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Level II

## Balance, Orthogonality and Fractionally Weighted Bootstrapping

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 ta...

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?

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Staff

## Re: Balance, Orthogonality and Fractionally Weighted Bootstrapping

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.

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Staff

## Re: Balance, Orthogonality and Fractionally Weighted Bootstrapping

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

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Level II

## Re: Balance, Orthogonality and Fractionally Weighted Bootstrapping

@markbaileyThis 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?

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Staff

## Re: Balance, Orthogonality and Fractionally Weighted Bootstrapping

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

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Level II

## Re: Balance, Orthogonality and Fractionally Weighted Bootstrapping

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?

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Staff

## Re: Balance, Orthogonality and Fractionally Weighted Bootstrapping

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.

Learn it once, use it forever!
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