Optimal Designs for Mixed-Effects Models with Two Random Nested Factors

• Activity Number: 246
• Type: Topic Contributed
• Date/Time: Tuesday, August 13, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical & Engineering Sciences*
• Author(s): Ivelisse Avilés*+
• Affiliation(s): National Institute of Standards & Technology
• Keywords: Assembled Designs ; Crossed and Nested Factors ; D-Optimality ; Experimental Design ; Maximum Likelihood ; Variance Components

Abstract

The main objective of this talk is to provide experimental designs for the estimation of fixed effects and two variance components in the presence of nested random effects. Random nested factors arise from quantity designations such as lot or batch and from sampling and measurement procedures. We introduce a general class of designs for mixed-effects models with random nested factors, called assembled designs, where the nested factors are nested under the treatment combinations of the crossed factors. We provide parameters and notation for describing and enumerating assembled designs. Theorems establishing conditions for existence and uniqueness of D-optimal assembled designs for the case of two variance components are presented. Specifically, we show that, in most practical situations, designs that are most balanced (i.e., where the samples are distributed as uniformly as possible among batches) result in D-optimal designs for maximum likelihood estimation.