D-Efficiency and resolution?

[#1]

I was wondering if you can use the D-Efficiency to determine the resolution of a design.

For example, a D-Efficiency of 60% automatically enables a resolution III design.

Does anybody know if this is possible? Does anybody know a study analyzing this?

Thanks a lot

[#2 · Accepted solution]

You are confusing design methods. You can compute the D-efficiency for any design and so it can be used to compare any two or more designs. The resolution of a design is only a characteristic of a regular fractional factorial design (specific method) and so it can only be used to compare two or more such designs.

[#3]

I would recommend reading Goos and Jones's Optimal Design of Experiments if you want to find out more about design evaluation measures including D-efficiency.

[#4]

I should add that the D-efficiency is model dependent...

I believe that all the regular fractional factorial designs for a given set of factors are 100% D-efficient for the intended first-order model (i.e., main effects only) as required by screening principles. These designs, though, would exhibit a wide range of resolutions. So, no, you cannot use the D-efficiency to determine the resolution.

You can prove this conclusion to yourself:

1. Select DOE > Classical > Screening Design.
2. Enter a reasonable number of factors, say 10, in Add N Factors.
3. Click Continuous. (The conclusion does not depend on the type of factor.)
4. Click Continue.
5. Click Continue again to select one of the fractional factorial designs.
6. Choose a (regular) Fractional Factorial design, note the resolution of this design, and click Continue.
7. Open Design Evaluation > Design Diagnostics, and note the D-efficiency. (Bet is 100%)
8. Click Back.
9. Repeat steps 4-8 with a different selection for the Fractional Factorial designs.

What did you find?

[#5]

Thank you for your answers. You were right, a reg. fractional factorial design has a D-Efficiency of 100%.

We already developed our design and send it to respondents (14 vignettes devided into two sets - 7 vignettes each). We only have relied on the D-Efficiency (97%). Currently we are evaluating the data and I am still not sure whether we can reliably estimate the main effects (or even interaction effects).

[#6]

If the D-efficiency of 97% that you quote is for the main effects model, then the design will enable you to estimate that model. If it is for the model with main effects and 2-factor interactions, then you will be able to estimate that model.

D-efficiencies are most useful for comparing similar designs. A D-efficiency of 100% indicates that the design is completely orthogonal for the model. A D-efficiency of <100% indicates some correlation of model effects. You might want to use some of the other design diagnostics to explore esimatiion efficiency of the individual effects. The color map on correlations and there is also a useful diagnostic called "estimation efficiency".