Browse
Submit Data
Databases
API
Help

Dataset Information

25 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Robust model selection using the out-of-bag bootstrap in linear regression.

ABSTRACT: Outlying observations have a large influence on the linear model selection process. In this article, we present a novel approach to robust model selection in linear regression to accommodate the situations where outliers are present in the data. The model selection criterion is based on two components, the robust conditional expected prediction loss, and a robust goodness-of-fit with a penalty term. We estimate the conditional expected prediction loss by using the out-of-bag stratified bootstrap approach. In the presence of outliers, the stratified bootstrap ensures that we obtain bootstrap samples that are similar to the original sample data. Furthermore, to control the undue effect of outliers, we use the robust MM-estimator and a bounded loss function in the proposed criterion. Specifically, we observe that instead of minimizing the penalized loss function or the conditional expected prediction loss separately, it is better to minimize them simultaneously. The simulation and real-data based studies confirm the consistent and satisfactory behavior of our bootstrap model selection procedure in the presence of response outliers and covariate outliers.

SUBMITTER: Rabbi F

PROVIDER: S-EPMC9243146 | biostudies-literature |

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Similar Datasets

Fast Bootstrap Confidence Intervals for Continuous Threshold Linear Regression.

Project description:Continuous threshold regression is a common type of nonlinear regression that is attractive to many practitioners for its easy interpretability. More widespread adoption of thresh-old regression faces two challenges: (i) the computational complexity of fitting threshold regression models and (ii) obtaining correct coverage of confidence intervals under model misspecification. Both challenges result from the non-smooth and non-convex nature of the threshold regression model likelihood function. In this paper we first show that these two issues together make the ideal approach for making model-robust inference in continuous threshold linear regression an impractical one. The need for a faster way of fitting continuous threshold linear models motivated us to develop a fast grid search method. The new method, based on the simple yet powerful dynamic programming principle, improves the performance by several orders of magnitude.

| S-EPMC6713448 | biostudies-literature

A unifying framework for robust association testing, estimation, and genetic model selection using the generalized linear model.

Project description:The analysis of genome-wide genetic association studies generally starts with univariate statistical tests of each single-nucleotide polymorphism. The standard approach is the Cochran-Armitage trend test or its logistic regression equivalent although this approach can lose considerable power if the underlying genetic model is not additive. An alternative is the MAX test, which is robust against the three basic modes of inheritance. Here, the asymptotic distribution of the MAX test is derived using the generalized linear model together with the Delta method and multiple contrasts. The approach is applicable to binary, quantitative, and survival traits. It may be used for unrelated individuals, family-based studies, and matched pairs. The approach provides point and interval effect estimates and allows selecting the most plausible genetic model using the minimum P-value. R code is provided. A Monte-Carlo simulation study shows that the asymptotic MAX test framework meets type I error levels well, has good power, and good model selection properties for minor allele frequencies ≥0.3. Pearson's χ(2)-test is superior for lower minor allele frequencies with low frequencies for the rare homozygous genotype. In these cases, the model selection procedure should be used with caution. The use of the MAX test is illustrated by reanalyzing findings from seven genome-wide association studies including case-control, matched pairs, and quantitative trait data.

| S-EPMC3820468 | biostudies-literature

Bootstrap Enhanced Penalized Regression for Variable Selection with Neuroimaging Data.

Project description:Recent advances in fMRI research highlight the use of multivariate methods for examining whole-brain connectivity. Complementary data-driven methods are needed for determining the subset of predictors related to individual differences. Although commonly used for this purpose, ordinary least squares (OLS) regression may not be ideal due to multi-collinearity and over-fitting issues. Penalized regression is a promising and underutilized alternative to OLS regression. In this paper, we propose a nonparametric bootstrap quantile (QNT) approach for variable selection with neuroimaging data. We use real and simulated data, as well as annotated R code, to demonstrate the benefits of our proposed method. Our results illustrate the practical potential of our proposed bootstrap QNT approach. Our real data example demonstrates how our method can be used to relate individual differences in neural network connectivity with an externalizing personality measure. Also, our simulation results reveal that the QNT method is effective under a variety of data conditions. Penalized regression yields more stable estimates and sparser models than OLS regression in situations with large numbers of highly correlated neural predictors. Our results demonstrate that penalized regression is a promising method for examining associations between neural predictors and clinically relevant traits or behaviors. These findings have important implications for the growing field of functional connectivity research, where multivariate methods produce numerous, highly correlated brain networks.

| S-EPMC4964314 | biostudies-literature

Robust best linear estimation for regression analysis using surrogate and instrumental variables.

Project description:We investigate methods for regression analysis when covariates are measured with errors. In a subset of the whole cohort, a surrogate variable is available for the true unobserved exposure variable. The surrogate variable satisfies the classical measurement error model, but it may not have repeated measurements. In addition to the surrogate variables that are available among the subjects in the calibration sample, we assume that there is an instrumental variable (IV) that is available for all study subjects. An IV is correlated with the unobserved true exposure variable and hence can be useful in the estimation of the regression coefficients. We propose a robust best linear estimator that uses all the available data, which is the most efficient among a class of consistent estimators. The proposed estimator is shown to be consistent and asymptotically normal under very weak distributional assumptions. For Poisson or linear regression, the proposed estimator is consistent even if the measurement error from the surrogate or IV is heteroscedastic. Finite-sample performance of the proposed estimator is examined and compared with other estimators via intensive simulation studies. The proposed method and other methods are applied to a bladder cancer case-control study.

| S-EPMC3413079 | biostudies-literature

Bootstrap Aggregation for Model Selection in the Model-free Formalism.

Project description:The ability to make robust inferences about the dynamics of biological macromolecules using NMR spectroscopy depends heavily on the application of appropriate theoretical models for nuclear spin relaxation. Data analysis for NMR laboratory-frame relaxation experiments typically involves selecting one of several model-free spectral density functions using a bias-corrected fitness test. Here, advances in statistical model selection theory, termed bootstrap aggregation or bagging, are applied to 15N spin relaxation data, developing a multimodel inference solution to the model-free selection problem. The approach is illustrated using data sets recorded at four static magnetic fields for the bZip domain of the S. cerevisiae transcription factor GCN4.

| S-EPMC8372780 | biostudies-literature

Robust Moiety Model Selection Using Mass Spectrometry Measured Isotopologues.

Project description:Stable isotope resolved metabolomics (SIRM) experiments use stable isotope tracers to provide superior metabolomics datasets for metabolic flux analysis and metabolic modeling. Since assumptions of model correctness can seriously compromise interpretation of metabolic flux results, we have developed a metabolic modeling software package specifically designed for moiety model comparison and selection based on the metabolomics data provided. Here, we tested the effectiveness of model selection with two time-series mass spectrometry (MS) isotopologue datasets for uridine diphosphate N-acetyl-d-glucosamine (UDP-GlcNAc) generated from different platforms utilizing direct infusion nanoelectrospray and liquid chromatography. Analysis results demonstrate the robustness of our model selection methods by the successful selection of the optimal model from over 40 models provided. Moreover, the effects of specific optimization methods, degree of optimization, selection criteria, and specific objective functions on model selection are illustrated. Overall, these results indicate that over-optimization can lead to model selection failure, but combining multiple datasets can help control this overfitting effect. The implication is that SIRM datasets in public repositories of reasonable quality can be combined with newly acquired datasets to improve model selection. Furthermore, curation efforts of public metabolomics repositories to maintain high data quality could have a huge impact on future metabolic modeling efforts.

| S-EPMC7143054 | biostudies-literature

FLCRM: Functional linear cox regression model.

Project description:We consider a functional linear Cox regression model for characterizing the association between time-to-event data and a set of functional and scalar predictors. The functional linear Cox regression model incorporates a functional principal component analysis for modeling the functional predictors and a high-dimensional Cox regression model to characterize the joint effects of both functional and scalar predictors on the time-to-event data. We develop an algorithm to calculate the maximum approximate partial likelihood estimates of unknown finite and infinite dimensional parameters. We also systematically investigate the rate of convergence of the maximum approximate partial likelihood estimates and a score test statistic for testing the nullity of the slope function associated with the functional predictors. We demonstrate our estimation and testing procedures by using simulations and the analysis of the Alzheimer's Disease Neuroimaging Initiative (ADNI) data. Our real data analyses show that high-dimensional hippocampus surface data may be an important marker for predicting time to conversion to Alzheimer's disease. Data used in the preparation of this article were obtained from the ADNI database (adni.loni.usc.edu).

| S-EPMC5832538 | biostudies-literature

Bootstrap-adjusted quasi-likelihood information criteria for mixed model selection.

Project description:We propose two model selection criteria relying on the bootstrap approach, denoted by QAICb1 and QAICb2, in the framework of linear mixed models. Similar to the justification of Akaike Information Criterion (AIC), the proposed QAICb1 and QAICb2 are proved as asymptotically unbiased estimators of the Kullback-Leibler discrepancy between a candidate model and the true model. However, they are defined on the quasi-likelihood function instead of the likelihood and are proven to be asymptotically equivalent. The proposed selection criteria are constructed by the quasi-likelihood of a candidate model and a bias estimation term in which the bootstrap method is adopted to improve the estimation for the bias caused by using the candidate model to estimate the true model. The simulations across a variety of mixed model settings are conducted to demonstrate that the proposed selection criteria outperform some other existing model selection criteria in selecting the true model. Generalized estimating equations (GEE) are utilized to calculate QAICb1 and QAICb2 in the simulations. The effectiveness of the proposed selection criteria is also demonstrated in an application of Parkinson's Progression Markers Initiative (PPMI) data.

| S-EPMC10896141 | biostudies-literature

Empirical Likelihood for Censored Linear Regression and Variable Selection.

Project description:The linear regression model for right censored data, also known as the accelerated failure time model using the logarithm of survival time as the response variable, is a useful alternative to the Cox proportional hazards model. Empirical likelihood as a nonparametric approach has been demonstrated to have many desirable merits thanks to its robustness against model misspecification. However, the linear regression model with right censored data cannot directly benefit from the empirical likelihood for inferences mainly due to dependent elements in estimating equations of the conventional approach. In this paper, we propose an empirical likelihood approach with a new estimating equation for linear regression with right censored data. A nested coordinate algorithm with majorization is used for solving the optimization problems with nondifferentiable objective function. We show that the Wilks theorem holds for the new empirical likelihood. We also consider the variable selection problem with empirical likelihood when the number of predictors can be large. Since the new estimating equation is nondifferentiable, a quadratic approximation is applied to study the asymptotic properties of penalized empirical likelihood. We prove the oracle properties and evaluate the properties with simulated data. We apply our method to a SEER small intestine cancer dataset.

| S-EPMC6516784 | biostudies-literature

SPReM: Sparse Projection Regression Model For High-dimensional Linear Regression.

Project description:The aim of this paper is to develop a sparse projection regression modeling (SPReM) framework to perform multivariate regression modeling with a large number of responses and a multivariate covariate of interest. We propose two novel heritability ratios to simultaneously perform dimension reduction, response selection, estimation, and testing, while explicitly accounting for correlations among multivariate responses. Our SPReM is devised to specifically address the low statistical power issue of many standard statistical approaches, such as the Hotelling's T2 test statistic or a mass univariate analysis, for high-dimensional data. We formulate the estimation problem of SPREM as a novel sparse unit rank projection (SURP) problem and propose a fast optimization algorithm for SURP. Furthermore, we extend SURP to the sparse multi-rank projection (SMURP) by adopting a sequential SURP approximation. Theoretically, we have systematically investigated the convergence properties of SURP and the convergence rate of SURP estimates. Our simulation results and real data analysis have shown that SPReM out-performs other state-of-the-art methods.

| S-EPMC4627720 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

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