Bayesian model selection in additive partial linear models via locally adaptive splines
Author(s)
Jeong, Seonghyun
Park, Taeyoung
Dyk, David A van
Type
Journal Article
Abstract
We provide a flexible framework for selecting among a class of additive
partial linear models that allows both linear and nonlinear additive
components. In practice, it is challenging to determine which additive
components should be excluded from the model while simultaneously determining
whether nonzero additive components should be represented as linear or
non-linear components in the final model. In this paper, we propose a Bayesian
model selection method that is facilitated by a carefully specified class of
models, including the choice of a prior distribution and the nonparametric
model used for the nonlinear additive components. We employ a series of latent
variables that determine the effect of each variable among the three
possibilities (no effect, linear effect, and nonlinear effect) and that
simultaneously determine the knots of each spline for a suitable penalization
of smooth functions. The use of a pseudo-prior distribution along with a
collapsing scheme enables us to deploy well-behaved Markov chain Monte Carlo
samplers, both for model selection and for fitting the preferred model. Our
method and algorithm are deployed on a suite of numerical studies and are
applied to a nutritional epidemiology study. The numerical results show that
the proposed methodology outperforms previously available methods in terms of
effective sample sizes of the Markov chain samplers and the overall
misclassification rates.
partial linear models that allows both linear and nonlinear additive
components. In practice, it is challenging to determine which additive
components should be excluded from the model while simultaneously determining
whether nonzero additive components should be represented as linear or
non-linear components in the final model. In this paper, we propose a Bayesian
model selection method that is facilitated by a carefully specified class of
models, including the choice of a prior distribution and the nonparametric
model used for the nonlinear additive components. We employ a series of latent
variables that determine the effect of each variable among the three
possibilities (no effect, linear effect, and nonlinear effect) and that
simultaneously determine the knots of each spline for a suitable penalization
of smooth functions. The use of a pseudo-prior distribution along with a
collapsing scheme enables us to deploy well-behaved Markov chain Monte Carlo
samplers, both for model selection and for fitting the preferred model. Our
method and algorithm are deployed on a suite of numerical studies and are
applied to a nutritional epidemiology study. The numerical results show that
the proposed methodology outperforms previously available methods in terms of
effective sample sizes of the Markov chain samplers and the overall
misclassification rates.
Date Issued
2021-12-16
Date Acceptance
2021-10-21
Citation
Journal of Computational and Graphical Statistics, 2021, 31 (2), pp.324-336
ISSN
1061-8600
Publisher
American Statistical Association
Start Page
324
End Page
336
Journal / Book Title
Journal of Computational and Graphical Statistics
Volume
31
Issue
2
Copyright Statement
© 2021 The Author(s). Published with license by Taylor & Francis Group, LLC.
This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.
This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.
Identifier
http://arxiv.org/abs/2008.06213v2
Subjects
stat.ME
stat.ME
Publication Status
Published
Date Publish Online
2021-11-04