A dual algorithm for convex-concave data smoothing by cubic C2-splines
Numerische Mathematik
Direct generalized additive modeling with penalized likelihood
Computational Statistics & Data Analysis
Generalized structured additive regression based on Bayesian P-splines
Computational Statistics & Data Analysis
Fast simulation of truncated Gaussian distributions
Statistics and Computing
Revisiting fitting monotone polynomials to data
Computational Statistics
Testing constancy in monotone response models
Computational Statistics & Data Analysis
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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.