Reduced model in DOE

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    Hi all,
    1.I would like to ask why we should reduced model in classical DOE,
    instead use full model. In addition, while we use reduced model, should we reduced the term of not significant  one by one. If yes, Why? 
    2. If in full model the lack of fit (curvature) is not significant, but  significant during reduced term. Should we go RSM direclty?


    Ken Myers

    Hi Anderson,
    Here’s my take on basic empirical model development with classical DOE’s:
    1a. When developing an empirical model you want to include only the terms that are statistically significant.  These terms are the ones that have the greatest likelihood of providing an explanation of the observed effects.  Any additional non-significant terms would produce a poorer predictive model.
    1b. Empirical model development is part science and part art.  That means there are no specific rules supporting how many terms should be eliminated at each stage of the process.  I typically remove one term at a time, but sometimes find myself removing as many as three.  When eliminating main effects, you should consider removing any interactions that contain the non-significant main effects.  Minitab helps by forcing you to follow this rule of thumb.
    2.  When determining the significance of curvature in a model always use the final reduced model.  If lack of fit is NOT significant from the reduced model, then your process could benefit by additional optimization through the use of RSM.
    Hope this helps.



    Hi Ken,
    Thank you, it did help. But I don’t quite understand the item 2, why you say if the final reduced term, lack of fit test NOT significant, go RSM would benefit. In general, only did RSM, once we find lack of fit test significant, right?
    2nd, if we have two response, if one response, lack of fit, significant, but the other one response, lack of fit, NOT significant, should we do RSM. If do, how to do?
    thanks in advance,     


    Robert Butler

      Your initial post suggests the following:
         1. You have run some kind of experimental design.
         2. You have taken the results of the design and put the X’s and Y’s in some kind of spreadsheet and run a regression.
         3. You do not have access to any kind of stepwise regression software (forward selection, forward selection with replacement, etc.) so, if you are interested in model reduction, you will have to do it manually.
         4. Your computer package has some kind of test for lack-of-fit.
       If the above is true then your initial post also suggests:
       a. You are depending on computer generated numeric printout.
       b. You have not examined your residual plots at any time during the process.
        If points 1-4 are true then I would recommend the following:
       1. Normalize all of your X’s from -1 to 1 to put them on a level playing field. Regressions can be unduly influenced by numeric differences in the X’s.
       2. Since you don’t know what type of SS your program is using for variable assessment perform backward elimination (i.e. removal of non-significant terms) one variable at a time.   Remove only one variable at a time always eliminating the least significant variable first. Usually, interaction terms will disappear before main effects but this is not always the case.  There are many instances where the interaction is significant but the main effects are not. In cases of this type your model is telling you that the “total is greater than the sum of the parts.”
       Non-significant terms are removed from a model because, for the data you are examining, the effect of changing these variables, over the ranges you have examined, produces an effect that is not significantly different from the random variation in the data.  Thus, your data is suggesting the non-significant variables have no appreciable impact on your process.
     3. At each stage in your backward elimination process do a residual analysis of the reduced model (i.e. plot the residuals against the predicted values, against the various X’s and against anything else that makes sense)  The fact that you are somehow reducing a model to a point where lack-of-fit becomes significant after the elimination of a non-significant term suggests you may have one or more odd data points driving your regression. 
    4. Plot your data some more.  Plot the Y’s against the X’s.  If you know the time sequence of your data, plot the data against time. I realize there are many tests for various and sundry aspects of regression but you should never forget that residual analysis is the core of regression analysis.  If you don’t perform residual analysis every time you attempt to build a regression model you are shirking your responsibility as a Six Sigma professional and reducing your roll to that of button pusher.

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