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Optimization of a group of responses using fit group option and prediction profiler

SimonFuchs

Dear JMP-Experts,

We optimize very often a set of responses (which we fit separately before) with the fit group option.

Now the question rised, how the fit group prediction profiler optimizes several responses in parallel, since often not for every response the optimal factor setting is choosen, but rather a compromise is shown? Also if we click several times on maximize desirability, the factor setting is changing (seems like a global fit minimum is not achieved after first fit). How can we achieve the optimal factor combination here with just one click (we already played around with the desirability function options, but didnt progress).

Thanks for your help!

Accepted answers

Victor_G

Hi @SimonFuchs,

You can have more information about the optimization done by the profiler here : Desirability Profiling and Optimization (jmp.com)

To answer your first question, you'll find on this page the answer : "The overall desirability for all responses is defined as the geometric mean of the desirability functions for the individual responses."

So as you guess, if you have several responses to optimize, the Profiler will try to find the best compromise that reach an overall best desirability score (weighted geometric mean of individual desirability score for each responses). You can specify different weight for the responses (called "importance", CTRL+click on desirability curve of the response to specify goal, high/medium/low values and importance) if you want to emphasize the optimization on some responses compared to others. The importance, slope/curve of the desirability functions and objective (maximize/minimize/reach target/none) have all an influence on the optimum found.

The true global optimum is not always possible to find, as there may be no exact solution to the problem you try to optimize (or multiple solutions may be possible). This is why you may have sometimes slightly different answers, depending on the optimization process: convergence tolerance, number of iterations, method used (depending on the problem: Construction of Desirability Functions (jmp.com)) : Maximization Options Window (jmp.com) but also depending on your responses' characteristics, like uncertainty (the optimum found will only be an approximation of the true unknown optimum), desirability profiles (a steep slope in the desirability profile may have a less variation in the differences from several optimums found than a slower slope (=less constraint in the optimization)), and values of your factors (but JMP uses several random starts for the optimization process, so this shouldn't be a big problem and the probability to get stuck in a local optimum should be limited).

I hope this complementary response will help you,

All comments

statman

I'm not sure I can provide much advice, but here are my thoughts:

Note: Much depends on how you got the data you are trying to model.

1. First, you should check for correlation among your multiple Y's (Analyze>Multivariate Methods>Multivariate). When there is significant positive correlation, the models will be similar. If, the correlation is something else or insignificant, the models for each Y can be quite different.

2. Optimization in a multivariate environment can be quite challenging. It might require using alternative measures (Y's). It might require complete re-design of the process (which can include identification of factors not previously considered and which may not be significant in a univariate approach). And likely it will require some trade-offs.

3. I believe the Group Fit platform in JMP will provide Profilers for each of Y's simultaneously so you can evaluate what happens to each Y as the model is changed for any one Y.

4. Depending on how you get your data there are other options to evaluate the multiple Y's (e.g., overlays of the surfaces)

Victor_G

Hi @SimonFuchs,

You can have more information about the optimization done by the profiler here : Desirability Profiling and Optimization (jmp.com)

SimonFuchs

Hi Victor,

Thanks, this covers all my questions. Its sometimes hard as a daily user, whos background is not hard statistics, to dig deep into this topics. And the answer of you and your colleges is super helpful in this cases and avoids time consuming searches in the JMP database and google.

So thanks again and best regards!

Simon