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Assembled Designs for Estimation of Location, Dispersion, and Random Effects



A Aviles, B E. Ankenman, J C. Pinheiro


In many experimental settings, different types of factors affect the measured response. The factors that can be set independently of each other are called crossed factors. Nested factors cannot be set independently because the level of one factor takes on a different meaning when other factors are changed. Random nested factors arise from quantity designations and from sampling and measurement procedures. The variances of the random effects associated with nested factors are called variance components. Factor effects on the average are called location effects. Dispersion effects are the effects of the crossed factors on the variance of a response. For situations where crossed factors have effects on the different variance components, then sets of dispersion effects must be identified and estimated to achieve robustness. The main objective of this research is to provide nearly D-optimal experimental design procedures for estimating the location effects of crossed factors, the variance components associated with two nested factors, and the dispersion effects that crossed factors may have on the two variance components.A general class of experimental designs for mixed-effects models with random nested factors, called assembled designs, is introduced in Ankenman, Avil s, and Pinheiro (2003). The use of assembled designs for robustness experiments is introduced. When there are dispersion effects, a heuristic algorithm for finding a nearly D-optimal assembled design with two variance components for a given budget is provided. Ready to use computer programs for the presented experimental design procedures and analysis technique are discussed. This research provides the practitioner with clear guidelines about the best design available for their needs.


assembled designs, crossed and nested factors, D-optimality, hierarchical nested design, location and dispersion effects, maximum likelihood, variance components


Aviles, A. , Ankenman, B. and Pinheiro, J. (2005), Assembled Designs for Estimation of Location, Dispersion, and Random Effects, Technometrics (Accessed June 15, 2024)


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Created March 1, 2005, Updated February 17, 2017