Optimal Designs for Correlated Data

Correlated data occur naturally and frequently in small and big data, and methods for analyzing correlated data have seen great advances in recent decades. Attention to design issues typically lags behind that paid to estimation issues, and it is also true that construction of optimal designs for models with correlated data lags that for models with uncorrelated data. A key problem in constructing optimal designs for models with correlated observations is that more technical assumptions are needed than when models have uncorrelated errors. In the former case, approximations to the information matrix are needed, and there are also no general and effective algorithms for finding various types of optimal designs. In addition, there are no tools to confirm optimality of a design. This article first gives a short review of optimal designs for linear models, before we focus on a review of finding optimal designs for models with correlated data. We discuss various approaches and their difficulties in a few selected areas. Along the way, we provide examples and recommend use of nature-inspired metaheuristic algorithms to find all kinds of optimal designs for any criterion or model with or without correlated data.