1Winona State University, Department of Mathematics and Statistics, Winona, United States. Assistant Professor. Email: THooks@winona.edu
2University of Nebraska, Department of Statistics, Lincoln, United States. Professors. Email: DMarx1@unl.edu
3University of Nebraska, Department of Statistics, Lincoln, United States. Professors. Email: SKachman1@unl.edu
4University of Nebraska, USDA-ARS Research, Department of Agronomy and Horticulture, Lincoln, United States. Geneticist and Professor. Email: JPedersen1@unl.edu
5University of Nebraska, USDA-ARS Research, Department of Agronomy and Horticulture, Lincoln, United States. Researcher. Email: REigenberg2@unl.edu
Advances in precision agriculture allow researchers to capture data more frequently and in more detail. For example, it is typical to collect "on-the-go" data such as soil electrical conductivity readings. This creates the opportunity to use these measurements as covariates for the primary response variable to possibly increase experimental precision. Moreover, these measurements are also spatially referenced to one another, creating the need for methods in which spatial locations play an explicit role in the analysis of the data. Data sets which contain measurements on a spatially referenced response and covariate are analyzed using either cokriging or spatial analysis of covariance. While cokriging accounts for the correlation structure of the covariate, it is purely a predictive tool. Alternatively, spatial analysis of covariance allows for parameter estimation yet disregards the correlation structure of the covariate. A method is proposed which both accounts for the correlation in and between the response and covariate and allows for the estimation of model parameters; also, this method allows for analysis of covariance when the response and covariate are not colocated.
Key words: Covariance Analysis, Spatial Analysis, Cokriging, Covariate.
Los avances en agricultura de precisión permiten a los investigadores obtener datos con más frecuencia y en detalle. Por ejemplo, es común colectar "en el transcurso" datos como lecturas de electro-conductividad del suelo. Esto crea la oportunidad de usar estas medidas como covariables para incrementar la precisión experimental de la variable de respuesta. Aún más, estas medidas están espacialmente relacionadas entre sí, creando la necesidad de métodos en los cuales la ubicación espacial representa un papel explícito en el análisis de los datos. Se analizan conjuntos de datos que contienen variables de respuesta y covariables espacialmente relacionadas, usando el método cokriging o el análisis espacial de covarianza. Aunque el método cokriging usa la estructura de correlación de la covariable, es una herramienta puramente predictiva. Alternativamente, el análisis espacial de covarianza permite la estimación de parámetros pero sin tener en cuenta la estructura de correlación de la covariable. El presente artículo propone un método que tiene en cuenta la correlación en la covariable, así como la correlación entre la covariable y la variable de respuesta, permitiendo la estimación de los parámetros del modelo. De la misma manera, este método permite el análisis espacial de covarianza cuando la variable de respuesta y la covariable no están colocalizadas.
Palabras clave: análisis de covarianzas, covarianza espacial, cokriging, covarianza.
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References
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv31n1a06,
AUTHOR = {Hooks, Tisha and Marx, David and Kachman, Stephen and Pedersen, Jeffrey and Eigenberg, Roger},
TITLE = {{Analysis of Covariance with Spatially Correlated Secondary Variables}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2008},
volume = {31},
number = {1},
pages = {95-109}
}