Predicted values for conversion over 100%.

[#1]

Hello everyone,

I’m running a Central Composite Rotatable Design (CCRD) in JMP to optimize a chemical reaction, with conversion (%) as my response variable. By definition, conversion should range from 0% to 100%. However, my fitted model sometimes predicts conversion values greater than 100% (and occasionally less than 0%) for certain factor combinations.

Here’s what I’ve done so far:

• My experimental data only includes conversion values between 0% and 100%.

• I used standard least squares regression to fit the model.

• I noticed these out-of-bounds predictions especially when using the Profiler to explore the design space.

My questions:

1. Why is the model predicting physically impossible values?

2. Is this a limitation of the modeling approach, or am I missing a setting in JMP?

3. What is the best practice to ensure predictions stay within the 0–100% range for bounded responses like conversion?

4. Are there recommended workflows or JMP features that can help constrain predictions within physical limits?

I am attaching my data and model output for reference.

Thank you for your help and insights!

[#2]

The main problem with least squares applied to bounded responses is that it does not intrinsically respect the bounds imposed on them- the most common, of course, being 0-100%. For that reason, you could consider beta regression or transforming your response (for example, to logit) in order to keep the predictions within the bounds.

[#3]

Sometimes the model will predict out of bounds values when it is looking at combinations of factors that it is not confident in (for example, in a CCD you test the centrepoint with the axials 00a, but you never test the + or - values with the axials ie '--a'). This means that the prediction error. You can try to limit this by activating extrapolation control in the profiler, this will stop you from extrapolating to factor conditions that are invalid for your model. 

This can happen because It is a mixture of a limitation in the modelling type with SLS and also that your data may not be sufficient to build an entirely accurate model, this is where you should look at the model diagnostics to understand how well the model is performing. 

Another consideration is that the SLS approach is assuming a linear model with normally distributed data, which your data may not fit well, there are good options to explore other distributions and data with Generalised Regression in JMP Pro, for example with a beta distribution. Here is an interesting community post where other options are explored such as a logit transformation.