731 research outputs found
Quantile regression for mixed models with an application to examine blood pressure trends in China
Cardiometabolic diseases have substantially increased in China in the past 20
years and blood pressure is a primary modifiable risk factor. Using data from
the China Health and Nutrition Survey, we examine blood pressure trends in
China from 1991 to 2009, with a concentration on age cohorts and urbanicity.
Very large values of blood pressure are of interest, so we model the
conditional quantile functions of systolic and diastolic blood pressure. This
allows the covariate effects in the middle of the distribution to vary from
those in the upper tail, the focal point of our analysis. We join the
distributions of systolic and diastolic blood pressure using a copula, which
permits the relationships between the covariates and the two responses to share
information and enables probabilistic statements about systolic and diastolic
blood pressure jointly. Our copula maintains the marginal distributions of the
group quantile effects while accounting for within-subject dependence, enabling
inference at the population and subject levels. Our population-level regression
effects change across quantile level, year and blood pressure type, providing a
rich environment for inference. To our knowledge, this is the first quantile
function model to explicitly model within-subject autocorrelation and is the
first quantile function approach that simultaneously models multivariate
conditional response. We find that the association between high blood pressure
and living in an urban area has evolved from positive to negative, with the
strongest changes occurring in the upper tail. The increase in urbanization
over the last twenty years coupled with the transition from the positive
association between urbanization and blood pressure in earlier years to a more
uniform association with urbanization suggests increasing blood pressure over
time throughout China, even in less urbanized areas. Our methods are available
in the R package BSquare.Comment: Published at http://dx.doi.org/10.1214/15-AOAS841 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Semiparametric Regression During 2003–2007
Semiparametric regression is a fusion between parametric regression and nonparametric regression and the title of a book that we published on the topic in early 2003. We review developments in the field during the five year period since the book was written. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application
Nonlinear quantile mixed models
In regression applications, the presence of nonlinearity and correlation
among observations offer computational challenges not only in traditional
settings such as least squares regression, but also (and especially) when the
objective function is non-smooth as in the case of quantile regression. In this
paper, we develop methods for the modeling and estimation of nonlinear
conditional quantile functions when data are clustered within two-level nested
designs. This work represents an extension of the linear quantile mixed models
of Geraci and Bottai (2014, Statistics and Computing). We develop a novel
algorithm which is a blend of a smoothing algorithm for quantile regression and
a second order Laplacian approximation for nonlinear mixed models. To assess
the proposed methods, we present a simulation study and two applications, one
in pharmacokinetics and one related to growth curve modeling in agriculture.Comment: 26 pages, 8 figures, 8 table
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Prior elicitation and variable selection for bayesian quantile regression
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Bayesian subset selection suffers from three important difficulties: assigning priors over model space, assigning priors to all components of the regression coefficients vector given a specific model and Bayesian computational efficiency (Chen et al., 1999). These difficulties become more challenging in Bayesian quantile regression framework when one is interested in assigning priors that depend on different quantile levels. The objective of Bayesian quantile regression (BQR), which is a newly proposed tool, is to deal with unknown parameters and model uncertainty in quantile regression (QR). However, Bayesian subset selection in quantile regression models is usually a difficult issue due to the computational challenges and nonavailability of conjugate prior distributions that are dependent on the quantile level. These challenges are rarely addressed via either penalised likelihood function or stochastic search variable selection (SSVS). These methods typically use symmetric prior distributions for regression coefficients, such as the Gaussian and Laplace, which may be suitable for median regression. However, an extreme quantile regression should have different regression coefficients from the median regression, and thus the priors for quantile regression coefficients should depend on quantiles. This thesis focuses on three challenges: assigning standard quantile dependent prior distributions for the regression coefficients, assigning suitable quantile dependent priors over model space and achieving computational efficiency. The first of these challenges is studied in Chapter 2 in which a quantile dependent prior elicitation scheme is developed. In particular, an extension of the Zellners prior which allows for a conditional conjugate prior and quantile dependent prior on Bayesian quantile regression is proposed. The prior is generalised in Chapter 3 by introducing a ridge parameter to address important challenges that may arise in some applications, such as multicollinearity and overfitting problems. The proposed prior is also used in Chapter 4 for subset selection of the fixed and random coefficients in a linear mixedeffects QR model. In Chapter 5 we specify normal-exponential prior distributions for the regression coefficients which can provide adaptive shrinkage and represent an alternative model to the Bayesian Lasso quantile regression model. For the second challenge, we assign a quantile dependent prior over model space in Chapter 2. The prior is based on the percentage bend correlation which depends on the quantile level. This prior is novel and is used in Bayesian regression for the first time. For the third challenge of computational efficiency, Gibbs samplers are derived and setup to facilitate the computation of the proposed methods. In addition to the three major aforementioned challenges this thesis also addresses other important issues such as the regularisation in quantile regression and selecting both random and fixed effects in mixed quantile regression models
Prior elicitation in Bayesian quantile regression for longitudinal data
© 2011 Alhamzawi R, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original auhor and source are credited.This article has been made available through the Brunel Open Access Publishing Fund.In this paper, we introduce Bayesian quantile regression for longitudinal data in terms of informative priors and Gibbs sampling. We develop methods for eliciting prior distribution to incorporate historical data gathered from similar previous studies. The methods can be used either with no prior data or with complete prior data. The advantage of the methods is that the prior distribution is changing automatically when we change the quantile. We propose Gibbs sampling methods which are computationally efficient and easy to implement. The methods are illustrated with both simulation and real data.This article is made available through the Brunel Open Access Publishing Fund
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