Dataset Information

Smoothing spline ANOVA decomposition of arbitrary splines: an application to eye movements in reading.

ABSTRACT: The Smoothing Spline ANOVA (SS-ANOVA) requires a specialized construction of basis and penalty terms in order to incorporate prior knowledge about the data to be fitted. Typically, one resorts to the most general approach using tensor product splines. This implies severe constraints on the correlation structure, i.e. the assumption of isotropy of smoothness can not be incorporated in general. This may increase the variance of the spline fit, especially if only a relatively small set of observations are given. In this article, we propose an alternative method that allows to incorporate prior knowledge without the need to construct specialized bases and penalties, allowing the researcher to choose the spline basis and penalty according to the prior knowledge of the observations rather than choosing them according to the analysis to be done. The two approaches are compared with an artificial example and with analyses of fixation durations during reading.

SUBMITTER: Matuschek H

PROVIDER: S-EPMC4376895 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Smoothing spline ANOVA decomposition of arbitrary splines: an application to eye movements in reading.

Matuschek Hannes H Kliegl Reinhold R Holschneider Matthias M

PloS one 20150327 3

The Smoothing Spline ANOVA (SS-ANOVA) requires a specialized construction of basis and penalty terms in order to incorporate prior knowledge about the data to be fitted. Typically, one resorts to the most general approach using tensor product splines. This implies severe constraints on the correlation structure, i.e. the assumption of isotropy of smoothness can not be incorporated in general. This may increase the variance of the spline fit, especially if only a relatively small set of observati ...[more]

PMID: 25816246

Similar Datasets

Project description:Multilevel functional data is collected in many biomedical studies. For example, in a study of the effect of Nimodipine on patients with subarachnoid hemorrhage (SAH), patients underwent multiple 4-hour treatment cycles. Within each treatment cycle, subjects' vital signs were reported every 10 minutes. This data has a natural multilevel structure with treatment cycles nested within subjects and measurements nested within cycles. Most literature on nonparametric analysis of such multilevel functional data focus on conditional approaches using functional mixed effects models. However, parameters obtained from the conditional models do not have direct interpretations as population average effects. When population effects are of interest, we may employ marginal regression models. In this work, we propose marginal approaches to fit multilevel functional data through penalized spline generalized estimating equation (penalized spline GEE). The procedure is effective for modeling multilevel correlated generalized outcomes as well as continuous outcomes without suffering from numerical difficulties. We provide a variance estimator robust to misspecification of correlation structure. We investigate the large sample properties of the penalized spline GEE estimator with multilevel continuous data and show that the asymptotics falls into two categories. In the small knots scenario, the estimated mean function is asymptotically efficient when the true correlation function is used and the asymptotic bias does not depend on the working correlation matrix. In the large knots scenario, both the asymptotic bias and variance depend on the working correlation. We propose a new method to select the smoothing parameter for penalized spline GEE based on an estimate of the asymptotic mean squared error (MSE). We conduct extensive simulation studies to examine property of the proposed estimator under different correlation structures and sensitivity of the variance estimation to the choice of smoothing parameter. Finally, we apply the methods to the SAH study to evaluate a recent debate on discontinuing the use of Nimodipine in the clinical community.

Project description:BackgroundNext-generation sequencing has been used by investigators to address a diverse range of biological problems through, for example, polymorphism and mutation discovery and microRNA profiling. However, compared to conventional sequencing, the error rates for next-generation sequencing are often higher, which impacts the downstream genomic analysis. Recently, Wang et al. (BMC Bioinformatics 13:185, 2012) proposed a shadow regression approach to estimate the error rates for next-generation sequencing data based on the assumption of a linear relationship between the number of reads sequenced and the number of reads containing errors (denoted as shadows). However, this linear read-shadow relationship may not be appropriate for all types of sequence data. Therefore, it is necessary to estimate the error rates in a more reliable way without assuming linearity. We proposed an empirical error rate estimation approach that employs cubic and robust smoothing splines to model the relationship between the number of reads sequenced and the number of shadows.ResultsWe performed simulation studies using a frequency-based approach to generate the read and shadow counts directly, which can mimic the real sequence counts data structure. Using simulation, we investigated the performance of the proposed approach and compared it to that of shadow linear regression. The proposed approach provided more accurate error rate estimations than the shadow linear regression approach for all the scenarios tested. We also applied the proposed approach to assess the error rates for the sequence data from the MicroArray Quality Control project, a mutation screening study, the Encyclopedia of DNA Elements project, and bacteriophage PhiX DNA samples.ConclusionsThe proposed empirical error rate estimation approach does not assume a linear relationship between the error-free read and shadow counts and provides more accurate estimations of error rates for next-generation, short-read sequencing data.

Dataset Information

Smoothing spline ANOVA decomposition of arbitrary splines: an application to eye movements in reading.

Publications

Smoothing spline ANOVA decomposition of arbitrary splines: an application to eye movements in reading.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets