Bootstrapping Robust Estimates for Clustered Data

Field, Chris; Pang, Zhen; Welsh, A. H.

doi:10.1198/jasa.2010.tm09541

Cited by 16 publications

(14 citation statements)

References 13 publications

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“…Field and Welsh and Field et al . also suggest three main approaches for bootstrapping LMMs including the random‐effects bootstrap, the modified bootstrap and the generalised cluster bootstrap. Sherman and le Cessie call the cases bootstrap the ‘all‐block’ bootstrap and advocate its use.…”

Section: Methodsmentioning

confidence: 99%

Constructing longitudinal disease progression curves using sparse, short‐term individual data with an application to Alzheimer's disease

Budgeon

Murray

Turlach

et al. 2017

Statistics in Medicine

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In epidemiology, cohort studies utilised to monitor and assess disease status and progression often result in short-term and sparse follow-up data. Thus, gaining an understanding of the full-term disease pathogenesis can be difficult, requiring shorter-term data from many individuals to be collated. We investigate and evaluate methods to construct and quantify the underlying long-term longitudinal trajectories for disease markers using short-term follow-up data, specifically applied to Alzheimer's disease. We generate individuals' follow-up data to investigate approaches to this problem adopting a four-step modelling approach that (i) determines individual slopes and anchor points for their short-term trajectory, (ii) fits polynomials to these slopes and anchor points, (iii) integrates the reciprocated polynomials and (iv) inverts the resulting curve providing an estimate of the underlying longitudinal trajectory. To alleviate the potential problem of roots of polynomials falling into the region over which we integrate, we propose the use of non-negative polynomials in Step 2. We demonstrate that our approach can construct underlying sigmoidal trajectories from individuals' sparse, short-term follow-up data. Furthermore, to determine an optimal methodology, we consider variations to our modelling approach including contrasting linear mixed effects regression to linear regression in Step 1 and investigating different orders of polynomials in Step 2. Cubic order polynomials provided more accurate results, and there were negligible differences between regression methodologies. We use bootstrap confidence intervals to quantify the variability in our estimates of the underlying longitudinal trajectory and apply these methods to data from the Alzheimer's Disease Neuroimaging Initiative to demonstrate their practical use. Copyright © 2017 John Wiley & Sons, Ltd.

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Section: Methodsmentioning

confidence: 99%

Constructing longitudinal disease progression curves using sparse, short‐term individual data with an application to Alzheimer's disease

Budgeon

Murray

Turlach

et al. 2017

Statistics in Medicine

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show abstract

“…On the other hand, our bootstrap is similar to that of Carpenter, Goldstein, and Rasbash () or Field et al (, ), who examined the so‐called random effects bootstrap in classical statistics. We go further by demonstrating the validity of the bootstrap for both the ML estimates of the mixed linear model (see theorem 2) and for a more general and complex parameter, which is the robust estimator of the small‐area mean or total.…”

Section: The Mse Bootstrap Estimatormentioning

confidence: 56%

“…The choice of the contaminations in , which converge to 0 at rate

\sqrt{k}

, is therefore made to achieve the same goal for the model parameters and obtain our asymptotic results. Our contamination scheme is more general than that of Field et al () and Sinha and Rao (), who only consider the case where

α_{i}^{*}

and

ε_{i j}^{*}

belong to a Gaussian distribution with mean 0. We consider the more general case of asymmetric contamination including the random intercept and the random slope as well as the contamination with a non‐Gaussian distribution.…”

Section: Introductionmentioning

confidence: 99%

Bootstrapping mean‐squared errors of robust small‐area estimators: Application to the method‐of‐payments surveys data

Jiongo

Nguimkeu

2019

Scandinavian J Statistics

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This paper proposes a new bootstrap procedure for mean‐squared errors of robust small‐area estimators. We formally prove the asymptotic validity of the proposed bootstrap method and examine its finite‐sample performance through Monte Carlo simulations. The results show that our procedure performs well and competes with existing ones. We also provide an application to the estimation of the total volume and value of cash, debit card, and credit card transactions in Canada as well as in its provinces and subgroups of households. In particular, we found that there is a significant average annual decline rate of 3.1% in the volume of cash transactions and that this decline is relatively higher among high‐income households living in heavily populated provinces. Our bootstrap estimator also provides indicators of quality useful in selecting the best small‐area predictor among several alternatives in practice.

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“…Davison & Hinkley (1997);McCullagh (2000); Field et al (2010). To make a concise rundown of the procedures in the LMM, we can mention that the REB requires that the random structure of the model be decomposed into independent sources of variation as in equation (6), whereas the TB reparametrizes the general LMM (7) as y = Xβ + Σ 1/2 δ where Σ = Z∆Z T + φI N and δ drawn from a multivariate standard normal distribution.…”

Section: Resampling-based Bootstrapsmentioning

confidence: 99%

“…A third bootstrap scheme for LMM relies on random weighting of the Estimating Equations such as the Generalized Cluster Bootstrap (GCB), see Field et al (2010); Pang & Welsh (2014); Ding & Welsh (2017). Inspired by this approach, we propose the Random Weighted Laplace Bootstrap (RWLB), a procedure that consists in inserting random weights at the level of the exponent of the Joint PDF of outcomes and random effects of equation (3), which translates into weighting contributions i of equation (2), as in:…”

Section: Random Weighted Laplace Bootstrapmentioning

confidence: 99%

Bootstrap estimation of uncertainty in prediction for generalized linear mixed models

Flores-Agreda

Cantoni

2019

Computational Statistics & Data Analysis

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In this article, we focus on the estimation of the Mean Squared Error for the Predictors (MSEP) of Random Effects (RE) in Generalized Linear Mixed Models (GLMM) by means of non-parametric bootstrap methods. In the frequentist paradigm, the MSEP is used as a measure of the uncertainty in prediction and has been shown to be affected by the estimation of the model parameters. In the particular case of linear mixed models (LMM), two solutions are provided to practitioners: on one hand, secondorder correct approximations which yield estimators of this quantity and, on the other hand, several Parametric Bootstrap algorithms. We propose a non-parametric bootstrap scheme, consisting of an adaptation of the Random Weighted Laplace Bootstrap (RWLB) that can be used in the entire class of GLMM. On a first stage, the RWLB is used to generate bootstrap replicates of the parameters while, on a second stage, simulation is used to generate bootstrap samples of standardized RE. We conduct a first simulation study in the framework of Gaussian LMM to contrast the quality of our approach with respect to: (i) analytical estimators of MSEP based on approximations, (ii) Conditional Variances obtained with a Bayesian representation and (iii) other bootstrap schemes, on the grounds of their relative bias, relative efficiency and the coverage ratios of resulting prediction intervals. A second simulation study serves the purpose to illustrate the use and benefits of our proposal against other feasible alternatives in a pure, Non-Gaussian, GLMM setting.

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Bootstrapping Robust Estimates for Clustered Data

Cited by 16 publications

References 13 publications

Constructing longitudinal disease progression curves using sparse, short‐term individual data with an application to Alzheimer's disease

Constructing longitudinal disease progression curves using sparse, short‐term individual data with an application to Alzheimer's disease

Bootstrapping mean‐squared errors of robust small‐area estimators: Application to the method‐of‐payments surveys data

Bootstrap estimation of uncertainty in prediction for generalized linear mixed models

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