| Summary: | In this research, a class of nonlinear split plot design models where the mean function of the split-plot model is not linearizable is presented. This was done by fitting intrinsically nonlinear split-plot design (INSPD) models using the Chapman-Richards function. The fitted model parameters were estimated using estimated generalized least square (EGLS) techniques based on Gauss-Newton with Taylor series expansion by minimizing their respective objective functions. The variance components for the whole plot and subplot random effects are estimated using the restricted maximum likelihood estimation (REML) technique. The adequacy of the fitted INSPD model was tested using four median adequacy measures: resistant coefficient of determination, resistant prediction coefficient of determination, resistant modeling efficiency statistic, and median square error prediction statistic based on the residuals of the fitted models, which are influenced by the parameter estimation techniques being applied. Akaike's Information Criteria, Corrected Akaike's Information Criteria, and Bayesian Information criteria statistics were used to select the best parameter estimation technique. The results obtained showed that the Chapman-Richards SPD model via EGLS-REML fitted model is a good fit that is adequate, stable, and reliable for prediction compared to EGLS-MLE and OLS fitted models.
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