Hoteling's T-squared and DModX

Question

Hello All,

I have a customer who is looking for some insights in using Hoteling's T2 and DModX to improve model performance....see below.  We have talked about using both formulae in the profiler to find a "best" option, but I am not sure what the guidance would be for his question below.  Any ideas or thoughts?!

"As I’m working through some of the options for improving my model that we discussed last week, I am wondering how else I can use Hotelling’s T2 and DModX to improve my model.

I understand how I can bring those in with a prediction formula and use the profiler to help determine what are the best values for my factors (X’s), but is there another way I can bring them in to the model tuning process to help generate a model that is closer to the center of the model plane and has low deviation within the model plane?

I know a good model will have minimized values of these two statistics, but other than using them in the profiler, I’m not sure how I can use them to help improve the modeling process. Could I, for example, use them as part of a weighting function? If so, what is the appropriate way to do so?

I’m trying to think of how to use these statistics that describe deviations of data to (and within) the model plane as a way to improve how a model is built within JMP. Right now, I see how it’s used to find the optimal values of the X’s, but I don’t see how I can use them in other ways.

Any thoughts on this would be greatly appreciated."

Thanks,

Bill

malcolm_moore1 · Answer

Hi Bill,

I agree that DOE is the best way forward as your user needs to understand what is causing the out of control behaviour not just predict it. Even if your user can identify a better predictive model as a function of batch/time, this will be of little help in preventing future drastic swings in yield unless the process inputs that are also varying with batch/time can be identified as part of the model building process.

Malcolm

Bill_Worley · Answer

Thanks for your input and ideas Malcolm!

Here's a little more context.  We worked with the customer regarding his modeling approach last week and he talked about using DModX and T-square to help improve the model fit.  It is kind of a weird situation because he is looking at process yield for batch data and he was using Time Series to try and predict when they might see sharp drops or upticks in the yield.  He feels like Time Series offers the best predictive model for his needs.

Based on what we saw there is some odd phenomena that is contributing to these rather drastic swings in the yield and they are having trouble producing to a target value.  As I am writing this it seems like they would be best served running a DOE to try and ferret out some potentially important inputs they may have missed before trying to improve model performance.

Thanks again for your ideas and inputs.  I will reach out to the customer and see if he is open to a DOE.

Best,

Bill

malcolm_moore1 · Answer

Hi Bill, I'm assuming since your customer is referencing DModX they are using PLS as the modelling method? Do you know if other PLS software is using min DModX or T-squared as a model seletion criteria? If so, what is the evidence this results in a better (non-overfitted) model?

In the absence of that, I would try and change the conversation to model validation using hold-back to prevent over fitting and see how your user feels about using some hold-back strategy and validation PRESS as model selection criteria. Along with simplifing the model using VIP so that we avoid over-fitting. Stress the risk of over-fitting with some PLS approaches.