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A methodology is proposed to jointly model treatments with quantitativelevels measured throughout time by combining the response surface andgrowth curve techniques. The model parameters, which measure the effectthroughout time of the factors related to the second-order response surfacemodel, are estimated. These estimates are made through a suitable transformationthat allows to express the model as a classic MANOVA model,so the traditional hypotheses are formulated and tested. In addition, theoptimality conditions throughout time are established as a set of specificcombination factors by the fitted model. As a final step, two applicationsare analyzed using our proposed model: the first was previously analyzedwith growth curves in another paper, and the second involves two factorsthat are optimized over time.

Tipo de documento: Artículo - Article

Palabras clave: Growth curves, Multiple optimization, Response surfaces, Second order models





Fuente: http://www.bdigital.unal.edu.co


Introducción



Revista Colombiana de Estadística Junio 2013, volumen 36, no.
1, pp.
153 a 176 Response Surface Optimization in Growth Curves Through Multivariate Analysis Optimización de superficies de respuesta en curvas de crecimiento a través de análisis multivariado Felipe Ortiz1,a , Juan C.
Rivera2,b , Oscar O.
Melo2,c 1 Facultad de Estadística, Universidad Santo Tomás, Bogotá, Colombia 2 Departamento de Estadística, Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá, Colombia Abstract 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, Second order models. Resumen 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 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 ...






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