Response surface model with neighbour effects and correlated observations

Article type: Research Article

Authors: Varghese, Eldho^{; *} | Jaggi, Seema | Sarika,

Affiliations: Indian Agricultural Statistics Research Institute, Library Avenue, New Delhi, India

Correspondence: [*] Corresponding author: Eldho Varghese, Indian Agricultural Statistics Research Institute, Library Avenue, New Delhi-110 012, India. E-mail: eldho@iasri.res.in.

Abstract: Two of the underlying assumptions in the classical response surface model are that the response from a unit to a particular treatment combination does not affect the response on the neighbouring units and the errors are uncorrelated. These assumptions are concerned with the treatment effect and the environmental effect. Violation of these assumptions results in neighbour effects between units and dependent or correlated observations. The experimental situation being considered in this study is that the experimental units experience the neighbour effects from adjacent units and the observations are correlated as well. The conditions for rotatability, the variance function and designs with neighbour effects under correlated structure of errors (equi-correlated and auto-correlated) for first order response model have been studied.

Keywords: Neighbour effects, border units, equi-correlated errors, auto-correlated errors, rotatable designs

DOI: 10.3233/MAS-2012-0235

Journal: Model Assisted Statistics and Applications, vol. 8, no. 1, pp. 41-49, 2013