The Use of Model Reduction Method in the Combined Analysis of Two Randomized Complete Block Designs - Muhammad Tri Harsono; Edwin Russel; Riza Sawitri; Widiarti; Faiz A.M. Elfaki (Magister Program of Mathematics, Universitas Lampung, 2026)
Randomized Complete Block Design (RCBD) is an experimental design frequently used to control variability due to confounding factors. This design groups experimental units into relatively homogeneous blocks. However, the RCBD mathematical model contains linear constraints on the treatment and block effect parameters, which causes the design matrix to be non-full rank. Structural problems become more complex when combining two RCBD models in one analytical framework to expand information. This study applies the Model Reduction Method (MRM) to the combination of two RCBD models, focusing on the formation of a full rank model, parameter estimation using the Least Squares method, and evaluation of the estimator properties based on the Best Linear Unbiased Estimator (BLUE) criteria. This study also includes simulations using SAS 9.4 software to assess the performance of parameter estimation and hypothesis testing. The results demonstrate that MRM is effective in transforming a non-full rank model into a full rank model. Parameter estimation in the full rank model produces an estimator that is unbiased and has minimum variance, in accordance with the BLUE criteria. The results of the hypothesis testing show that the model obtained has good test power under low error variance conditions, and continues to show consistent performance reaching a value of one under all error variance conditions as the parameter distribution increases.