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Semiparametric regression with shape-constrained penalized splines

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  • Hazelton, Martin L.
  • Turlach, Berwin A.

Abstract

In semiparametric regression models, penalized splines can be used to describe complex, non-linear relationships between the mean response and covariates. In some applications it is desirable to restrict the shape of the splines so as to enforce properties such as monotonicity or convexity on regression functions. We describe a method for imposing such shape constraints on penalized splines within a linear mixed model framework. We employ Markov chain Monte Carlo (MCMC) methods for model fitting, using a truncated prior distribution to impose the requisite shape restrictions. We develop a computationally efficient MCMC sampler by using a correspondingly truncated multivariate normal proposal distribution, which is a restricted version of the approximate sampling distribution of the model parameters in an unconstrained version of the model. We also describe a cheap approximation to this methodology that can be applied for shape-constrained scatterplot smoothing. Our methods are illustrated through two applications, the first involving the length of dugongs and the second concerned with growth curves for sitka spruce trees.

Suggested Citation

  • Hazelton, Martin L. & Turlach, Berwin A., 2011. "Semiparametric regression with shape-constrained penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2871-2879, October.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:10:p:2871-2879
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    References listed on IDEAS

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    Cited by:

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    2. Kevin Murray & Samuel Müller & Berwin Turlach, 2013. "Revisiting fitting monotone polynomials to data," Computational Statistics, Springer, vol. 28(5), pages 1989-2005, October.
    3. Claudia Köllmann & Björn Bornkamp & Katja Ickstadt, 2014. "Unimodal regression using Bernstein–Schoenberg splines and penalties," Biometrics, The International Biometric Society, vol. 70(4), pages 783-793, December.
    4. Colubi, Ana & Domínguez-Menchero, J. Santos & González-Rodríguez, Gil, 2014. "Testing constancy in monotone response models," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 45-56.
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    7. Minggen Lu, 2015. "Spline estimation of generalised monotonic regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 19-39, March.

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