共查询到13条相似文献,搜索用时 0 毫秒
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Getachew A. Dagne 《Biometrical journal. Biometrische Zeitschrift》2004,46(6):653-663
This article presents two‐component hierarchical Bayesian models which incorporate both overdispersion and excess zeros. The components may be resultants of some intervention (treatment) that changes the rare event generating process. The models are also expanded to take into account any heterogeneity that may exist in the data. Details of the model fitting, checking and selecting alternative models from a Bayesian perspective are also presented. The proposed methods are applied to count data on the assessment of an efficacy of pesticides in controlling the reproduction of whitefly. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Comparison of Hierarchical Bayesian Models for Overdispersed Count Data using DIC and Bayes' Factors
Russell B. Millar 《Biometrics》2009,65(3):962-969
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. 相似文献
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Predictive fit for natural exponential families 总被引:1,自引:0,他引:1
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M. Tariqul Hasan Gary Sneddon Renjun Ma 《Biometrical journal. Biometrische Zeitschrift》2009,51(6):946-960
Analysis of longitudinal data with excessive zeros has gained increasing attention in recent years; however, current approaches to the analysis of longitudinal data with excessive zeros have primarily focused on balanced data. Dropouts are common in longitudinal studies; therefore, the analysis of the resulting unbalanced data is complicated by the missing mechanism. Our study is motivated by the analysis of longitudinal skin cancer count data presented by Greenberg, Baron, Stukel, Stevens, Mandel, Spencer, Elias, Lowe, Nierenberg, Bayrd, Vance, Freeman, Clendenning, Kwan, and the Skin Cancer Prevention Study Group[New England Journal of Medicine 323 , 789–795]. The data consist of a large number of zero responses (83% of the observations) as well as a substantial amount of dropout (about 52% of the observations). To account for both excessive zeros and dropout patterns, we propose a pattern‐mixture zero‐inflated model with compound Poisson random effects for the unbalanced longitudinal skin cancer data. We also incorporate an autoregressive of order 1 correlation structure in the model to capture longitudinal correlation of the count responses. A quasi‐likelihood approach has been developed in the estimation of our model. We illustrated the method with analysis of the longitudinal skin cancer data. 相似文献
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Josemar Rodrigues Luis A. Milan Jos G. Leite 《Biometrical journal. Biometrische Zeitschrift》2001,43(6):737-746
This paper is concerned with the estimation of the number of species in a population through a fully hierarchical Bayesian model using the Metropolis algorithm. The proposed Bayesian estimator is based on Poisson random variables with means that are distributed according to some prior distributions with unknown hyperparameters. An empirical Bayes approach is considered and compared with the fully Bayesian approach based on biological data. 相似文献
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Local Influence to Detect Influential Data Structures for Generalized Linear Mixed Models 总被引:1,自引:0,他引:1
This article discusses the generalization of the local influence measures for normally distributed responses to local influence measures for generalized linear models with random effects. For these models, it is shown that the subject-oriented influence measure is a special case of the proposed observation-oriented influence measure. A two-step diagnostic procedure is proposed. The first step is to search for influential subjects. A search for influential observations is proposed as the second step. An illustration of a two-treatment, multiple-period crossover trial demonstrates the practical importance of the detection of influential observations in addition to the detection of influential subjects. 相似文献
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For time series of count data, correlated measurements, clustering as well as excessive zeros occur simultaneously in biomedical applications. Ignoring such effects might contribute to misleading treatment outcomes. A generalized mixture Poisson geometric process (GMPGP) model and a zero‐altered mixture Poisson geometric process (ZMPGP) model are developed from the geometric process model, which was originally developed for modelling positive continuous data and was extended to handle count data. These models are motivated by evaluating the trend development of new tumour counts for bladder cancer patients as well as by identifying useful covariates which affect the count level. The models are implemented using Bayesian method with Markov chain Monte Carlo (MCMC) algorithms and are assessed using deviance information criterion (DIC). 相似文献
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Robert M. Dorazio 《Biometrics》2012,68(4):1303-1312
Summary Several models have been developed to predict the geographic distribution of a species by combining measurements of covariates of occurrence at locations where the species is known to be present with measurements of the same covariates at other locations where species occurrence status (presence or absence) is unknown. In the absence of species detection errors, spatial point‐process models and binary‐regression models for case‐augmented surveys provide consistent estimators of a species’ geographic distribution without prior knowledge of species prevalence. In addition, these regression models can be modified to produce estimators of species abundance that are asymptotically equivalent to those of the spatial point‐process models. However, if species presence locations are subject to detection errors, neither class of models provides a consistent estimator of covariate effects unless the covariates of species abundance are distinct and independently distributed from the covariates of species detection probability. These analytical results are illustrated using simulation studies of data sets that contain a wide range of presence‐only sample sizes. Analyses of presence‐only data of three avian species observed in a survey of landbirds in western Montana and northern Idaho are compared with site‐occupancy analyses of detections and nondetections of these species. 相似文献
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Navaratna WC Del Rio Vilas VJ Böhning D 《Biometrical journal. Biometrische Zeitschrift》2008,50(4):584-596
Estimation of population size with missing zero-class is an important problem that is encountered in epidemiological assessment studies. Fitting a Poisson model to the observed data by the method of maximum likelihood and estimation of the population size based on this fit is an approach that has been widely used for this purpose. In practice, however, the Poisson assumption is seldom satisfied. Zelterman (1988) has proposed a robust estimator for unclustered data that works well in a wide class of distributions applicable for count data. In the work presented here, we extend this estimator to clustered data. The estimator requires fitting a zero-truncated homogeneous Poisson model by maximum likelihood and thereby using a Horvitz-Thompson estimator of population size. This was found to work well, when the data follow the hypothesized homogeneous Poisson model. However, when the true distribution deviates from the hypothesized model, the population size was found to be underestimated. In the search of a more robust estimator, we focused on three models that use all clusters with exactly one case, those clusters with exactly two cases and those with exactly three cases to estimate the probability of the zero-class and thereby use data collected on all the clusters in the Horvitz-Thompson estimator of population size. Loss in efficiency associated with gain in robustness was examined based on a simulation study. As a trade-off between gain in robustness and loss in efficiency, the model that uses data collected on clusters with at most three cases to estimate the probability of the zero-class was found to be preferred in general. In applications, we recommend obtaining estimates from all three models and making a choice considering the estimates from the three models, robustness and the loss in efficiency. 相似文献
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D. A. Fordham B. W. Brook M. J. Caley C. J. A. Bradshaw C. Mellin 《Diversity & distributions》2013,19(10):1299-1312