A COMPARISON OF CHAPMAN-RICHARDS AND JOHNSON-SCHUMACHER SPLIT-PLOT DESIGN MODELS
Keywords:
Split-Plot design model, Chapman-Richards function, Johnson-Schumacher function, parameter estimation, information criteria, adequacy measuresAbstract
In this research, intrinsically nonlinear split-plot design models (INSPDMs) are formulated and compared by tailoring the mean part of the split-plot design model (SPDM) to follow Chapman-Richards and Johnson-Schumacher functions. The fitted INSPDMs parameter estimates are obtained by applying the estimated generalized least squares (EGLS) technique. The whole plot and subplot random effects variance components of the INSPDMs are estimated using maximum likelihood estimation (MLE) and restricted maximum likelihood estimation (REML) techniques. The adequacy of the fitted INSPDMs is tested and compared by applying four median adequacy measures (MAM), namely, the resistant coefficient of determination, the resistant prediction coefficient of determination, the resistant modeling efficiency statistic, and the median square error prediction. Also, Akaike’s Information Criteria (AIC), Corrected Akaike’s Information Criteria (AICC), and Bayesian Information Criteria (BIC) statistics are applied to select the best parameter estimation technique and best model. The results obtained showed that EGLS-REML produced better estimates when compared to EGLS-MLE, and the fitted INSPDM using the Chapman-Richards function is adequate, reliable, stable, and a good fit compared to INSPDM using the Johnson-Schumacher function based on the obtained MAM and IC values.
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