Open AccessD-Optimal Split-plot Designs With Random Whole Plot Factor and Fixed Sub-plot Factor
Author(s) -
Oluwole Adegoke Nuga,
Abba Zakirai Abdulhamid,
Shobanke Emmanuel Omobola Kayode
Publication year - 2021
Publication title -
international journal of statistics and probability
Language(s) - English
Resource type - Journals
eISSN - 1927-7040
pISSN - 1927-7032
DOI - 10.5539/ijsp.v11n1p1
Subject(s) - mathematics , restricted randomization , plot (graphics) , estimator , statistics , split plot , variance (accounting) , randomization , accounting , business , randomized controlled trial , medicine , randomized block design , surgery
This study examines design preference in Completely Randomized (CR) split-plot experiments involving random whole plot factor effect and fixed sub-plot factor effect. Many previous works on optimally designing split-plot experiments assumed only factors with fixed levels. However, the cases where interests are on random factors have received little attention. These problems have similarities with optimal design of experiments for fixed parameters of non-linear models because the solution rely on the unknown parameters. Design Space (DS) containing exhaustive list of balanced designs for a fixed sample size were compared for optimality using the product of determinants of derived information matrices of the Maximum Likelihood (ML) estimators equivalent to random and fixed effect in the model. Different magnitudes of components of variance configurations where variances of factor effects are larger than variances of error term were empirically used for the comparisons. The results revealed that the D-optimal designs are those with whole plot factor levels greater than replicates within each level of whole plot.