Application of Response Surface Methodology in Modelling a Farm Production Process in the Presence of Random-Effects

Abstract

Response Surface Methodology (RSM) for several explanatory variables and one response variable in the presence of random-effects was considered. In past studies, an assumption of non-randomness for explanatory variables was made. However, emerging situations reveal that randomness of explanatory variables is an aspect worth consideration (Kipchumba, 2008). In this thesis, a Random-effects Response Surface Model (RRSM) which is applicable to such situations is developed. The Bayesian approach is used to estimate the RRSM. A simulation study was undertaken to test the practicability of the RRSM and later, real data on maize farming in Eldoret East District of Kenya was used. WinBUGS and R Statistical Programming Packages were used in analysis. The simulation results showed that RRSM clearly reveals the randomness of explanatory variables when modeling a farm production process in the presence of random effects. When real data was used, RRSM similarly revealed the randomness in the real data.