A partial least squares approach for function-on-function interaction regression

Beyaztaş, Ufuk; Shang, Han Lin

doi:10.1007/s00180-020-01058-z

Cited by 12 publications

(6 citation statements)

References 59 publications

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“…In the present study, we only consider the main effects of the functional predictors. However, recent studies (see, e.g., previous works 61–66 ) have shown that functional regression models with quadratic and interaction effects of the functional predictors perform better than main effects models. When the functional predictors include outliers, the effects of outliers on the model may be greater in the functional predictors' quadratic and interaction terms than the main effects.…”

Section: Discussionmentioning

confidence: 96%

A robust functional partial least squares for scalar‐on‐multiple‐function regression

Beyaztaş

Shang

2022

Journal of Chemometrics

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The scalar‐on‐function regression model has become a popular analysis tool to explore the relationship between a scalar response and multiple functional predictors. Most of the existing approaches to estimate this model are based on the least‐squares estimator, which can be seriously affected by outliers in empirical datasets. When outliers are present in the data, it is known that the least‐squares‐based estimates may not be reliable. This paper proposes a robust functional partial least squares method, allowing a robust estimate of the regression coefficients in a scalar‐on‐multiple‐function regression model. In our method, the functional partial least squares components are computed via the partial robust M‐regression. The predictive performance of the proposed method is evaluated using several Monte Carlo experiments and two chemometric datasets: glucose concentration spectrometric data and sugar process data. The results produced by the proposed method are compared favorably with some of the classical functional or multivariate partial least squares and functional principal component analysis methods.

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Section: Discussionmentioning

confidence: 96%

A robust functional partial least squares for scalar‐on‐multiple‐function regression

Beyaztaş

Shang

2022

Journal of Chemometrics

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“…3) In the present study, we only consider the main effects of the functional predictors. However, recent studies (see, e.g., Fuchs et al, 2015;Usset et al, 2016;Luo and Qi, 2019;Sun and Wang, 2020;Matsui, 2020;Beyaztas and Shang, 2021) have shown that functional regression models with quadratic and interaction effects of the functional predictors perform better than main effects models. When the functional predictors include outliers, the effects of outliers on the model may be greater in the functional predictors' quadratic and interaction terms than the main effects.…”

Section: Discussionmentioning

confidence: 99%

A Robust Functional Partial Least Squares for Scalar-on-Multiple-Function Regression

Beyaztaş¹,

Shang²

2022

Preprint

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The scalar-on-function regression model has become a popular analysis tool to explore the relationship between a scalar response and multiple functional predictors. Most of the existing approaches to estimate this model are based on the least-squares estimator, which can be seriously affected by outliers in empirical datasets. When outliers are present in the data, it is known that the least-squares-based estimates may not be reliable. This paper proposes a robust functional partial least squares method, allowing a robust estimate of the regression coefficients in a scalar-onmultiple-function regression model. In our method, the functional partial least squares components are computed via the partial robust M-regression. The predictive performance of the proposed method is evaluated using several Monte Carlo experiments and two chemometric datasets: glucose concentration spectrometric data and sugar process data. The results produced by the proposed method are compared favorably with some of the classical functional or multivariate partial least squares and functional principal component analysis methods.

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“…For example, in such models,

20 \times 20 = 400

tensor product basis expansion functions are used to approximate the quadratic and interaction effects of the functional predictors if

K = 20

basis expansion functions are used to approximate a specific functional predictor. Second, the FRM with quadratic and interaction effects of functional predictors requires considerably more basis coefficients and parameters to be estimated in a model (see, e.g., previous studies 54–59 ). Therefore, such models require much more computing time than the main effect models in the estimation step.…”

Section: Discussionmentioning

confidence: 99%

On partial least‐squares estimation in scalar‐on‐function regression models

Saricam

Beyaztaş²,

Aşikgil³

et al. 2022

Journal of Chemometrics

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Scalar-on-function regression, where the response is scalar valued and the predictor consists of random functions, is one of the most important tools for exploring the functional relationship between a scalar response and functional predictor(s). The functional partial least-squares method improves estimation accuracy for estimating the regression coefficient function compared to other existing methods, such as least squares, maximum likelihood, and maximum penalized likelihood. The functional partial least-squares method is often based on the SIMPLS or NIPALS algorithm, but these algorithms can be computationally slow for analyzing a large dataset. In this study, we propose two modified functional partial least-squares methods to efficiently estimate the regression coefficient function under the scalar-on-function regression. In the proposed methods, the infinite-dimensional functional predictors are first projected onto a finite-dimensional space using a basis expansion method. Then, two partial least-squares algorithms, based on re-orthogonalization of the score and loading vectors, are used to estimate the linear relationship between scalar response and the basis coefficients of the functional predictors.The finite-sample performance and computing speed are evaluated using a series of Monte Carlo simulation studies and a sugar process dataset.

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A partial least squares approach for function-on-function interaction regression

Cited by 12 publications

References 59 publications

A robust functional partial least squares for scalar‐on‐multiple‐function regression

A robust functional partial least squares for scalar‐on‐multiple‐function regression

A Robust Functional Partial Least Squares for Scalar-on-Multiple-Function Regression

On partial least‐squares estimation in scalar‐on‐function regression models

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