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Flores M, Llambo Á, Loza D, Naya S, Tarrío-Saavedra J. Predicting rainfall and irrigation requirements of corn in Ecuador. Heliyon 2023; 9:e18334. [PMID: 37576264 PMCID: PMC10412904 DOI: 10.1016/j.heliyon.2023.e18334] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2022] [Revised: 07/13/2023] [Accepted: 07/13/2023] [Indexed: 08/15/2023] Open
Abstract
This work is a case study whose objective is prediction of irrigation needs of corn crops in different regions of Ecuador; being this a fundamental basic food for the country's economy, as in the remaining countries of the Andean area. The proposed methodology seeks to help improving the quality of corn crop. Specifically, we propose the application of regression models, within the framework of Functional Data Analysis (FDA), to predict the amount of rainfall (scalar response variable) in the places with the highest production of corn in Ecuador, as a function of functional covariates such as temperature and wind speed. From the estimation of the amount of rainfall, effective precipitation is calculated. This is the fraction of water used by the crops, from which the value of real evapotranspiration or ETc is obtained and, more importantly, the irrigation requirements at each stage of the corn crop, for its adequate physiological development. Application of regression models based on functional basis, Functional Principal Components (FPC) or Functional Partial Least Squares (FPLS) for scalar response variable, allows us to use the information of variables such as wind speed and temperature (of functional nature) in a better way than using multivariate models, for predicting the amount of rainfall, obtaining, as a result, very explicative models, defined by a high goodness of fit (R 2 = 0.97 , with 6 significant parameters and an error of 0.14) and practical utility. The model has been also applied to North Peru regions, obtaining rainfall prediction errors between 9% and 22%. Thus, the geographical limitations of the model could be the Andean regions with similar climate. In addition, this study proposes the application of FDA exploratory analysis and FDA outlier detection techniques as a common and useful practice in the specific domain of rainfall prediction studies, prior to applying the regression models.
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Affiliation(s)
- Miguel Flores
- Departamento de Matemática, Grupo MODES, Facultad de Ciencias, Escuela Politécnica Nacional, Ladrón de Guevara E11–253, Quito, 17–01–2759, Pichincha, Ecuador
| | - Ángel Llambo
- Departamento de Matemática, Facultad de Ciencias, Escuela Politécnica Nacional, Ladrón de Guevara E11–253, Quito, 17–01–2759, Pichincha, Ecuador
| | - Danilo Loza
- Departamento de Matemática, Facultad de Ciencias, Escuela Politécnica Nacional, Ladrón de Guevara E11–253, Quito, 17–01–2759, Pichincha, Ecuador
| | - Salvador Naya
- Grupo MODES, CITIC, Departamento de Matemáticas, Escola Politécnica de Enxeñaría de Ferrol, Universidade da Coruña, Mendizábal s/n, Ferrol, 15403, A Coruña, Spain
| | - Javier Tarrío-Saavedra
- Grupo MODES, CITIC, Departamento de Matemáticas, Escola Politécnica de Enxeñaría de Ferrol, Universidade da Coruña, Mendizábal s/n, Ferrol, 15403, A Coruña, Spain
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Parker PA, Holan SH. A bayesian functional data model for surveys collected under informative sampling with application to mortality estimation using NHANES. Biometrics 2022. [PMID: 35561139 DOI: 10.1111/biom.13696] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Accepted: 05/02/2022] [Indexed: 11/30/2022]
Abstract
Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non-Gaussian data and can be applied in multivariate settings. In addition, we make use of a variety of Bayesian modeling techniques to ensure that the model is fit in a computationally efficient manner. We illustrate the value of our approach through two simulation studies as well as an example of mortality estimation using NHANES data. This article is protected by copyright. All rights reserved.
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Affiliation(s)
- Paul A Parker
- Department of Statistics, University of California Santa Cruz, 1156 High St, Santa Cruz, CA
| | - Scott H Holan
- Department of Statistics, University of Missouri, 146 Middlebush Hall, Columbia, MO.,Research and Methodology Directorate, U.S. Census Bureau, 4600 Silver Hill Road, Washington, D.C
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Cavicchioli M. Generalised cepstral models for the spectrum of vector time series. Electron J Stat 2020. [DOI: 10.1214/19-ejs1672] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Davenport CA, Maity A, Baladandayuthapani V. Functional interaction-based nonlinear models with application to multiplatform genomics data. Stat Med 2018; 37:2715-2733. [PMID: 29737021 DOI: 10.1002/sim.7671] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Revised: 02/05/2018] [Accepted: 03/09/2018] [Indexed: 11/11/2022]
Abstract
Functional regression allows for a scalar response to be dependent on a functional predictor; however, not much work has been done when a scalar exposure that interacts with the functional covariate is introduced. In this paper, we present 2 functional regression models that account for this interaction and propose 2 novel estimation procedures for the parameters in these models. These estimation methods allow for a noisy and/or sparsely observed functional covariate and are easily extended to generalized exponential family responses. We compute standard errors of our estimators, which allows for further statistical inference and hypothesis testing. We compare the performance of the proposed estimators to each other and to one found in the literature via simulation and demonstrate our methods using a real data example.
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Affiliation(s)
- Clemontina A Davenport
- Department of Biostatistics and Bioinformatics, Duke University Medical Center, Durham, NC, 27705, USA
| | - Arnab Maity
- Department of Statistics, North Carolina State University, Raleigh, NC, 27695, USA
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Reiss PT, Goldsmith J, Shang HL, Ogden RT. Methods for scalar-on-function regression. Int Stat Rev 2017; 85:228-249. [PMID: 28919663 PMCID: PMC5598560 DOI: 10.1111/insr.12163] [Citation(s) in RCA: 72] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2015] [Accepted: 12/28/2015] [Indexed: 01/16/2023]
Abstract
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.
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Affiliation(s)
- Philip T. Reiss
- Department of Child and Adolescent Psychiatry and Department of Population Health, New York University School of Medicine
- Department of Statistics, University of Haifa
| | - Jeff Goldsmith
- Department of Biostatistics, Columbia University Mailman School of Public Health
| | - Han Lin Shang
- Research School of Finance, Actuarial Studies and Statistics, Australian National University
| | - R. Todd Ogden
- Department of Biostatistics, Columbia University Mailman School of Public Health
- New York State Psychiatric Institute
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Zhang L, Baladandayuthapani V, Zhu H, Baggerly KA, Majewski T, Czerniak BA, Morris JS. Functional CAR models for large spatially correlated functional datasets. J Am Stat Assoc 2016; 111:772-786. [PMID: 28018013 DOI: 10.1080/01621459.2015.1042581] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Abstract
We develop a functional conditional autoregressive (CAR) model for spatially correlated data for which functions are collected on areal units of a lattice. Our model performs functional response regression while accounting for spatial correlations with potentially nonseparable and nonstationary covariance structure, in both the space and functional domains. We show theoretically that our construction leads to a CAR model at each functional location, with spatial covariance parameters varying and borrowing strength across the functional domain. Using basis transformation strategies, the nonseparable spatial-functional model is computationally scalable to enormous functional datasets, generalizable to different basis functions, and can be used on functions defined on higher dimensional domains such as images. Through simulation studies, we demonstrate that accounting for the spatial correlation in our modeling leads to improved functional regression performance. Applied to a high-throughput spatially correlated copy number dataset, the model identifies genetic markers not identified by comparable methods that ignore spatial correlations.
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Affiliation(s)
- Lin Zhang
- The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A
| | | | | | - Keith A Baggerly
- The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A
| | - Tadeusz Majewski
- The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A
| | - Bogdan A Czerniak
- The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A
| | - Jeffrey S Morris
- The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A
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Meyer MJ, Coull BA, Versace F, Cinciripini P, Morris JS. Bayesian function-on-function regression for multilevel functional data. Biometrics 2015; 71:563-74. [PMID: 25787146 PMCID: PMC4575250 DOI: 10.1111/biom.12299] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2013] [Revised: 12/01/2014] [Accepted: 01/01/2015] [Indexed: 11/30/2022]
Abstract
Medical and public health research increasingly involves the collection of complex and high dimensional data. In particular, functional data-where the unit of observation is a curve or set of curves that are finely sampled over a grid-is frequently obtained. Moreover, researchers often sample multiple curves per person resulting in repeated functional measures. A common question is how to analyze the relationship between two functional variables. We propose a general function-on-function regression model for repeatedly sampled functional data on a fine grid, presenting a simple model as well as a more extensive mixed model framework, and introducing various functional Bayesian inferential procedures that account for multiple testing. We examine these models via simulation and a data analysis with data from a study that used event-related potentials to examine how the brain processes various types of images.
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Affiliation(s)
- Mark J. Meyer
- Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania, U.S.A
| | - Brent A. Coull
- Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts, U.S.A
| | - Francesco Versace
- The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A
| | - Paul Cinciripini
- The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A
| | - Jeffrey S. Morris
- The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A
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