Johnson–Schumacher Split-Plot Design Modelling of Rice Yield

In this research, an intrinsically nonlinear split-plot design model (INSPDM) is formulated and studied. It was formulated by fitting a Johnson–Schumacher (JS) function to the split-plot model mean function. The fitted model parameters are estimated using the estimated generalized least squares (EGLS) technique based on a Gauss–Newton procedure with Taylor series expansion, by minimizing the objective function of the model. The variance components for the whole plot and subplot random effects are estimated using restricted maximum likelihood estimation (REML) techniques. The adequacy of the fitted INSPDM was tested using four median adequacy measures: resistant coefficient of determination, resistant prediction coefficient of determination, the resistant modeling efficiency statistic, and the median square error prediction statistic based on the residuals of the fitted model. Akaike’s Information Criterion (AIC), Corrected Akaike’s Information Criterion (AICC) and Bayesian Information Criterion (BIC) statistics are used to select the best parameter estimation technique. The results obtained are compared with the techniques of ordinary least squares (OLS) and EGLS via maximum likelihood estimation (MLE). The results showed the model to be adequate, reliable, stable, and a good fit based on EGLS-REML when compared with OLS and EGLS-MLE fitted model parameter estimates.