On the Compounds of Hat Matrix for Six-Factor Central Composite Design with Fractional Replicates of the Factorial Portion
Year: 2017
Type: article
Abstract: The bahaviours of the first compound of the hat matrix and the determinant-based loss criterion are examined for effects of a missing observation in three configurations of six-factor central composite design, varying in factorial portion. The hat matrix varies between one design configuration and another but remains unchanged within same design configuration with different defining relations. The diagonal entries of each corresponding hat matrix associated with a factorial point, an axial point and a center point respectively correspond to the losses computed using the determinant-based criterion. Loss due to missing center point in the three categories of design is very minimal when compared with loss due to either missing factorial point or missing axial point. The configuration with one-quarter fractional factorial portion attracts significantly higher losses to a missing observation of either factorial, axial or center portion when compared with either the configuration with one-half fractional factorial portion or the configuration with complete factorial portion. This is possibly because the configuration with one-quarter fractional factorial portion is near saturated. Variances associated with parameter estimates are minimum for the design category with complete factorial portion and maximum for the design category with one-quarter fractional factorial portion. Interestingly, the design category that minimizes the variances also minimizes the losses.
Author: M. P. Iwundu
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: diamond
OpenAlex ID: W2746240363