A Bayesian Approach to a Logistic Regression Model with Incomplete Information

Choi, Tae-Yong; Schervish, Mark J.; Schmitt, Ketra; Small, Mitchell J.

doi:10.1111/j.1541-0420.2007.00887.x

Cited by 10 publications

(4 citation statements)

References 3 publications

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“…Bayesian analysis of logistic model has received a lot of attention recently; see Johnson and Albert [34] and Congdon [35]. For example, Choi et al [36] discussed a Bayesian statistical inference about missing information on the basis of the logistic regression model. They also used Gibbs sampler to get the estimates and the posterior analysis of the posited model.…”

Section: Discussionmentioning

confidence: 99%

Bayesian Analysis for Dynamic Generalized Linear Latent Model with Application to Tree Survival Rate

Cheng

Ding

Xia

et al. 2014

Journal of Applied Mathematics

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Logistic regression model is the most popular regression technique, available for modeling categorical data especially for dichotomous variables. Classic logistic regression model is typically used to interpret relationship between response variables and explanatory variables. However, in real applications, most data sets are collected in follow-up, which leads to the temporal correlation among the data. In order to characterize the different variables correlations, a new method about the latent variables is introduced in this study. At the same time, the latent variables about AR (1) model are used to depict time dependence. In the framework of Bayesian analysis, parameters estimates and statistical inferences are carried out via Gibbs sampler with Metropolis-Hastings (MH) algorithm. Model comparison, based on the Bayes factor, and forecasting/smoothing of the survival rate of the tree are established. A simulation study is conducted to assess the performance of the proposed method and a pika data set is analyzed to illustrate the real application. Since Bayes factor approaches vary significantly, efficiency tests have been performed in order to decide which solution provides a better tool for the analysis of real relational data sets.

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Section: Discussionmentioning

confidence: 99%

Bayesian Analysis for Dynamic Generalized Linear Latent Model with Application to Tree Survival Rate

Cheng

Ding

Xia

et al. 2014

Journal of Applied Mathematics

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“…There is some controversy over the appropriate mechanistic model relating thyroid hypertrophy and hyperplasia to the effect of perchlorate, and analysis of these measurements will not be presented here. Some analyses of these additional measurements have been attempted by Choi et al (2004Choi et al ( , 2008.…”

Section: Springborn 90-day Studymentioning

confidence: 99%

Bayesian Hierarchical Analysis for Multiple Health Endpoints in a Toxicity Study

Choi¹,

Schervish

Schmitt³

et al. 2010

JABES

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Bayesian hierarchical models are built to fit multiple health endpoints from a doseresponse study of a chemical contaminant, perchlorate. Perchlorate exposure results in iodine uptake inhibition in the thyroid, with health effects manifested by changes in blood hormone concentrations and histopathological effects on the thyroid. We propose empirical models to fit blood hormone concentration and thyroid histopathology data for rats exposed to perchlorate in the 90-day study of Springborn Laboratories Inc. (1998), based upon a mechanistic model derived from the assumed toxicological relationships between dose and the various endpoints. All of the models are fit in a Bayesian framework, and predictions about each endpoint in response to dose are simulated based on the posterior predictive distribution. A hierarchical model tries to exploit possible similarities between different combinations of sex and exposure duration, and it allows us to produce more stable estimates of dose-response curves. We also illustrate how the Bayesian model specification allows us to address additional questions that arise after the analysis.

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“…The proposed method is motivated by the work done by Choi, Schervish, Schmitt, and Small (2008), who developed a Bayesian approach to a logistic regression model applied to partially aggregate data. The objective of the proposed method is to, simultaneously, predict the missing values of Y and to estimate the regression model parameters, β and σ 2 , based on only the partially aggregate data D P A .…”

Section: Introductionmentioning

confidence: 99%

A Bayesian Approach to Estimate a Linear Regression Model with Aggregate Data

Rawashdeh

Obeidat

2019

AJS

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The main purpose of this paper is to perform linear regression analysis on a continuous aggregate outcome from a Bayesian perspective using a Markov chain Monte Carlo algorithm (Gibbs sampling). In many situations, data are partially available due to privacy and confidentiality of the subjects in the sample. So, in this study, the vector of outcomes, Y, is realistically assumed to be missing and is partially available through summary statistics, sum(Y), aggregated over groups of subjects, while the covariate values, X, are availablefor all subjects in the sample. The results of the simulation study highlight both the efficiency of the regression parameter estimates and the predictive power of the proposed model compared with classicalmethods. The proposed approach is fully implemented in an example regarding systolic blood pressure for illustrative purposes.

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A Bayesian Approach to a Logistic Regression Model with Incomplete Information

Cited by 10 publications

References 3 publications

Bayesian Analysis for Dynamic Generalized Linear Latent Model with Application to Tree Survival Rate

Bayesian Analysis for Dynamic Generalized Linear Latent Model with Application to Tree Survival Rate

Bayesian Hierarchical Analysis for Multiple Health Endpoints in a Toxicity Study

A Bayesian Approach to Estimate a Linear Regression Model with Aggregate Data

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