Optimal Design and Planning for Random Effect Models and Models with Measurement Errors.

Abstract

This project addresses optimal design problems for linear mixed models with covariates (mixed ANCOVA models), and linear fixed models with measurement errors. First, we examine ANCOVA mixed models, focusing on efficient treatment allocations. We develop optimal designs using a general framework based on D-optimality, proposing a two-stage design approach to account for unknown parameters. In this approach, variances of random effects across treatment groups are considered distinct. Second, we formulate A-optimal designs for measurement error models, addressing errors in the response alone or in both response and explanatory variables. We propose that optimal designs for models with measurement errors significantly outperform classical designs. Furthermore, our results in A-optimal design for the models with measurement errors in both explanatory and response variables provide significantly greater efficiencies compared to classical designs.