Please use this identifier to cite or link to this item: http://repository.futminna.edu.ng:8080/jspui/handle/123456789/12852
Title: Missing Observations in Split-Plot Central Composite Designs: The Loss in Relative A-, G-, and V- Efficiency
Authors: Yakubu, Yisa
Chukwu, AU
Keywords: Missing Observations
Efficiency Loss
Prediction variance
Issue Date: Feb-2021
Publisher: Journal of Applied Sciences and Environmental Management, UNIPORT
Citation: Yakubu and Angela (2021). Missing Observations in Split-Plot Central Composite Designs: The Loss in Relative A-, G-, and V- Efficiency
Abstract: The trace (A), maximum average prediction variance (G), and integrated average prediction variance (V) criteria are experimental design evaluation criteria, which are based on precision of estimates of parameters and responses. Central Composite Designs(CCD) conducted within a split-plot structure (split-plot CCDs) consists of factorial (𝑓), whole-plot axial (𝛼), subplot axial (𝛽), and center (𝑐) points, each of which play different role in model estimation. This work studies relative A-, G- and V-efficiency losses due to missing pairs of observations in split-plot CCDs under different ratios (d) of whole-plot and sub-plot error variances. Three candidate designs of different sizes were considered and for each of the criteria, relative efficiency functions were formulated and used to investigate the efficiency of each of the designs when some observations were missing relative to the full one. Maximum A-efficiency losses of 19.1, 10.6, and 15.7% were observed at 𝑑 = 0.5, due to missing pairs 𝑓𝑓, 𝛽𝛽, and 𝑓𝛽, respectively, indicating a negative effect on the precision of estimates of model parameters of these designs. However, missing observations of the pairs- 𝑐𝑐, 𝛼𝛼, 𝛼𝑐, 𝑓𝑐, and 𝑓𝛼 did not exhibit any negative effect on these designs' relative A-efficiency. Maximum G- and Vefficiency losses of 10.1,16.1,0.1% and 0.1, 1.1, 0.2%, were observed, respectively, at 𝑑 = 0.5, when the pairs- 𝑓𝑓, 𝛽𝛽, 𝑐𝑐, were missing, indicating a significant increase in the designs' maximum and average variances of prediction. In all, the efficiency losses become insignificant as d increases. Thus, the study has identified the positive impact of correlated observations on efficiency of experimental designs.
URI: http://repository.futminna.edu.ng:8080/jspui/handle/123456789/12852
ISSN: PRINT ISSN 1119-8362
Electronic ISSN 1119-8362
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