The Effective Model Selection algorithm expresses the response, Y, in terms of two responses YME and Y2nd, so that Y = YME + Y2nd.
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YME is the predicted value obtained from a regression of Y on the main effects and fake factors.

There is no need to include the block factor in YME because of the foldover structure of the design. The block factor is included in Y2nd.
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Stage 2: The response Y2nd is used to identify secondorder effects. Stage 2 considers all secondorder terms in the active main effects from Stage 1 and determines a subset of these containing effects considered to be active.

2.

Using YME, main effects are tested against this estimate. Main effects with pvalues less than a threshold pvalue are considered active. The threshold values are the following:

3.

If no main effect has a pvalue less than the threshold value, conclude that there are no active main effects and no active twofactor effects. The procedure terminates.

1.

The absolute values of the estimated effects, using YME as the response, are ordered from largest to smallest.

2.

For each 1 ≤ i < m, the effect with the ith largest absolute value is tested against the adjusted residual sum of squares for the model containing that effect and all effects with larger absolute values.

3.

The effects in the model with the smallest pvalue are considered to be the active effects.

4.

1.

The variability for Y2nd is tested against the error estimate from Stage 1 to determine if there is additional variability due to secondorder effects.

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If the pvalue for this test exceeds the threshold value the procedure terminates and no active secondorder effects are identified.

2.

If the pvalue for this test is less than or equal to the threshold value, then subsets of size k, k = 1,2,3,... are successively tested, starting with k = 1.

3.

For each k, the residual sum of squares for each subset of that size is tested against the error estimate from Stage 1. The subset with the smallest RMSE is identified.

4.

The procedure continues until a k is found whose RMSE is smaller than the Stage 1 RMSE.

5.

The effects in the subset preceding the one that corresponds to the terminal value of k are considered to be the active twofactor effects.
