Methods for Scalar‐on‐Function Regression

Reiss, Philip T.; Goldsmith, Jeff; Shang, Han Lin; Ogden, R. Todd

doi:10.1111/insr.12163

Cited by 144 publications

(120 citation statements)

References 162 publications

(289 reference statements)

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“…The methods discussed in this paper do not completely represent all published scalar‐on‐image models, but largely cover all main classes and their assumptions and focus on methods with available implementations. Variations include, eg, the LASSO‐variant of WNET (implemented in the R package refund.wave), all types of models that combine smoothness of the coefficient image with a sparsity assumption as in SparseGMRF , tensor‐based methods as PCR2D , or methods for scalar‐on‐function regression that can easily be extended to the scalar‐on‐image case . All of these methods have in common that they build on a (linear) regression approach, which is obviously a strong (meta) assumption in itself.…”

Section: Discussionmentioning

confidence: 99%

The impact of model assumptions in scalar‐on‐image regression

Happ

Greven

Schmid

2018

Statistics in Medicine

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Complex statistical models such as scalar-on-image regression often require strong assumptions to overcome the issue of nonidentifiability. While in theory, it is well understood that model assumptions can strongly influence the results, this seems to be underappreciated, or played down, in practice. This article gives a systematic overview of the main approaches for scalar-on-image regression with a special focus on their assumptions. We categorize the assumptions and develop measures to quantify the degree to which they are met. The impact of model assumptions and the practical usage of the proposed measures are illustrated in a simulation study and in an application to neuroimaging data. The results show that different assumptions indeed lead to quite different estimates with similar predictive ability, raising the question of their interpretability. We give recommendations for making modeling and interpretation decisions in practice based on the new measures and simulations using hypothetic coefficient images and the observed data.

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Section: Discussionmentioning

confidence: 99%

The impact of model assumptions in scalar‐on‐image regression

Happ

Greven

Schmid

2018

Statistics in Medicine

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“…al. (24) for a recent review. More broadly, it may be useful to model bidirectional associations between patterns of activity and health outcomes from a functional data perspective, although doing so will require additional methods development.…”

Section: Discussionmentioning

confidence: 99%

New Insights into Activity Patterns in Children, Found Using Functional Data Analyses

Goldsmith

Jacobson

Rundle

2016

Medicine &Amp; Science in Sports &Amp; Exercise

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Introduction/Purpose Continuous monitoring of activity using accelerometers and other wearable devices provides objective, unbiased measurement of physical activity in minute-by-minute or finer resolutions. Accelerometers have already been widely deployed in studies of healthy aging, recovery of function after heart surgery, and other outcomes. While common analyses of accelerometer data focus on single summary variables, such as the total or average activity count, there is growing interest in the determinants of diurnal profiles of activity. Methods We use tools from functional data analysis (FDA), an area with an established statistical literature, to treat complete 24-hour diurnal profiles as outcomes in a regression model. We illustrate the use of such models by analyzing data collected in New York City from 420 children participating in a Head Start program. Covariates of interest include season, sex, BMI Z-score, presence of an asthma diagnosis, and mother’s birthplace. Results The FDA model finds several meaningful associations between several covariates and diurnal profiles of activity. In some cases, including shifted activity patterns for children of foreign-born mothers and time-specific effects of asthma on activity, these associations exist for covariates that are not associated with average activity count. Conclusion FDA provides a useful statistical framework for settings in which the effect of covariates on the timing of activity is of interest. The use of similar models in other applications should be considered, and we make code public to facilitate this process.

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“…The same basic concept—namely, predicting the response by preferentially weighting observations that are nearby in a relevant sense—underlies previous methodology for non-parametric scalar-on-function regression (see Reiss et al, 2016, for a review). But unlike previous proposals, our approach can be implemented using existing software for generalized additive and related models (e.g., Wood, 2006, 2011).…”

Section: Introductionmentioning

confidence: 99%

Penalized Nonparametric Scalar-on-Function Regression via Principal Coordinates

Reiß

Miller

et al. 2017

Journal of Computational and Graphical Statistics

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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. In the proposed method, which we call principal coordinate ridge regression, one regresses 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, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model.

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Methods for Scalar‐on‐Function Regression

Cited by 144 publications

References 162 publications

The impact of model assumptions in scalar‐on‐image regression

The impact of model assumptions in scalar‐on‐image regression

New Insights into Activity Patterns in Children, Found Using Functional Data Analyses

Penalized Nonparametric Scalar-on-Function Regression via Principal Coordinates

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