Balance, Orthogonality and Fractionally Weighted BootstrappingHi,
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?
DOERe: Balance, Orthogonality and Fractionally Weighted BootstrappingAssuming that the design was balanced and orthogonal, such changes will introduce an imbalance and a loss of orthogonality.
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?
Re: Balance, Orthogonality and Fractionally Weighted BootstrappingWhat is unique about "DOE context" with regard to orthogonal design? Why do you think that the design must be orthogonal?
Re: Balance, Orthogonality and Fractionally Weighted BootstrappingGiven 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?
Re: Balance, Orthogonality and Fractionally Weighted BootstrappingEvery 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.
