1Universidad Santo Tomás, Facultad de Estadística, Bogotá, Colombia. Lecturer. Email: andresortiz@usantotomas.edu.co
2Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística, Bogotá, Colombia. MsC in Statistics. Email: jcriverar@unal.edu.co
3Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística, Bogotá, Colombia. Associate professor. Email: oomelom@unal.edu.co ]]>
A methodology is proposed to jointly model treatments with quantitative levels measured throughout time by combining the response surface and growth curve techniques. The model parameters, which measure the effect throughout time of the factors related to the second-order response surface model, are estimated. These estimates are made through a suitable transformation that allows to express the model as a classic MANOVA model, so the traditional hypotheses are formulated and tested. In addition, the optimality conditions throughout time are established as a set of specific combination factors by the fitted model. As a final step, two applications are analyzed using our proposed model: the first was previously analyzed with growth curves in another paper, and the second involves two factors that are optimized over time.
Key words: Growth curves, Multiple optimization, Response surfaces, \linebreak Second order models.
En este artículo se propone una metodología para modelar conjuntamente tratamientos con niveles cuantitativos medidos en el tiempo, mediante la combinación de técnicas de superficies de respuesta con curvas de\linebreak crecimiento. Se estiman los parámetros del modelo, los cuales miden el efecto en el tiempo de los factores relacionados con el modelo de superficie de respuesta de segundo orden. Estas estimaciones se realizan a través de una transformación que permite expresar el modelo como un modelo clásico de MANOVA; de esta manera, se expresan y juzgan las hipótesis tradicionales. Además, las condiciones de optimización a través del tiempo son establecidas para un conjunto de factores específicos por medio del modelo ajustado. Como paso final, se analizan dos aplicaciones utilizando el modelo propuesto: la primera fue analizada mediante curvas de crecimiento en otro artículo, y la segunda consiste en dos factores que son optimizados a lo largo del tiempo.
Palabras clave: curvas de crecimiento, optimización múltiple, superficies de respuesta, modelos de segundo orden.
Texto completo disponible en PDF
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv36n1a09,
AUTHOR = {Ortiz, Felipe and Rivera, Juan C. and Melo, Oscar O.},
TITLE = {{Response Surface Optimization in Growth Curves Through Multivariate Analysis}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2013},
volume = {36}, ]]>
number = {1},
pages = {153-176}
}