Analysis of data from nonorthogonal multi-stratum designs

Split-plot and other multi-stratum structures are widely used in factorial and response surface experiments and residual maximum likelihood (REML) and generalized least squares (GLS) estimation is seen as the state-of-the-art method of data analysis for nonorthogonal designs. We analyze data from an experiment run to study the effects of five process factors on the drying rate for freeze dried coffee and find that the main-plot variance component is estimated to be zero. We show that this is a typical property of REML-GLS estimation which is highly undesirable and can give misleading conclusions. In the classical approach, it is possible to fix the main-plot variance at some positive value, but this is not satisfactory either. Instead, we recommend a Bayesian analysis, using an informative prior distribution for the main-plot variance component and implemented using Markov chain Monte Carlo sampling. Paradoxically, the Bayesian analysis is less dependent on prior assumptions than the REML-GLS analysis. Bayesian analyses of the coffee freeze drying data give more realistic conclusions than REML-GLS analysis, providing support for our recommendation.