Philip T. Reisshttps://works.bepress.com/phil_reiss/Recent works by Philip T. Reissen-usCopyright (c) 2020 All rights reserved.Wed, 01 Jan 2020 00:00:00 +00003600Tensor product splines and functional principal componentshttps://works.bepress.com/phil_reiss/46/<div class="line" id="line-17"><span style="font-family: CMR12; font-size: 12pt;">Functional principal component analysis for sparse longitudinal data usually proceeds by first smoothing the covariance surface, and then obtaining an eigendecomposition of the associated covariance operator. Here we consider the use of penalized tensor product splines for the initial smoothing step. Drawing on a result regarding finite-rank symmetric integral operators, we derive an explicit spline representation of the estimated eigenfunctions, and show that the effect of penalization can be notably disparate for alternative approaches to tensor product smoothing. The latter phenomenon is illustrated with two data sets derived from magnetic resonance imaging of the human brain.</span></div>Prof. Philip T. Reiss et al.Wed, 01 Jan 2020 00:00:00 +0000https://works.bepress.com/phil_reiss/46/Published and in-press articlesA problem of distributive justice, solved by the lassohttps://works.bepress.com/phil_reiss/48/<div class="line" id="line-17"><span style="font-family: CMR10; font-size: 11pt;">The problem of dividing an estate among creditors, when their claims total more than the value of the estate, was posed in the Talmud and has been analyzed in the game theory literature. Here we reveal a close connection between schemes for estate division and linear regression solution paths obtained by least angle regression or by the lasso. We focus primarily on the division scheme known as constrained equal awards, but also consider a more complex approach described by Aumann and Maschler (1985).</span></div>Prof. Philip T. ReissWed, 01 Jan 2020 00:00:00 +0000https://works.bepress.com/phil_reiss/48/Published and in-press articlesA time-varying measure of dyadic synchrony for three-dimensional motionhttps://works.bepress.com/phil_reiss/45/<div class="line" id="line-17"><span style="font-family: CMR12; font-size: 12pt;">We propose a novel approach to the analysis of synchronized three-dimensional motion in dyads. Motion recorded at high time resolution, as with a gaming device, is preprocessed in each of the three spatial dimensions by spline smoothing. Synchrony is then defined, at each time point, as the cosine between the two individualsâ€™ estimated velocity vectors. The approach is extended to allow a time lag, allowing for the analysis of leader-follower dynamics. Mean square cosine over the time range is proposed as a scalar summary of dyadic synchrony, and this measure is found to be positively associated with cognitive empathy. </span></div>Philip T. Reiss et al.Tue, 01 Jan 2019 00:00:00 +0000https://works.bepress.com/phil_reiss/45/Published and in-press articlesGeneralized reliability based on distanceshttps://works.bepress.com/phil_reiss/47/<div class="line" id="line-17"><span style="font-family: CMR9; font-size: 9pt;">The intraclass correlation coefficient (ICC) is a classical index of measurement reliability. With the</span></div><div class="line" id="line-41"><span style="font-family: CMR9; font-size: 9pt;">advent of new and complex types of data for which the ICC is not defined, there is a need for new ways to assess</span></div><div class="line" id="line-46"><span style="font-family: CMR9; font-size: 9pt;">reliability. To meet this need, we propose a new distance-based intraclass correlation coefficient (dbICC), defined in</span></div><div class="line" id="line-51"><span style="font-family: CMR9; font-size: 9pt;">terms of arbitrary distances among observations. We introduce a bias correction to improve the coverage of bootstrap</span></div><div class="line" id="line-56"><span style="font-family: CMR9; font-size: 9pt;">confidence intervals for the dbICC, and demonstrate its efficacy via simulation. We illustrate the proposed method by</span></div><div class="line" id="line-61"><span style="font-family: CMR9; font-size: 9pt;">analyzing the test-retest reliability of brain connectivity matrices derived from a set of repeated functional magnetic</span></div><div class="line" id="line-66"><span style="font-family: CMR9; font-size: 9pt;">resonance imaging scans. The Spearman-Brown formula, which shows how more intensive measurement increases</span></div><div class="line" id="line-71"><span style="font-family: CMR9; font-size: 9pt;">reliability, is extended to encompass the dbICC.</span></div>Meng Xu et al.Tue, 01 Jan 2019 00:00:00 +0000https://works.bepress.com/phil_reiss/47/PreprintsCross-sectional versus longitudinal designs for function estimation, with an application to cerebral cortex developmenthttps://works.bepress.com/phil_reiss/44/<div class="line" id="line-17">Motivated by studies of the development of the human cerebral cortex, we consider</div><div class="line" id="line-19">the estimation of a mean growth trajectory and the relative merits of cross-sectional</div><div class="line" id="line-21">and longitudinal data for that task. We define a class of relative efficiencies that</div><div class="line" id="line-23">compare function estimates in terms of aggregate variance of a parametric function</div><div class="line" id="line-25">estimate. These generalize the classical design effect for estimating a scalar with</div><div class="line" id="line-27">cross-sectional versus longitudinal data, and in particular cases are shown to be</div><div class="line" id="line-29">bounded above by it. Turning to nonparametric function estimation, we find that a</div><div class="line" id="line-31">longitudinal fits may tend to have higher aggregate variance than cross-sectional</div><div class="line" id="line-33">ones, but that this may occur because the former have higher effective degrees of</div><div class="line" id="line-35">freedom reflecting greater sensitivity to subtle features of the estimand. These ideas</div><div class="line" id="line-37">are illustrated with cortical thickness data from a longitudinal neuroimaging study.</div>Philip T. ReissMon, 01 Jan 2018 00:00:00 +0000https://works.bepress.com/phil_reiss/44/Published and in-press articlesMethods for scalar-on-function regressionhttps://works.bepress.com/phil_reiss/40/<div class="line" id="line-17">Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images, etc. are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorizing the basic model types as linear, nonlinear and nonparametric. We discuss publicly available software packages, and illustrate some of the procedures by application to a functional magnetic resonance imaging dataset.</div>Philip T. Reiss et al.Tue, 01 Aug 2017 00:00:00 +0000https://works.bepress.com/phil_reiss/40/Published and in-press articlesPenalized nonparametric scalar-on-function regression via principal coordinateshttps://works.bepress.com/phil_reiss/42/<div class="line" id="line-21">A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This paper introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. The core idea is to regress the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, the proposed principal coordinate ridge regression is shown to outperform a functional generalized linear model.</div>Philip T. Reiss et al.Sun, 01 Jan 2017 00:00:00 +0000https://works.bepress.com/phil_reiss/42/Published and in-press articlesPointwise influence matrices for functional-response regressionhttps://works.bepress.com/phil_reiss/43/<div class="line" id="line-47">We extend the notion of an influence or hat matrix to regression with functional responses and scalar predictors. For responses depending linearly on a set of predictors, our definition is shown to reduce to the conventional influence matrix for linear models. The pointwise degrees of freedom, the trace of the pointwise hat matrix, are shown to have an adaptivity property that motivates a two-step bivariate smoother for modeling nonlinear dependence on a single predictor. This procedure adapts to varying complexity of the nonlinear model at different locations along the function, and thereby achieves better performance than competing tensor product smoothers in an analysis of the development of white matter microstructure in the brain. </div><div class="line" id="line-49"><br></div>Philip T. Reiss et al.Sun, 01 Jan 2017 00:00:00 +0000https://works.bepress.com/phil_reiss/43/Published and in-press articlesFlexible penalized regression for functional data...and other complex data objectshttps://works.bepress.com/phil_reiss/41/Philip T. ReissSun, 01 Nov 2015 00:00:00 +0000https://works.bepress.com/phil_reiss/41/PresentationsWavelet-domain regression and predictive inference in psychiatric neuroimaginghttps://works.bepress.com/phil_reiss/29/<p>An increasingly important goal of psychiatry is the use of brain imaging data to develop predictive models. Here we present two contributions to statistical methodology for this purpose. First, we propose and compare a set of wavelet-domain procedures for fitting generalized linear models with scalar responses and image predictors: sparse variants of principal component regression and of partial least squares, and the elastic net. Second, we consider assessing the contribution of image predictors over and above available scalar predictors, in particular via permutation tests and an extension of the idea of confounding to the case of functional or image predictors. Using the proposed methods, we assess whether maps of a spontaneous brain activity measure, derived from functional magnetic resonance imaging, can meaningfully predict presence or absence of attention deficit/hyperactivity disorder (ADHD). Our results shed light on the role of confounding in the surprising outcome of the recent ADHD-200 Global Competition, which challenged researchers to develop algorithms for automated image-based diagnosis of the disorder.</p>
Philip T. Reiss et al.Mon, 01 Jun 2015 00:00:00 +0000https://works.bepress.com/phil_reiss/29/Published and in-press articles