Understanding of Construct Model Effects - Factor*Factor vs Factor Interactions

[#1]

Hi,

I am trying to understand the 'construct model effects' section when conducting a 'fit model' analysis 'model specification'.

In this 'construct model effects' section, there is the ability to assess quadratic terms where a factor for example compression force exists both on its own and as a factor interaction with itself i.e 'compression force' and 'compression force*compression force'. 

I have included an image of this 'construct model effects' section in this post below:

I do not understand what the difference is from a physical standpoint of significance. Why is it we have the ability to assess a factor interaction where it is just the factor in an interaction with itself? You cannot change compression force and vary it with itself. I can understand compression force vs compression speed interaction since a change in compression force will impact itself and the compression force vs compression speed interaction. 

Is it purely as a means of including a quadratic term. If so what is the purpose/use of this? 

Many thanks for taking the time to read my post and I look forward to engaging with fellow JMP users on this topic. 

Kind regards,

Joe 

[#2]

Hi Joe,
It is a bit confusing indeed. As far as I understand it, the "FACTOR Y * FACTOR Y" expression is a means to transform your variable into a quadratic space which is equivalent to calculate in a new column the square of FACTOR Y and use it in your model. Considering that the formulation of interactions between 2 different factors, I can see where the confusion stems from.
Other members may have a more technical feedback on this question.
Best,
TS

[#3]

Hi Joe,

You are correct in assuming this variable represents a quadratic term in your model.

When we build a model we are attempting to explain how certain factors impact a response in our data. A Main Effects model can help here but it is oftentimes beneficial to include additional quadratic or interaction effects to further explain variation we see in our response data.

The prediction profiler is an excellent interactive tool for making sense of a model from a physical standpoint. A great example demonstrating this can be found in JMP’s Help->Sample Data->Industrial Experiments->Tablet Production.jmp example. Run the Fit Model and Fit Model with Interaction Profiles scripts and observe the difference between the two models.

Main Effects model:

Main Effects+Interactions+Quadratic model

In the 2^nd Profiler, observe the Mill Time variable showing the effect of introducing a quadratic effect on our model. As you adjust the Mill Time value from 5 to 30 you will observe the physical impact of this term on our model: a peak in our Disso response between the two extremes.

This is in contrast to the Main Effects model where we see a linear trend, leading us to expect improving performance in Disso as we increase Mill Time.

JMP’s Statistics Knowledge Portal provides excellent an excellent description, including visuals, of how the math works with Multiple Linear Regression. You might also take a look at the Statistical Thinking for Industrial Problem Solving Correlation and Regression module to learn more.

[#4]

To reiterate, simply enough JMP represents the quadratic as factor times itself (essentially the square of the factor) in the model.  Provided you have more than 2-levels for the factor in question in your data set, polynomial terms (non-linear) can be estimated.