Monte Carlo methods for estimating Mallows's Cp and AIC criteria for PLSR models. Illustration on agronomic spectroscopic NIR data
Mallows's Cp and Akaike information criterion (AIC) are common criteria for selecting the dimensionality of regression models, as an alternative to cross- validation (CV) and nonparametric bootstrap. A key parameter in the calcula- tion of Cp and AIC is the effective number of degrees of freedom of the model, or model complexity (d). Parameter d is generally easy to calculate for linear smoothers, that is, models for which the prediction of the training response y is given by by = S y where S is a projector matrix that does not involve y. Never- theless, d is more difficult to estimate for nonlinear smoothers, such as partial least squares regression (PLSR). In this article, we present two algorithms for estimating d for PLSR based on Monte Carlo simulation methods (parametric bootstrap and perturbation analysis) and with the particular case of high dimensional data. We compare these Monte Carlo methods to three other algorithms already published. We used the d estimates to compute Cp and AIC and select PLSR model dimensionalities that we then compare to CV. Two real and heterogeneous agronomic near infrared (NIR) datasets were considered as examples.
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Subjects: | modèle de simulation, modèle mathématique, technique de prévision, critère de sélection, méthode statistique, http://aims.fao.org/aos/agrovoc/c_24242, http://aims.fao.org/aos/agrovoc/c_24199, http://aims.fao.org/aos/agrovoc/c_3041, http://aims.fao.org/aos/agrovoc/c_1078, http://aims.fao.org/aos/agrovoc/c_7377, |
Online Access: | http://agritrop.cirad.fr/600014/ http://agritrop.cirad.fr/600014/1/lesnoff2021.pdf |
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dig-cirad-fr-6000142024-01-29T05:44:56Z http://agritrop.cirad.fr/600014/ http://agritrop.cirad.fr/600014/ Monte Carlo methods for estimating Mallows's Cp and AIC criteria for PLSR models. Illustration on agronomic spectroscopic NIR data. Lesnoff Matthieu, Roger Jean-Michel, Rutledge Douglas N.. 2021. Journal of Chemometrics, 35 (10):e3369, 21 p.https://doi.org/10.1002/cem.3369 <https://doi.org/10.1002/cem.3369> Monte Carlo methods for estimating Mallows's Cp and AIC criteria for PLSR models. Illustration on agronomic spectroscopic NIR data Lesnoff, Matthieu Roger, Jean-Michel Rutledge, Douglas N. eng 2021 Journal of Chemometrics modèle de simulation modèle mathématique technique de prévision critère de sélection méthode statistique http://aims.fao.org/aos/agrovoc/c_24242 http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_3041 http://aims.fao.org/aos/agrovoc/c_1078 http://aims.fao.org/aos/agrovoc/c_7377 Mallows's Cp and Akaike information criterion (AIC) are common criteria for selecting the dimensionality of regression models, as an alternative to cross- validation (CV) and nonparametric bootstrap. A key parameter in the calcula- tion of Cp and AIC is the effective number of degrees of freedom of the model, or model complexity (d). Parameter d is generally easy to calculate for linear smoothers, that is, models for which the prediction of the training response y is given by by = S y where S is a projector matrix that does not involve y. Never- theless, d is more difficult to estimate for nonlinear smoothers, such as partial least squares regression (PLSR). In this article, we present two algorithms for estimating d for PLSR based on Monte Carlo simulation methods (parametric bootstrap and perturbation analysis) and with the particular case of high dimensional data. We compare these Monte Carlo methods to three other algorithms already published. We used the d estimates to compute Cp and AIC and select PLSR model dimensionalities that we then compare to CV. Two real and heterogeneous agronomic near infrared (NIR) datasets were considered as examples. article info:eu-repo/semantics/article Journal Article info:eu-repo/semantics/publishedVersion http://agritrop.cirad.fr/600014/1/lesnoff2021.pdf text Cirad license info:eu-repo/semantics/restrictedAccess https://agritrop.cirad.fr/mention_legale.html https://doi.org/10.1002/cem.3369 10.1002/cem.3369 info:eu-repo/semantics/altIdentifier/doi/10.1002/cem.3369 info:eu-repo/semantics/altIdentifier/purl/https://doi.org/10.1002/cem.3369 info:eu-repo/grantAgreement/EC///// |
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modèle de simulation modèle mathématique technique de prévision critère de sélection méthode statistique http://aims.fao.org/aos/agrovoc/c_24242 http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_3041 http://aims.fao.org/aos/agrovoc/c_1078 http://aims.fao.org/aos/agrovoc/c_7377 modèle de simulation modèle mathématique technique de prévision critère de sélection méthode statistique http://aims.fao.org/aos/agrovoc/c_24242 http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_3041 http://aims.fao.org/aos/agrovoc/c_1078 http://aims.fao.org/aos/agrovoc/c_7377 |
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modèle de simulation modèle mathématique technique de prévision critère de sélection méthode statistique http://aims.fao.org/aos/agrovoc/c_24242 http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_3041 http://aims.fao.org/aos/agrovoc/c_1078 http://aims.fao.org/aos/agrovoc/c_7377 modèle de simulation modèle mathématique technique de prévision critère de sélection méthode statistique http://aims.fao.org/aos/agrovoc/c_24242 http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_3041 http://aims.fao.org/aos/agrovoc/c_1078 http://aims.fao.org/aos/agrovoc/c_7377 Lesnoff, Matthieu Roger, Jean-Michel Rutledge, Douglas N. Monte Carlo methods for estimating Mallows's Cp and AIC criteria for PLSR models. Illustration on agronomic spectroscopic NIR data |
description |
Mallows's Cp and Akaike information criterion (AIC) are common criteria for selecting the dimensionality of regression models, as an alternative to cross- validation (CV) and nonparametric bootstrap. A key parameter in the calcula- tion of Cp and AIC is the effective number of degrees of freedom of the model, or model complexity (d). Parameter d is generally easy to calculate for linear smoothers, that is, models for which the prediction of the training response y is given by by = S y where S is a projector matrix that does not involve y. Never- theless, d is more difficult to estimate for nonlinear smoothers, such as partial least squares regression (PLSR). In this article, we present two algorithms for estimating d for PLSR based on Monte Carlo simulation methods (parametric bootstrap and perturbation analysis) and with the particular case of high dimensional data. We compare these Monte Carlo methods to three other algorithms already published. We used the d estimates to compute Cp and AIC and select PLSR model dimensionalities that we then compare to CV. Two real and heterogeneous agronomic near infrared (NIR) datasets were considered as examples. |
format |
article |
topic_facet |
modèle de simulation modèle mathématique technique de prévision critère de sélection méthode statistique http://aims.fao.org/aos/agrovoc/c_24242 http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_3041 http://aims.fao.org/aos/agrovoc/c_1078 http://aims.fao.org/aos/agrovoc/c_7377 |
author |
Lesnoff, Matthieu Roger, Jean-Michel Rutledge, Douglas N. |
author_facet |
Lesnoff, Matthieu Roger, Jean-Michel Rutledge, Douglas N. |
author_sort |
Lesnoff, Matthieu |
title |
Monte Carlo methods for estimating Mallows's Cp and AIC criteria for PLSR models. Illustration on agronomic spectroscopic NIR data |
title_short |
Monte Carlo methods for estimating Mallows's Cp and AIC criteria for PLSR models. Illustration on agronomic spectroscopic NIR data |
title_full |
Monte Carlo methods for estimating Mallows's Cp and AIC criteria for PLSR models. Illustration on agronomic spectroscopic NIR data |
title_fullStr |
Monte Carlo methods for estimating Mallows's Cp and AIC criteria for PLSR models. Illustration on agronomic spectroscopic NIR data |
title_full_unstemmed |
Monte Carlo methods for estimating Mallows's Cp and AIC criteria for PLSR models. Illustration on agronomic spectroscopic NIR data |
title_sort |
monte carlo methods for estimating mallows's cp and aic criteria for plsr models. illustration on agronomic spectroscopic nir data |
url |
http://agritrop.cirad.fr/600014/ http://agritrop.cirad.fr/600014/1/lesnoff2021.pdf |
work_keys_str_mv |
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1792500287312756736 |