Order-Of-Addition Modeling

The current literature on order-of-addition experiments generally relies on main effects models constructed from pair-wise ordering (PWO) factors. This study constructs models utilizing interactions of PWO factors to explain variations that are best accounted for by the ordering of sets of three or more components. Orderof-addition orthogonal arrays are optimal for fitting the main effects PWO model, but they differ in terms of their susceptibility to bias due to model misspecification. A measure computed from the alias matrix is proposed to identify robust PWO designs, and is illustrated for cases with four and five components. Applications with constraints on the ordering and order-of-addition experiments with additional mixture proportion and factorial factors are discussed briefly. Two drug sequence experiments based on data from private consultations are used to compare the usefulness of different order-of-addition models.