effects and anisotropic spatial residuals, and a large dataset from a Scots pine (Pinus sylvestris L.) progeny study conducted in northern Sweden. Our approaches enable us to provide a comprehensive analysis of this large trial, which amply demonstrates that, in addition to violating basic assumptions of the linear model, ignoring spatial effects can result in downwardly biased measures of heritability. [source]

    When Should Epidemiologic Regressions Use Random Coefficients?

    BIOMETRICS, Issue 3 2000
    Sander Greenland
    Summary. Regression models with random coefficients arise naturally in both frequentist and Bayesian approaches to estimation problems. They are becoming widely available in standard computer packages under the headings of generalized linear mixed models, hierarchical models, and multilevel models. I here argue that such models offer a more scientifically defensible framework for epidemiologic analysis than the fixed-effects models now prevalent in epidemiology. The argument invokes an antiparsimony principle attributed to L. J. Savage, which is that models should be rich enough to reflect the complexity of the relations under study. It also invokes the countervailing principle that you cannot estimate anything if you try to estimate everything (often used to justify parsimony). Regression with random coefficients offers a rational compromise between these principles as well as an alternative to analyses based on standard variable-selection algorithms and their attendant distortion of uncertainty assessments. These points are illustrated with an analysis of data on diet, nutrition, and breast cancer. [source]