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.
