We derive randomization-based models for experiments with a chain of randomizations. Estimation theory for these models leads to formulae for the estimators of treatment effects, their standard errors and expected mean squares in the analysis of variance. We discuss the practicalities in fitting these models and outline the difficulties that can occur, many of which do not arise in two-tiered experiments.
"Randomization-based models for multitiered experiments: I. A chain of randomizations." Ann. Statist. 44 (3) 1131 - 1164, June 2016. https://doi.org/10.1214/15-AOS1400