Bayesian inference for additive mixed quantile regression models

Yu, Yue; Rue, Håvard

doi:10.1016/j.csda.2010.05.006

Cited by 98 publications

(83 citation statements)

References 29 publications

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“…A fully Bayesian method for nonparametric quantile regression might achieve similar results with greater computational efficiency than the algorithm of Section 4.3. After completing this paper we became aware of a non-spline-based approach of this type, due to Yue and Rue (2011), that uses integrated nested Laplace approximations with Gaussian Markov random field priors. Yue and Rue (2011) note that their method encounters some difficulties with ex-…”

Section: Simulation Studymentioning

confidence: 99%

Smoothness Selection for Penalized Quantile Regression Splines

Reiss

Huang²

2012

The International Journal of Biostatistics

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Modern data-rich analyses may call for fitting a large number of nonparametric quantile regressions. For example, growth charts may be constructed for each of a collection of variables, to identify those for which individuals with a disorder tend to fall in the tails of their agespecific distribution; such variables might serve as developmental biomarkers. When such a large set of analyses are carried out by penalized spline smoothing, reliable automatic selection of the smoothing parameter is particularly important. We show that two popular methods for smoothness selection may tend to overfit when estimating extreme quantiles as a smooth function of a predictor such as age; and that improved results can be obtained by multifold cross-validation or by a novel likelihood approach. A simulation study, and an application to a functional magnetic resonance imaging data set, demonstrate the favorable performance of our methods.

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Section: Simulation Studymentioning

confidence: 99%

Smoothness Selection for Penalized Quantile Regression Splines

Reiss

Huang²

2012

The International Journal of Biostatistics

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“…The quantile function of the model in Yue and Rue [16] comes closest to structured additive quantile predictors as in eq. [1], although it contains only a random intercept and no varying-coefficient terms.…”

Section: Introductionmentioning

confidence: 99%

Boosting Structured Additive Quantile Regression for Longitudinal Childhood Obesity Data

Fenske

Fahrmeir

Hothorn

et al. 2013

The International Journal of Biostatistics

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Childhood obesity and the investigation of its risk factors has become an important public health issue. Our work is based on and motivated by a German longitudinal study including 2,226 children with up to ten measurements on their body mass index (BMI) and risk factors from birth to the age of 10 years. We introduce boosting of structured additive quantile regression as a novel distribution-free approach for longitudinal quantile regression. The quantile-specific predictors of our model include conventional linear population effects, smooth nonlinear functional effects, varying-coefficient terms, and individual-specific effects, such as intercepts and slopes. Estimation is based on boosting, a computer intensive inference method for highly complex models. We propose a component-wise functional gradient descent boosting algorithm that allows for penalized estimation of the large variety of different effects, particularly leading to individual-specific effects shrunken toward zero. This concept allows us to flexibly estimate the nonlinear age curves of upper quantiles of the BMI distribution, both on population and on individual-specific level, adjusted for further risk factors and to detect age-varying effects of categorical risk factors. Our model approach can be regarded as the quantile regression analog of Gaussian additive mixed models (or structured additive mean regression models), and we compare both model classes with respect to our obesity data.

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“…The Markov Chain Monte Carlo (MCMC) approaches for implementing Step 1 are now well known (e.g. see Yue and Rue 2011). Therefore,β n and 1 n V −1 n can be obtained as the mean and covariance matrix computed based on the MCMC simulations of β from Step 1.…”

Section: The Sandwich Likelihood Methodsmentioning

confidence: 99%

“…Therefore, the approach has been useful in many applications (e.g. Yu et al 2005;Yue and Rue 2011;Benoit and Van den Poel 2012;Alhamzawi and Yu 2013;Waldmann et al 2013). …”

Section: Introductionmentioning

confidence: 99%