Approximate uniform shrinkage prior for a multivariate generalized linear mixed model

Chen, Hsiang-Chun; Wehrly, Thomas E.

doi:10.1016/j.jmva.2015.12.004

Cited by 5 publications

(5 citation statements)

References 22 publications

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“…Further research could study, for example, what the impact is of the other hyperparameter of the Wishart prior (i.e., the degrees of freedom) on the (co)variance estimates. Also, other adaptations of the Wishart prior, such as the uniform shrinkage prior (Chen & Wehrly, 2016; Natarajan & Kass, 2000), could be investigated. To that extent, researchers might also look into the impact of improper priors on the estimates of the variance components (Schuurman et al, 2016).…”

Section: Discussionmentioning

confidence: 99%

The Social Relations Model for Count Data

et al. 2019

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Abstract. The social relations model (SRM) is typically used to identify sources of variance in interpersonal dispositions in families. Traditionally, it uses dyadic measurements that are obtained from a round-robin design, where each family member rates each other family member. Those dyadic measurements are mostly considered to be continuous, but we, however, will discuss how the SRM can be adapted to count dyadic measurements. Such SRM for count data can be formulated in the SEM-framework by viewing it as a confirmatory factor analysis (CFA), but it can also be defined in the multilevel framework. These two frameworks result in equivalent models of which the parameters can be estimated using maximum likelihood estimation or a Bayesian approach. We perform a simulation study to compare the performance of those two estimators. As an illustration, we consider intergenerational co-activity data from a block design and contrast family dynamics between non-divorced families and stepfamilies.

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Section: Discussionmentioning

confidence: 99%

The Social Relations Model for Count Data

et al. 2019

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“…In this section, the application of our proposed semiparametric Bayesian approach is illustrated by the analysis of longitudinal semicontinuous data from the OAI, which was discussed in Section 2 . The OAI longitudinal data were analyzed by various approaches, such as Chen and Wehrly [ 25 , 26 ]. However, these authors only considered the observed data by reducing 4796 patients to 1499 patients and assumed the log transformation of the WOMAC score plus 1 to approximate the normal distribution.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Women are more vulnerable to greater intensity than men. Chen and Wehrly [ 25 , 26 ] assumed a linear age effect on the WOMAC score parametrically, but an insignificant effect on the WOMAC score are presented in their studies. It appears from Figure 4 that the Bayesian estimates of nonparametric function

based on the P-spline method has a significant nonlinear trend.…”

Section: Numerical Examplesmentioning

confidence: 99%

Bayesian Analysis of Tweedie Compound Poisson Partial Linear Mixed Models with Nonignorable Missing Response and Covariates

Duan

Zhang

2023

Entropy

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Under the Bayesian framework, this study proposes a Tweedie compound Poisson partial linear mixed model on the basis of Bayesian P-spline approximation to nonparametric function for longitudinal semicontinuous data in the presence of nonignorable missing covariates and responses. The logistic regression model is simultaneously used to specify the missing response and covariate mechanisms. A hybrid algorithm combining the Gibbs sampler and the Metropolis–Hastings algorithm is employed to produce the joint Bayesian estimates of unknown parameters and random effects as well as nonparametric function. Several simulation studies and a real example relating to the osteoarthritis initiative data are presented to illustrate the proposed methodologies.

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“…A review and comparison of shrinkage methods for VS are detailed in [ 27 ]. High-dimensional statistical modelling with Bayesian shrinkage prior method has been extended in several arenas such as longitudinal binary data with informative missingness [ 28 ], and for joint modelling of clustered mixed outcomes with uniform shrinkage prior [ 29 ]. The second piece of our proposed approach focuses on a convenient data augmentation representation of the logistic regression likelihood.…”

Section: Introductionmentioning

confidence: 99%

Applications of Bayesian shrinkage prior models in clinical research with categorical responses

Bhattacharyya

Pal

Mitra

et al. 2022

BMC Med Res Methodol

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Background Prediction and classification algorithms are commonly used in clinical research for identifying patients susceptible to clinical conditions such as diabetes, colon cancer, and Alzheimer’s disease. Developing accurate prediction and classification methods benefits personalized medicine. Building an excellent predictive model involves selecting the features that are most significantly associated with the outcome. These features can include several biological and demographic characteristics, such as genomic biomarkers and health history. Such variable selection becomes challenging when the number of potential predictors is large. Bayesian shrinkage models have emerged as popular and flexible methods of variable selection in regression settings. This work discusses variable selection with three shrinkage priors and illustrates its application to clinical data such as Pima Indians Diabetes, Colon cancer, ADNI, and OASIS Alzheimer’s real-world data. Methods A unified Bayesian hierarchical framework that implements and compares shrinkage priors in binary and multinomial logistic regression models is presented. The key feature is the representation of the likelihood by a Polya-Gamma data augmentation, which admits a natural integration with a family of shrinkage priors, specifically focusing on Horseshoe, Dirichlet Laplace, and Double Pareto priors. Extensive simulation studies are conducted to assess the performances under different data dimensions and parameter settings. Measures of accuracy, AUC, brier score, L1 error, cross-entropy, and ROC surface plots are used as evaluation criteria comparing the priors with frequentist methods as Lasso, Elastic-Net, and Ridge regression. Results All three priors can be used for robust prediction on significant metrics, irrespective of their categorical response model choices. Simulation studies could achieve the mean prediction accuracy of 91.6% (95% CI: 88.5, 94.7) and 76.5% (95% CI: 69.3, 83.8) for logistic regression and multinomial logistic models, respectively. The model can identify significant variables for disease risk prediction and is computationally efficient. Conclusions The models are robust enough to conduct both variable selection and prediction because of their high shrinkage properties and applicability to a broad range of classification problems.

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Approximate uniform shrinkage prior for a multivariate generalized linear mixed model

Cited by 5 publications

References 22 publications

The Social Relations Model for Count Data

The Social Relations Model for Count Data

Bayesian Analysis of Tweedie Compound Poisson Partial Linear Mixed Models with Nonignorable Missing Response and Covariates

Applications of Bayesian shrinkage prior models in clinical research with categorical responses

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