Demographic and Health Surveys collect child survival times that are clustered at the family and community levels. It is assumed that each cluster has a specific, unobservable, random frailty that induces an associati...
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Demographic and Health Surveys collect child survival times that are clustered at the family and community levels. It is assumed that each cluster has a specific, unobservable, random frailty that induces an association in the survival times within the cluster. The Cox proportional hazards model, with family and community random frailties acting multiplicatively on the hazard rate, is presented. The estimation of the fixed effect and the association parameters of the modified model is then examined using the Gibbs sampler and the expectation-maximization (em) algorithm. The methods are compared using child survival data collected in the 1992 Demographic and Health Survey of Malawi. The two methods lead to very similar estimates of fixed effect parameters. However, the estimates of random effect variances from the em algorithm are smaller than those of the Gibbs sampler. Both estimation methods reveal considerable family variation in the survival of children, and very little variability over the communities.
The accelerated failure time (AFT) model is an important alternative to the Cox proportional hazards model (PHM) in survival analysis. For multivariate failure time data we propose to use frailties to explicitly accou...
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The accelerated failure time (AFT) model is an important alternative to the Cox proportional hazards model (PHM) in survival analysis. For multivariate failure time data we propose to use frailties to explicitly account for possible correlations (and heterogeneity) among failure times. An em-like algorithm analogous to that in the frailty model for the Cox model is adapted. Through simulation it is shown that its performance compares favorably with that of the marginal independence approach. For illustration we reanalyze a real data set.
This study develops Bayesian methods for estimating the parameters of a stochastic switching regression model. Markov Chain Monte Carlo methods, data augmentation, and Gibbs sampling are used to facilitate estimation ...
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This study develops Bayesian methods for estimating the parameters of a stochastic switching regression model. Markov Chain Monte Carlo methods, data augmentation, and Gibbs sampling are used to facilitate estimation of the posterior means. The main feature of these methods is that the posterior means are estimated by the ergodic averages of samples drawn from conditional distributions, which are relatively simple in form and more feasible to sample from than the complex joint posterior distribution. A simulation study is conducted comparing model estimates obtained using data augmentation, Gibbs sampling, and the maximum likelihood em algorithm and determining the effects of the accuracy of and bias of the researcher's prior distributions on the parameter estimates.
Problems associated with missing covariate data are well known but often ignored. We present a method for estimating the parameters in the Cox proportional hazards model when the missing data are missing at random (MA...
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Problems associated with missing covariate data are well known but often ignored. We present a method for estimating the parameters in the Cox proportional hazards model when the missing data are missing at random (MAR) and censoring is noninformative. Due to the computational burden of this method, we introduce an approximation that allows us to use a weighted expectation-maximization (em) algorithm to estimate the parameters more easily. When the missing covariates are continuous rather than categorical, we implement a Monte Carlo version of the Ehl algorithm along with the Gibbs sampler to obtain parameter estimates. We also give the asymptotic distribution of these estimates. The primary advantage of this method over complete case analysis is that it produces more efficient parameter estimates and corrects for bias in the MAR setting. To motivate the methodology, we present an analysis of a phase III melanoma clinical trial conducted by the Eastern Cooperative Oncology Group.
We propose a method for estimating parameters in the generalised linear mixed model with nonignorable missing response data and with nonmonotone patterns of missing data in the response variable. We develop a Monte Ca...
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We propose a method for estimating parameters in the generalised linear mixed model with nonignorable missing response data and with nonmonotone patterns of missing data in the response variable. We develop a Monte Carlo em algorithm for estimating the parameters in the model via the Gibbs sampler. For the normal random effects model, we derive a novel analytical form for the E- and M-steps, which is facilitated by integrating out the random effects. This form leads to a computationally feasible and extremely efficient Monte Carlo em algorithm for computing maximum likelihood estimates and standard errors. In addition, we propose a very general joint multinomial model for the missing data indicators, which can be specified via a sequence of one-dimensional conditional distributions. This multinomial model allows for an arbitrary correlation structure between the missing data indicators, and has the potential of reducing the number of nuisance parameters. Real datasets from the International Breast Cancer Study Group and an environmental study involving dyspnoea in cotton workers are presented to illustrate the proposed methods.
An application of a latent class vector model to preference data is presented. Analysing hedonic ratings, this technique realises simultaneously the clustering of consumers in homogeneous classes on the basis of their...
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An application of a latent class vector model to preference data is presented. Analysing hedonic ratings, this technique realises simultaneously the clustering of consumers in homogeneous classes on the basis of their preferences and the joint representation of products and classes using a vector model. A probabilistic assumption allows performance of significance tests on the number of clusters and provides a useful tool for interpreting results of preference tests. (C) 2001 Elsevier Science Ltd. All rights reserved.
This work presents an application of the em-algorithm to two problems of estimation and testing in a multivariate normal distribution with missing data. The assumptions are that the observations are multivariate norma...
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This work presents an application of the em-algorithm to two problems of estimation and testing in a multivariate normal distribution with missing data. The assumptions are that the observations are multivariate normally distributed and that the missing values are missing at random. The two models are tested applying the log-likelihood ratio test;for deriving the maximum likelihood estimates and evaluating the corresponding log-likelihood functions the em algorithm is used. The problem of different and non-monotone patterns of missing data is solved introducing suitable transformations and partitions of the data matrix. The algorithm is proposed for general constraints on the mean vector;the topic of exchangeability of random vectors is also presented.
We consider a generalized linear model with canonical link when some of the covariates are subject to measurement error. In this article we propose a likelihood based method of adjusting the estimate of the regression...
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The paper proposes a hidden semi-Markov model for breakpoint rainfall data that consist of both the times at which rain-rate changes and the steady rates between such changes. The model builds on and extends the semin...
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The Probabilistic Multiple Hypothesis Tracker (PMHT) has previously been augmented and modified to deal with target maneuver. Unfortunately, although the resulting procedure tracks maneuvering targets reasonably well,...
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ISBN:
(纸本)0819441872
The Probabilistic Multiple Hypothesis Tracker (PMHT) has previously been augmented and modified to deal with target maneuver. Unfortunately, although the resulting procedure tracks maneuvering targets reasonably well, estimation of the maneuver process (i.e. the hidden Markov Model (HMM)) is not particularly reactive. In this paper, the PMHT is further investigated and several PMHT variants for maneuvering targets are discussed. These include: the ideas from Logothetis et al. and from Pulford and La Scala;the incorporation of the Interacting Multiple Mode (IMM) formalism to the PMHT;the extension of the "turbo" PMHT. We finally compare these em-based tracking schemes and provide the simulation results on the second benchmark problem from Blair et al.
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