How to deal with missing data?

[#1]

Hi,

Recently l ran a 2^4 factorial model for an extrusion experiment. I intend to model the quadratic terms including interaction terms.

however some of the points were a little ambitious and the extrusion failed. Hence, I was unable to collect certain responses for these points. I would like some advice on how to proceed. Should I repeat the experiment with less aggressive levels or can I just augment the design with axial points which is lower than the coded level of 1.

Thanks

[#2]

Either way can work. But if I had a choice I'd go with repeating the entire experiment again. And just so we're all clear who are reading this, a 2^4 full factorial experiment does not allow for estimation of quadrative effects. You've got to add runs...typically in the form of axial points, if possible spaced for rotatability, orthogonality of effects, or some other desirable design property.

[#3]

Hi P_Bartell,

Thank you for your advice. I'll add axial points to my current experiments to determine the quadratic effects.

Thanks and happy new year to you! 

[#4]

Here are my thoughts regarding loss of experimental units.  You don't say how many experimental units failed, so realize your options depend on this:

1. Is there another response variable(s) that quantifies the effect of the factors creating the lost extrusion(s)?  I remember when working with Dr. Taguchi, he would say those treatments may be the most informative in the experiment.

2. As Pete says, you can't estimate quadratic effects with a 2-level factorial.  You would need at least center points to estimate the departure from the linear assumption.

3. If you lost only one, try these options:

• Use the mean of the remaining treatments as a substitute for the missing run
• Use regression o estimate the missing run.   Run analyze fit model, enter a model with 1 less DF (usually the highest order effect). Save the model (Red triangle>Save Columns>Prediction Formula).  This will give you a prediction for the missing treatment.
• If you had predicted the results before running the experiment, try using your predicted result.

Do all 3 and see how well the results agree.  If they are in relative agreement, you can be confident in the analysis.  If not, then you have to think about running more runs.  Of course the additional runs may be in a different inference space so be aware of the "block" effect.

[#5]

Hi statman,

Thanks for your advice! Just to add on, I have run center points and from analysis, there was a deviation from the linear assumption. Thus, I'll be adding axial points in future experiments. As for the missing data, I'll try to use your advice and model from there again.

Thanks and have a happy new year!