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Balance, Orthogonality and Fractionally Weighted Bootstrapping

Elef

Hi,

To use the Fractional Weighted Bootstrap approach (method is described on the attached file and here) I need to use the Freq option on Fit Model menu.

However, Freq works as following, “Suppose that a row has a frequency f. Then the computed results are identical to those for a data table containing f copies of that row, each having a frequency of one.”

My question is, by adding copies of a row in a DoE context doesn't it break the balance and the orthogonality of the DoE?

Gotwalt-Ramsey Frankfurt 2018 Rev 07.pdf

Accepted answers

Mark_Bailey

Every design represents trade-offs. Some trade-offs are easy, some are difficult. The benefit of a balanced and orthogonal design is that it minimizes the variance of the estimates of the model parameters, but balance can come at a high cost in terms of the size of the design or constraints on the model and other things. Confounding is an extreme condition that means that two effects are inseparable; their estimates have infinite variance. In between orthogonal and confounded is correlated. You can still estimate the parameters that are correlated, albeit with higher variance. Trade-off: you must endure some correlation in the estimates if you want to use the model selection technique that you cited.

All comments

Mark_Bailey

Assuming that the design was balanced and orthogonal, such changes will introduce an imbalance and a loss of orthogonality.

Elef

@Mark_BaileyThis is what I understand too, and this is why bootstrapping or CV is not a choice in DoE context however, the Fractional Weighted boostrap method claims that is suitable for DoE so, what am I missing?

Mark_Bailey

What is unique about "DOE context" with regard to orthogonal design? Why do you think that the design must be orthogonal?

Elef

Given that an orthogonal design results independed factors, then I am expecting to estimate the effect of the "main effects" and their interactions in the response without having confounding problems. Isn't this a huge benefit for using DoE?