Statistica Sinica 26 (2016), 1021-1035
Abstract: An important issue in the design of experiments is the question of identifiability of models. This paper deals with a modelling process, where linear modeling goes beyond the simple relationship between input and output variables. Observations or predictions from the chosen experimental design are themselves input variables for an eventual output. Tools developed to analyze designs from algebraic statistics are extended to noisy, irregular designs. They enable an advanced study of model identifiability. Model building is opened towards higher order interactions rather than restricting the class of considered models to main effects or two-way interactions only. The new approach is compared to classical model building strategies in an application to a thermal spraying process.
Key words and phrases: Algebraic statistics, aliasing, identifiability, noisy design, vanishing ideal.