Fast Adaptive Penalized Splines

Krivobokova, Tatyana; Crainiceanu, Ciprian M.; Kauermann, Göran

doi:10.1198/106186008x287328

Cited by 79 publications

(65 citation statements)

References 28 publications

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“…Alternatively, a parametric bootstrap method can be used to estimate E y ðVarðbjyÞÞ by generating a set of bootstrap replicates y* from the empirical distribution b f ð yÞ according to model (1) with the parameters replaced by their estimates from the EM algorithm. ; which is the price of our Laplace approximation compared to a full Bayesian approach as previously noted (Krivobokova et al 2008;Skrondal and RabeHesketh 2009). Finally, the C.I.…”

Section: Detailed Derivation Of the Estimation In The Ace(t)-p Modelmentioning

confidence: 86%

“…Based on this strategy, Krivobokova proposed a unified EM-type iterative procedure (Krivobokova et al 2008) to estimate the spline coefficients and the penalizing coefficients (now transformed to the variances of random effects in the linear mixed model) simultaneously by estimating the spline coefficients through an iterated weighted least-squares (IWLS) algorithm and employing an approximation algorithm (Breslow and Clayton 1993) to iterate between the estimation of the spline coefficients and minimization of the marginal log-likelihood. More specifically, following the same spirit, the marginal likelihood in our case is whereK andL are the numbers of positive eigenvalues of D A and D C : By applying a Laplace approximation to the integrand of (4) with the condition of K; L ( n M þ n D ; we obtain the 22 loglikelihood…”

Section: Stable Estimation Of Variance Curves Using Penalized Splinesmentioning

confidence: 99%

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Estimating Modifying Effect of Age on Genetic and Environmental Variance Components in Twin Models

Sillanpää

Silventoinen

et al. 2016

Genetics

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Twin studies have been adopted for decades to disentangle the relative genetic and environmental contributions for a wide range of traits. However, heritability estimation based on the classical twin models does not take into account dynamic behavior of the variance components over age. Varying variance of the genetic component over age can imply the existence of geneenvironment (G 3 E) interactions that general genome-wide association studies (GWAS) fail to capture, which may lead to the inconsistency of heritability estimates between twin design and GWAS. Existing parametric G 3 E interaction models for twin studies are limited by assuming a linear or quadratic form of the variance curves with respect to a moderator that can, however, be overly restricted in reality. Here we propose spline-based approaches to explore the variance curves of the genetic and environmental components. We choose the additive genetic, common, and unique environmental variance components (ACE) model as the starting point. We treat the component variances as variance functions with respect to age modeled by B-splines or P-splines. We develop an empirical Bayes method to estimate the variance curves together with their confidence bands and provide an R package for public use. Our simulations demonstrate that the proposed methods accurately capture dynamic behavior of the component variances in terms of mean square errors with a data set of .10,000 twin pairs. Using the proposed methods as an alternative and major extension to the classical twin models, our analyses with a large-scale Finnish twin data set (19,510 MZ twins and 27,312 DZ same-sex twins) discover that the variances of the A, C, and E components for body mass index (BMI) change substantially across life span in different patterns and the heritability of BMI drops to $50% after middle age. The results further indicate that the decline of heritability is due to increasing unique environmental variance, which provides more insights into age-specific heritability of BMI and evidence of G 3 E interactions. These findings highlight the fundamental importance and implication of the proposed models in facilitating twin studies to investigate the heritability specific to age and other modifying factors.KEYWORDS twin models; penalized B-splines; age-specific heritability; empirical Bayes predictor; body mass index T WIN studies have been broadly used as a tool to investigate heritability for decades. A recent comprehensive meta-analysis reported 17,804 heritability estimates for various traits based on twin studies (Polderman et al. 2015).Estimation methods and software such as structural equation modeling (SEM) based on the classical twin models consisting of additive genetic, common, and unshared environmental effects have been well established and extensively adopted (Rijsdijk and Sham 2002). Extensions for longitudinal data or time-to-event phenotypes based on the classical twin models have been proposed (Boomsma et al. 1989;Pitkäniemi et al. 2007). Nevertheless, one of...

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Section: Detailed Derivation Of the Estimation In The Ace(t)-p Modelmentioning

confidence: 86%

Section: Stable Estimation Of Variance Curves Using Penalized Splinesmentioning

confidence: 99%

Estimating Modifying Effect of Age on Genetic and Environmental Variance Components in Twin Models

Sillanpää

Silventoinen

et al. 2016

Genetics

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“…A similar idea was suggested in a fully Bayesian framework with d = 1 and MCMC techniques by Crainiceanu et al (2007). To overcome the numerically intensive computations of the latter, Krivobokova et al (2008) suggested to use the Laplace approximation of the likelihood. They have shown, that the resulting estimator is nearly identical to the Bayesian one, but can be obtained with considerably smaller numerical effort.…”

Section: Simultaneous Bands For Additive Models With Spatially Heteromentioning

confidence: 99%

“…In this article we extend the flexible adaptive curve estimation of Krivobokova et al (2008) to account for heteroscedasticity in the data and the approach of Krivobokova et al (2010) to additive models in order to analyze the data on stunting by age in Kenya.…”

Section: Introductionmentioning

confidence: 99%

Direct Simultaneous Inference in Additive Models and Its Application to Model Undernutrition

Wiesenfarth

Krivobokova

Klasen

et al. 2012

Journal of the American Statistical Association

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract This article proposes a simple and fast approach to build simultaneous confidence bands and perform specification tests for smooth curves in additive models. The method allows for handling of spatially heterogeneous functions and its derivatives as well as heteroscedasticity in the data. It is applied to study the determinants of chronic undernutrition of Kenyan children, with particular focus on the highly non-linear age pattern in undernutrition. Model estimation using the mixed model representation of penalized splines in combination with simultaneous probability calculations based on the volume-of-tube formula enable the simultaneous inference directly, i.e. without resampling methods. Finite sample properties of simultaneous confidence bands and specification tests are investigated in simulations. To facilitate and enhance its application, the method has been implemented in the R package AdaptFitOS. Terms of use: Documents in

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“…A heuristic approach would be to pick γ 2 such that some smoothing is obtained, but not too much. Another approach is to estimate the parameter, using AIC, GVC or REML methods, see [11,14].…”

Section: Dependence Testingmentioning

confidence: 99%

Semiparametric lag dependent functions

Lindström¹

2013

ams

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This paper introduces a suite of tests for linear and general nonlinear serial dependence. The problem is complex as the number of variations of realistic non-linear alternatives is very large.The alternative model is defined in terms of penalized truncated polynomial splines, making the approximation capable of accurately approximating a large class of linear and non-linear processes.The asymptotic distribution for the test statistic is derived, and we show using Monte Carlo simulations that one test is equivalent to the Ljung-Box test, other linear tests corresponds to ordinary or partial sample autocorrelation while the non-linear versions are capable of detecting non-linear effects, even when other tests fail to do so.

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Fast Adaptive Penalized Splines

Cited by 79 publications

References 28 publications

Estimating Modifying Effect of Age on Genetic and Environmental Variance Components in Twin Models

Estimating Modifying Effect of Age on Genetic and Environmental Variance Components in Twin Models

Direct Simultaneous Inference in Additive Models and Its Application to Model Undernutrition

Semiparametric lag dependent functions

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