Browse
Submit Data
Databases
API
Help

Dataset Information

20 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Catalytic prior distributions with application to generalized linear models.

ABSTRACT: A catalytic prior distribution is designed to stabilize a high-dimensional "working model" by shrinking it toward a "simplified model." The shrinkage is achieved by supplementing the observed data with a small amount of "synthetic data" generated from a predictive distribution under the simpler model. We apply this framework to generalized linear models, where we propose various strategies for the specification of a tuning parameter governing the degree of shrinkage and study resultant theoretical properties. In simulations, the resulting posterior estimation using such a catalytic prior outperforms maximum likelihood estimation from the working model and is generally comparable with or superior to existing competitive methods in terms of frequentist prediction accuracy of point estimation and coverage accuracy of interval estimation. The catalytic priors have simple interpretations and are easy to formulate.

SUBMITTER: Huang D

PROVIDER: S-EPMC7275732 | biostudies-literature | 2020 Jun

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Catalytic prior distributions with application to generalized linear models.

Huang Dongming D Stein Nathan N Rubin Donald B DB Kou S C SC

Proceedings of the National Academy of Sciences of the United States of America 20200515 22

A catalytic prior distribution is designed to stabilize a high-dimensional "working model" by shrinking it toward a "simplified model." The shrinkage is achieved by supplementing the observed data with a small amount of "synthetic data" generated from a predictive distribution under the simpler model. We apply this framework to generalized linear models, where we propose various strategies for the specification of a tuning parameter governing the degree of shrinkage and study resultant theoretic ...[more]

PMID: 32414914

Similar Datasets

Weight Smoothing for Generalized Linear Models Using a Laplace Prior.

Project description:When analyzing data sampled with unequal inclusion probabilities, correlations between the probability of selection and the sampled data can induce bias if the inclusion probabilities are ignored in the analysis. Weights equal to the inverse of the probability of inclusion are commonly used to correct possible bias. When weights are uncorrelated with the descriptive or model estimators of interest, highly disproportional sample designs resulting in large weights can introduce unnecessary variability, leading to an overall larger mean square error compared to unweighted methods. We describe an approach we term 'weight smoothing' that models the interactions between the weights and the estimators as random effects, reducing the root mean square error (RMSE) by shrinking interactions toward zero when such shrinkage is allowed by the data. This article adapts a flexible Laplace prior distribution for the hierarchical Bayesian model to gain a more robust bias-variance tradeoff than previous approaches using normal priors. Simulation and application suggest that under a linear model setting, weight-smoothing models with Laplace priors yield robust results when weighting is necessary, and provide considerable reduction in RMSE otherwise. In logistic regression models, estimates using weight-smoothing models with Laplace priors are robust, but with less gain in efficiency than in linear regression settings.

| S-EPMC5719898 | biostudies-literature

Variable Selection with Prior Information for Generalized Linear Models via the Prior LASSO Method.

Project description:LASSO is a popular statistical tool often used in conjunction with generalized linear models that can simultaneously select variables and estimate parameters. When there are many variables of interest, as in current biological and biomedical studies, the power of LASSO can be limited. Fortunately, so much biological and biomedical data have been collected and they may contain useful information about the importance of certain variables. This paper proposes an extension of LASSO, namely, prior LASSO (pLASSO), to incorporate that prior information into penalized generalized linear models. The goal is achieved by adding in the LASSO criterion function an additional measure of the discrepancy between the prior information and the model. For linear regression, the whole solution path of the pLASSO estimator can be found with a procedure similar to the Least Angle Regression (LARS). Asymptotic theories and simulation results show that pLASSO provides significant improvement over LASSO when the prior information is relatively accurate. When the prior information is less reliable, pLASSO shows great robustness to the misspecification. We illustrate the application of pLASSO using a real data set from a genome-wide association study.

| S-EPMC4874534 | biostudies-literature

Generalized Linear Mixed Models with Gaussian Mixture Random Effects: Inference and Application.

Project description:We propose a new class of generalized linear mixed models with Gaussian mixture random effects for clustered data. To overcome the weak identifiability issues, we fit the model using a penalized Expectation Maximization (EM) algorithm, and develop sequential locally restricted likelihood ratio tests to determine the number of components in the Gaussian mixture. Our work is motivated by an application to nationwide kidney transplant center evaluation in the United States, where the patient-level post-surgery outcomes are repeated measures of the care quality of the transplant centers. By taking into account patient-level risk factors and modeling the center effects by a finite Gaussian mixture model, the proposed model provides a convenient framework to study the heterogeneity among the transplant centers and controls the false discovery rate when screening for transplant centers with non-standard performance.

| S-EPMC7021245 | biostudies-literature

An Information Matrix Prior for Bayesian Analysis in Generalized Linear Models with High Dimensional Data.

Project description:An important challenge in analyzing high dimensional data in regression settings is that of facing a situation in which the number of covariates p in the model greatly exceeds the sample size n (sometimes termed the "p > n" problem). In this article, we develop a novel specification for a general class of prior distributions, called Information Matrix (IM) priors, for high-dimensional generalized linear models. The priors are first developed for settings in which p < n, and then extended to the p > n case by defining a ridge parameter in the prior construction, leading to the Information Matrix Ridge (IMR) prior. The IM and IMR priors are based on a broad generalization of Zellner's g-prior for Gaussian linear models. Various theoretical properties of the prior and implied posterior are derived including existence of the prior and posterior moment generating functions, tail behavior, as well as connections to Gaussian priors and Jeffreys' prior. Several simulation studies and an application to a nucleosomal positioning data set demonstrate its advantages over Gaussian, as well as g-priors, in high dimensional settings.

| S-EPMC2909687 | biostudies-literature

Iterative hard thresholding in genome-wide association studies: Generalized linear models, prior weights, and double sparsity.

Project description:Consecutive testing of single nucleotide polymorphisms (SNPs) is usually employed to identify genetic variants associated with complex traits. Ideally one should model all covariates in unison, but most existing analysis methods for genome-wide association studies (GWAS) perform only univariate regression. We extend and efficiently implement iterative hard thresholding (IHT) for multiple regression, treating all SNPs simultaneously. Our extensions accommodate generalized linear models, prior information on genetic variants, and grouping of variants. In our simulations, IHT recovers up to 30% more true predictors than SNP-by-SNP association testing and exhibits a 2-3 orders of magnitude decrease in false-positive rates compared with lasso regression. We also test IHT on the UK Biobank hypertension phenotypes and the Northern Finland Birth Cohort of 1966 cardiovascular phenotypes. We find that IHT scales to the large datasets of contemporary human genetics and recovers the plausible genetic variants identified by previous studies. Our real data analysis and simulation studies suggest that IHT can (i) recover highly correlated predictors, (ii) avoid over-fitting, (iii) deliver better true-positive and false-positive rates than either marginal testing or lasso regression, (iv) recover unbiased regression coefficients, (v) exploit prior information and group-sparsity, and (vi) be used with biobank-sized datasets. Although these advances are studied for genome-wide association studies inference, our extensions are pertinent to other regression problems with large numbers of predictors.

| S-EPMC7268817 | biostudies-literature

Miscellanea Dependent generalized functional linear models.

Project description:This paper considers testing for no effect of functional covariates on response variables in multivariate regression. We use generalized estimating equations to determine the underlying parameters and establish their joint asymptotic normality. This is then used to test the significance of the effect of predictors on the vector of response variables. Simulations demonstrate the importance of considering existing correlation structures in the data. To explore the effect of treating genetic data as a function, we perform a simulation study using gene sequencing data and find that the performance of our test is comparable to that of another popular method used in sequencing studies. We present simulations to explore the behaviour of our test under varying sample size, cluster size and dimension of the parameter to be estimated, and an application where we are able to confirm known associations between nicotine dependence and neuronal nicotinic acetylcholine receptor subunit genes.

| S-EPMC5771479 | biostudies-literature

LINEAR HYPOTHESIS TESTING FOR HIGH DIMENSIONAL GENERALIZED LINEAR MODELS.

Project description:This paper is concerned with testing linear hypotheses in high-dimensional generalized linear models. To deal with linear hypotheses, we first propose constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are ?2 distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow non-central ?2 distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to ? at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures.

| S-EPMC6750760 | biostudies-literature

Variable Selection in Generalized Functional Linear Models.

Project description:Modern research data, where a large number of functional predictors is collected on few subjects are becoming increasingly common. In this paper we propose a variable selection technique, when the predictors are functional and the response is scalar. Our approach is based on adopting a generalized functional linear model framework and using a penalized likelihood method that simultaneously controls the sparsity of the model and the smoothness of the corresponding coefficient functions by adequate penalization. The methodology is characterized by high predictive accuracy, and yields interpretable models, while retaining computational efficiency. The proposed method is investigated numerically in finite samples, and applied to a diffusion tensor imaging tractography data set and a chemometric data set.

| S-EPMC4131701 | biostudies-literature

Generalized linear models with unspecified reference distribution.

Project description:We propose a new class of semiparametric generalized linear models. As with existing models, these models are specified via a linear predictor and a link function for the mean of response Y as a function of predictors X. Here, however, the "baseline" distribution of Y at a given reference mean mu(0) is left unspecified and is estimated from the data. The response distribution when the mean differs from mu(0) is then generated via exponential tilting of the baseline distribution, yielding a response model that is a natural exponential family, with corresponding canonical link and variance functions. The resulting model has a level of flexibility similar to the popular proportional odds model. Maximum likelihood estimation is developed for response distributions with finite support, and the new model is studied and illustrated through simulations and example analyses from aging research.

| S-EPMC2733172 | biostudies-literature

Bayesian inference for generalized linear mixed models.

Project description:Generalized linear mixed models (GLMMs) continue to grow in popularity due to their ability to directly acknowledge multiple levels of dependency and model different data types. For small sample sizes especially, likelihood-based inference can be unreliable with variance components being particularly difficult to estimate. A Bayesian approach is appealing but has been hampered by the lack of a fast implementation, and the difficulty in specifying prior distributions with variance components again being particularly problematic. Here, we briefly review previous approaches to computation in Bayesian implementations of GLMMs and illustrate in detail, the use of integrated nested Laplace approximations in this context. We consider a number of examples, carefully specifying prior distributions on meaningful quantities in each case. The examples cover a wide range of data types including those requiring smoothing over time and a relatively complicated spline model for which we examine our prior specification in terms of the implied degrees of freedom. We conclude that Bayesian inference is now practically feasible for GLMMs and provides an attractive alternative to likelihood-based approaches such as penalized quasi-likelihood. As with likelihood-based approaches, great care is required in the analysis of clustered binary data since approximation strategies may be less accurate for such data.

| S-EPMC2883299 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data