A Bertalanffy-Richards Split-Plot Design Model and Analysis

Abstract

This research presents a class of nonlinear split plot design (SPD) model where the mean function of the SPD model is not linearizable. This was done by fitting intrinsically nonlinear split-plot design (INSPD) model using Bertalanffy-Richards function. Estimated Generalized Least Square (EGLS) technique based on Gauss-Newton with Taylor series expansion by minimizing the model objective function was used for estimating the fitted INSPD model parameters. The variance components for the whole plot and subplot random effects are estimated using Restricted Maximum Likelihood Estimation (REML) and Maximum Likelihood Estimation (MLE) techniques. These techniques are established and paralleled with Ordinary Least Square (OLS) technique for a balanced 3¹ x 4² replicated mixed Level SPD data from Institute of Agricultural Research, Ahmadu Bello University, Zaria. The adequacy of the estimated INSPD model parameters for the EGLS and OLS are compared using four median adequacy measures. They are resistant coefficient of determination, resistant prediction coefficient of determination, resistant modeling efficiency statistic, and median square error prediction statistic. Also, Akaike’s information criterion, corrected Akaike’s information criterion, and Bayesian information criterion are used to select the best parameter estimation technique. The results obtained showed that the Bertalanffy-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 techniques.