Definitive? Really? I’m going to be taking a close look at definitive screening designs and I’ll try and not get hung-up on the name: calling them DSDs should solve that problem!
DSDs represent a revolutionary approach to designing screening experiments. I want to take a look at the motivation behind these designs and explore their characteristics in relation to traditional screening designs. DSDs are highly efficient in the use of resources required to conduct an experiment, but that efficiency can sometimes come at the price of more complexity when it comes to analysing the experiment data. I want to take a look at the assumptions that underpin the designs and how those assumptions impact modelling of the experimental results.
Traditionally fractional factorial designs are used to identify a large number of effects with a minimum number of runs. The efficiency of these designs is achieved through the use of aliasing patterns that result in confounding between specific effects. The principle of sparsity-of-effects leads us to believe that not all the effects will be important. If this assumption is correct the we can exploit the projection property of factorial designs that allow us to collapse the fractional factorial design into a higher-resolution design containing only the active effects. If the assumption is incorrect then the geometry of the design allows it to be folded-over to increase the design resolution.
The major challenge of factorial designs is one of ambiguity:
- Resolution III designs confound main effects with two-factor interactions. Resolving this ambiguity generally requires the practitioner to conduct additional experimental runs.
- Resolution IV designs are twice as large and have a more complex aliasing structure. Two factor interactions are confounded with each other which. Resolving the ambiguity associated with these estimates requires the assumption of strong heredity. Without being able to use this guiding principle follow-up work is often required.
- Designs are commonly augmented with centre points to assess curvature. From a modelling perspective measuring curvature means estimating quadratic effects. Whilst centre-points allow a global assessment of curvature, the effects are confounded and cannot be estimated individually.
Definitive screening designs seek to overcome these limitations.
I’ve articulated the motivation of DSDs in relation to factorial designs. But there are other types that can be used. In the whelm of classical designs there are Plackett-Burman designs and for computer generated designs there is the D-optimal algorithm. I will be referring to all these design types as I perform a closer review of the characteristics of a DSD. But first here is a summary of the key characteristics.
Summary of Characteristics
- The designs have three levels
- The number of runs is (2f+1) where f is the number of factors
- Main effects are not confounded with two-factor interactions
- Two-factor interactions may be correlated but are not fully confounded
- All quadratic effects are estimable
- Quadratic effects are correlated with two factor interactions but are not confounded with main effects
- Designs have fold-over properties similar to the projection property of factional designs
I have provided a high-level summary of the characteristics of a DSD and framed these properties in relation to those of factorial designs.
I want to take a closer look at each of the characteristics. Trying to do so in a single posting will not do them justice. For example, whilst the number of runs may be smaller, I want to understand the impact this has on power of estimation; and I want to know how the number of runs compares not only to a factorial design but also D-optimal designs. So I’ll be writing about each of these characteristics in separate posts.