MODELING THE YIELD OF SOYBEAN (Glycine max (L.) Merrill) USING A FOUR COMPONENT MIXTURE EXPERIMENT IN THE PRESENCE OF VARIATION CREATED BY TWO PROCESS VARIABLES WITHIN SPLIT-PLOT DESIGN

Abstract

Use of mixture design has become well-known in statistical modeling due to its utility in predicting any mixture's response and thus serving as the foundation for optimizing the predicted response on blends of different components. In most split-plot designs utilizing mixture-process variable settings, restricted randomization always exist. This study's primary goal was to find the best split-plot design (SPD) for performing the Glycine max experiment with the settings mixture-process variables. The SPD was made up with use of a Simplex Centroid Design (SCD) of four mixture blends and a 22 factorial design with a Central Composite Design (CCD) of the process variable and this was compared with six different designs of split-plot structure arrangement. The JMP software version 15 was used to create D-optimal split-plot designs. The study compared the constructed designs' relative efficiency using A-, D-, I-, and G- optimality criteria respectively. Furthermore, use of graphical technique (fraction of design space plot) was used to display, explain, and evaluate experimental designs' performance in terms of precision of the six designs' variance prediction properties. Results showed that arranging subplots with more SCD points as compared to the pure mixture design points within SPD with two high process variables provided more precise parameter estimates. Also use of the restricted maximum likelihood method was employed to estimate parameter values within the SPD. The current study thoroughly investigated estimation of parameters from MPV settings in conjunction with CCD within SPD using the Scheffe polynomial and Cox mixture models to predict optimal responses of Glycine max yield. The predicted maximum optimum yield for the total number of seeds per plant stem of Glycine max was 102.06 equivalent to 15.7832𝑔 using the screening methodology. Furthermore, the expected response from the simulated-based technique for {4, 2} SCD and the actual results obtained from field experiments using MPV settings within SPD were compared. The variety of Glycine max Blyvoor was found to have higher production in terms of yield as compared to R 184. Thus the study recommends farmers to use Blyvoor as an alternative variety. In addition, the study also recommends farmers to embrace SPDs in the context of mixture settings formulations in order to measure the interaction effects of both the mixture components and the processing conditions like soil pH and the seeding rate.