How can I evaluate a full factorial design with a quadratic regression model?

[#1]

Hi there, I'm new to the community and I'm still quite a beginner at JMP. I have the following problem: I did a full factorial 3 ^ 3 plan. The results I got are not linear but increase exponentially. When evaluating the "ordinary least squares" I only get a linear model. Is there a way to do a regression with a higher degree polynomial? If so, how could I do that? Thanks in advance.

[#2]

I assume that your factors are defined in the data table using the Numeric data type and the Continuous modeling type. They should also include column properties that agree with your DOE definitions.

You can open the Fit Model dialog by running the Model table script or by selecting Analyze > Fit Model. You can select the factor data columns and then click Macros > Response Surface Methodology. This action will add quadratic terms to model the non-linear response.

I don't think that you can tell just from the data that the response is changing exponentially. You might, though, have prior knowledge that an exponential model is appropriate. If it is, then you will need to define a custom non-linear model and fit it using the Nonlinear platform instead of Fit Least Squares.

Three levels are sufficient to fit a quadratic linear regression model or an exponential model with no more than two parameters per factor or interaction. Other members might have further guidance for you about how you might define the exponential model. JMP Help guides you in the steps to then define the selected model as a column formula.

[#3]

Thank you for your quick reply. I tried the Response Surface Methodology for the factors and received a slight improvement in the model. However, the values estimated by the regression model also include some negative values, which is not possible with my application in reality. is there a possibility to use a limit value for the estimated target value? And could it also be an option to log the measured values in order to obtain a better model quality? Or is that not allowed and would it falsify the result? Many thanks in advance.

[#4]

Which values are negative? Parameter estimates? Predicted response? Why is a negative response impossible?

What are the natural bounds for the response? Some cases can be addressed by either a transformation of the response as you suggest or by using a different distribution model for the statistical errors. Ordinary least squares (OLS) linear regression assumes that these errors are normally distributed, but the generalized linear model (GLM) allows more flexibility in the choice of the linear predictor, the link function for the mean response, and the distribution of the errors. What is the nature of your response?

[#5]

The predicted reaction will be negative, but the measured target is the electrical resistance. The limits would be 0 and open at the top. I would like to produce a conductive material and add different fillers to a non-conductive material. From a certain filling level, the material is conductive and before that it is an insulator. For this reason, the measured values vary from very low to very high values. Therefore I assume that the regression model must be approximately exponential.

After a transformation of the measured values via Box-Cox, the measured values are normally distributed. Is the transformation permissible or do I have to adapt the model?

[#6]

Transformations are very common. They often have some physical basis but generally they are justified because they are simply useful in empirical modeling.

If the value of the Box-Cox lambda parameter is close to 0, then you might also directly apply a log transform on the response. You could also change the fitting personality in the Fit Model launch dialog in JMP Pro to Generalized Regression and select the Lognormal distribution.

You can also define a custom non-linear model if you have a theoretical equation that applies to these factors, without transforming the response.. See the JMP Help about this platform.