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22
Not Asked Or Not Answered: Multiple Imputation for Multiple Surveys
 Journal of the American Statistical Association
, 1998
"... We present a method of analyzing a series of independent crosssectional surveys in which some questions are not answered in some surveys and some respondents do not answer some of the questions posed. The method is also applicable to a single survey in which different questions are asked, or differ ..."
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Cited by 45 (10 self)
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We present a method of analyzing a series of independent crosssectional surveys in which some questions are not answered in some surveys and some respondents do not answer some of the questions posed. The method is also applicable to a single survey in which different questions are asked, or different sampling methods used, in different strata or clusters. Our method involves multiplyimputing the missing items and questions by adding to existing methods of imputation designed for single surveys a hierarchical regression model that allows covariates at the individual and survey levels. Information from survey weights is exploited by including in the analysis the variables on which the weights were based, and then reweighting individual responses (observed and imputed) to estimate population quantities. We also develop diagnostics for checking the fit of the imputation model based on comparing imputed to nonimputed data. We illustrate with the example that motivated this project  a ...
Hidden Markov models for longitudinal comparisons
 Journal of the American Statistical Association
, 2005
"... Medical researchers interested in temporal, multivariate measurements of complex diseases have recently begun developing health state models which divide the space of patient characteristics into medically distinct clusters. The current state of the art in health services research uses kmeans clust ..."
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Cited by 8 (1 self)
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Medical researchers interested in temporal, multivariate measurements of complex diseases have recently begun developing health state models which divide the space of patient characteristics into medically distinct clusters. The current state of the art in health services research uses kmeans clustering to form the health states and a first order Markov chain to describe transitions between the states. This fitting procedure ignores information from temporally adjacent observations and prevents uncertainty from parameter estimation and cluster assignments from being incorporated into the analysis. A natural way to address these issues is to combine clustering and longitudinal analyses using a hidden Markov model. We fit hidden Markov models to longitudinal data using Bayesian methods which account for all the uncertainty in the parameters, conditional only on the underlying correctness of the model. Potential lack of time homogeneity in the Markov chain is accounted for by embedding transition probabilities into a hierarchical model that provides Bayesian shrinkage across time. We illustrate this approach by developing a hidden Markov health state model for comparing the effectiveness of clozapine and haloperidol, two antipsychotic medications for schizophrenia. We find that clozapine outperforms haloperidol and identify the types of patients where clozapine’s advantage is greatest and weakest. Finally, we discuss the advantages and disadvantages of hidden Markov models in comparison with the current methodology. Key Words: inhomogeneous hidden Markov model, Markov chain Monte Carlo, health state model, kmeans clustering, hierarchical model
On Monte Carlo methods for Bayesian multivariate regression models with heavytailed errors
 Journal of Multivariate Analysis
"... We consider Bayesian analysis of data from multivariate linear regression models whose errors have a distribution that is a scale mixture of normals. Such models are used to analyze data on financial returns, which are notoriously heavytailed. Let pi denote the intractable posterior density that re ..."
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Cited by 7 (3 self)
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We consider Bayesian analysis of data from multivariate linear regression models whose errors have a distribution that is a scale mixture of normals. Such models are used to analyze data on financial returns, which are notoriously heavytailed. Let pi denote the intractable posterior density that results when this regression model is combined with the standard noninformative prior on the unknown regression coefficients and scale matrix of the errors. Roughly speaking, the posterior is proper if and only if n ≥ d + k, where n is the sample size, d is the dimension of the response, and k is number of covariates. We provide a method of making exact draws from pi in the special case where n = d + k, and we study Markov chain Monte Carlo (MCMC) algorithms that can be used to explore pi when n> d+ k. In particular, we show how the Haar PXDA technology studied in Hobert and Marchev (2008) can be used to improve upon Liu’s (1996) data augmentation (DA) algorithm. Indeed, the new algorithm that we introduce is theoretically superior to the DA algorithm, yet equivalent to DA in terms of computational complexity. Moreover, we analyze the convergence rates of these MCMC algorithms in the important special case where the regression errors have a Student’s t distribution. We prove that, under conditions on n, d, k, and the degrees of freedom of the t distribution, both algorithms converge at a geometric rate. These convergence rate results are important from a practical standpoint because geometric ergodicity guarantees the existence of central limit theorems which are essential for the calculation of valid asymptotic standard errors for MCMC based estimates.
Modeling Customer Survey Data
"... In customer value analysis (CVA), a company conducts sample surveys of its customers and of its competitors’ customers to determine the relative performance of the company on many attributes ranging from product quality and technology to pricing and sales support. The data discussed in this paper ar ..."
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Cited by 5 (4 self)
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In customer value analysis (CVA), a company conducts sample surveys of its customers and of its competitors’ customers to determine the relative performance of the company on many attributes ranging from product quality and technology to pricing and sales support. The data discussed in this paper are from a quarterly survey run at Lucent Technologies. We have built a Bayesian model for the data that is partly hierarchical and has a time series component. By “model” we mean the full specification of information that allows the computation of posterior distributions of the data — sharp specifications such as independent errors with normal distributions and diffuse specifications such as probability distributions on parameters arising from sharp specifications. The model includes the following: (1) survey respondent effects are modeled by random location and scale effects, a tdistribution for the location and a Weibull distribution for the scale; (2) company effects for each attribute through time are modeled by integrated sumdifference processes; (3) error effects are modeled by a normal distribution whose variance depends on the attribute; in the model, the errors
Conjugate Analysis of Multivariate Normal Data with Incomplete Observations
"... In this article we discuss families of prior distributions that are conjugate to the multivariate normal likelihood when some of the observations are incomplete. We present a general class of priors, modifying a proposal of Kadane and Trader, to allow incorporation of information about unidentified ..."
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In this article we discuss families of prior distributions that are conjugate to the multivariate normal likelihood when some of the observations are incomplete. We present a general class of priors, modifying a proposal of Kadane and Trader, to allow incorporation of information about unidentified parameters in the covariance matrix within a conjugate setting. We analyze the important special case of monotone patterns of missing data, providing an explicit recursive form for the posterior distribution resulting from a conjugate prior distribution. We derive the relationship between the prior and posterior hyperparameters in the Kadane and Trader formulation and the hyperparameters in the recursive factorization of the posterior distribution. We develop algorithms for sampling from the posterior distribution, that take advantage of the conjugate structure. In particular, the monotone case results can be exploited to handle the general case as well, thus providing ways of sampling from ...
An Example of Algorithm Mining: Covariance Adjustment to Accelerate EM and Gibbs
 Development of Modern Statistics and Related Topics
, 2003
"... ..."
Statistical Modelling XXXX; XX(X): 1–23 © XXXX SAGE Publications 10.1177/1471082X14535527
"... Regression with compositional response having unobserved components or below detection limit values ..."
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Regression with compositional response having unobserved components or below detection limit values
Regression
"... with compositional response having unobserved components or below detection limit values ..."
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with compositional response having unobserved components or below detection limit values
bync/2.0/uk/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited. 1 Original Paper Bayesian Robust Analysis for Genetic Architecture of Quantita tive Traits
"... Motivation: In most QTL mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may affect the accuracy of QTL detection and lead to detection of spurious QTLs. To improve the robustness of QTL mapping methods, we replaced the normal distribution for r ..."
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Motivation: In most QTL mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may affect the accuracy of QTL detection and lead to detection of spurious QTLs. To improve the robustness of QTL mapping methods, we replaced the normal distribution for residuals in multiple interacting QTL models with the normal/independent distributions that are a class of symmetric and longtailed distributions and are able to accommodate residual outliers. Subsequently, we developed a Bayesian robust analysis strategy for dissecting genetic architecture of quantitative traits and for mapping genomewide interacting QTLs in line crosses. Results: Through computer simulations, we showed that our strategy had a similar power for QTL detection compared to traditional methods assuming normaldistributed traits, but had a substantially increased power for nonnormal phenotypes. When this strategy was applied to a group of traits associated with physicalchemical characteristics and quality in rice, more main and epistatic QTLs were detected than traditional Bayesian model analyses under the normal assumption. 1
DOI 10.1007/s1044000892128 Estimation Methods for the Multivariate t Distribution
"... Abstract The known estimation and simulation methods for multivariate t distributions are reviewed. A review of selected applications is also provided. We believe that this review will serve as an important reference and encourage further research activities in the area. ..."
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Abstract The known estimation and simulation methods for multivariate t distributions are reviewed. A review of selected applications is also provided. We believe that this review will serve as an important reference and encourage further research activities in the area.