Penalized Nonparametric Scalar-on-Function Regression via Principal Coordinates

Reiß, Philip; Miller, David L.; Wu, Pei Shien; Hua, Wen Yu

doi:10.1080/10618600.2016.1217227

Cited by 4 publications

(3 citation statements)

References 58 publications

(71 reference statements)

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“…While linear and smooth effects can be easily represented within the discussed framework, more complex relationships require additional work. Principal coordinates (Reiss et al, 2015) have recently been proposed as one way to extend the framework to allow more general non-linear features of functional covariates to influence a response (cf., e.g., Ferraty and Vieu, 2006 for alternatives using a different non-parametric framework). Self-interactions of functions can also be of interest and while Fuchs et al (2015) could be used for a linear self-interaction model, more complex potentially non-linear relationships would require additional development.…”

Section: Discussion and Outlookmentioning

confidence: 99%

A general framework for functional regression modelling

Greven

Scheipl

2017

Statistical Modelling

100

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Researchers are increasingly interested in regression models for functional data. This article discusses a comprehensive framework for additive (mixed) models for functional responses and/or functional covariates based on the guiding principle of reframing functional regression in terms of corresponding models for scalar data, allowing the adaptation of a large body of existing methods for these novel tasks. The framework encompasses many existing as well as new models. It includes regression for 'generalized' functional data, mean regression, quantile regression as well as generalized additive models for location, shape and scale (GAMLSS) for functional data. It admits many flexible linear, smooth or interaction terms of scalar and functional covariates as well as (functional) random effects and allows flexible choices of bases-particularly splines and functional principal components-and corresponding penalties for each term. It covers functional data observed on common (dense) or curve-specific (sparse) grids. Penalized-likelihood-based and gradient-boosting-based inference for these models are implemented in R packages refund and FDboost, respectively. We also discuss identifiability and computational complexity for the functional regression models covered. A running example on a longitudinal multiple sclerosis imaging study serves to illustrate the flexibility and utility of the proposed model class. Reproducible code for this case study is made available online.

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Section: Discussion and Outlookmentioning

confidence: 99%

A general framework for functional regression modelling

Greven

Scheipl

2017

Statistical Modelling

100

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“…Once they are aligned to a new functional domain, the amplitude variation of modularity and participation curves (e.g., the difference between m i ( t 0 ) and m j ( t 0 ) for persons i and j and time t 0 ) can be meaningfully interpreted as differences in network structure. A common strategy is to address phase and amplitude variation separately: functions are pre-aligned before applying a downstream analysis such as regression or clustering (Reiss and others , 2017).…”

Section: Functional Data Analysis Of Multiscale Network Topologymentioning

confidence: 99%

Regression and Alignment for Functional Data and Network Topology

Wrobel

Satterthwaite

et al. 2023

Preprint

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In the brain, functional connections form a network whose topological organization can be described by graph-theoretic network diagnostics. These include characterizations of the community structure, such as modularity and participation coefficient, which have been shown to change over the course of childhood and adolescence. To investigate if such changes in the functional network are associated with changes in cognitive performance during development, network studies often rely on an arbitrary choice of pre-processing parameters, in particular the proportional threshold of network edges. Because the choice of parameter can impact the value of the network diagnostic, and therefore downstream conclusions, we propose to circumvent that choice by conceptualizing the network diagnostic as a function of the parameter. As opposed to a single value, a network diagnostic curve describes the connectome topology at multiple scales--from the sparsest group of the strongest edges to the entire edge set. To relate these curves to executive function and other covariates, we use scalar-on-function regression, which is more flexible than previous functional data-based models used in network neuroscience. We then consider how systematic differences between networks can manifest in misalignment of diagnostic curves, and consequently propose a supervised curve alignment method that incorporates auxiliary information from other variables. Our algorithm performs both functional regression and alignment via an iterative, penalized, and nonlinear likelihood optimization. The illustrated method has the potential to improve the interpretability and generalizability of neuroscience studies where the goal is to study heterogeneity among a mixture of function- and scalar-valued measures.

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“…There has also been considerable work done in scalar on function regression. Fan and Zhang [2000] provides a two step method based on local polynomial smoothing, Cardot et al [2003] explores spline based methods, James et al [2009] incorporates shrinkage methods in estimating a functional predictor/scalar response model, Goldsmith and Scheipl [2014] focuses on minimizing the cross-validated prediction error, Reiss et al [2017a] develops a method called principal coordinate ridge regression which uses ridge regression on principal components and rank penalized splines, and Gertheiss et al [2013] uses functional Principal Component Regression. An extensive discussion has been provided in the review paper Reiss et al [2017b].…”

Section: Introductionmentioning

confidence: 99%

Hypothesis Testing in Nonlinear Function on Scalar Regression with Application to Child Growth Study

Biswas,

Maity

2019

Preprint

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We propose a kernel machine based hypothesis testing procedure in nonlinear function-on-scalar regression model. Our research is motivated by the Newborn Epigenetic Study (NEST) where the question of interest is whether a pre-specified group of toxic metals or methylation at any of 9 differentially methylated regions (DMRs) is associated with child growth. We take the child growth trajectory as the functional response, and model the toxic metal measurements jointly using a nonlinear function. We use a kernel machine approach to model the unknown function and transform the hypothesis of no effect to an appropriate variance component test. We demonstrate our proposed methodology using a simulation study and by applying it to analyze the NEST data.

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Penalized Nonparametric Scalar-on-Function Regression via Principal Coordinates

Cited by 4 publications

References 58 publications

A general framework for functional regression modelling

A general framework for functional regression modelling

Regression and Alignment for Functional Data and Network Topology

Hypothesis Testing in Nonlinear Function on Scalar Regression with Application to Child Growth Study

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