nav[aria-label="Primary Navigation"] { padding: 0; & ul { list-style: none; width: 100%; display: flex; flex-direction: row; justify-content: start; align-items: start; gap: 30px; padding: 0; & li { margin: 0; } & ul li { list-style: none; } } }

Analysis of a botched split-plot design

doechemist

Hi,

Long story short, I have tried to use a split-plot design for the analysis of a chemical reaction.

I designed the experiments with the custom designer, where the temperature is a parameter that is hard to change (hence split plot). I have 9 variables in total, two of which are categorical (identity of reagents). As a start, I am just interested to screen the main effects. As a result, I managed to use the custom designer to find a design with 20 experiments that gives the main effects with no alias. Interactions are aliased (second order interactions marked 'if nescessary' in the model), but as a first iteration, it'll be just fine for me.

Anyhow - when performing the experiments, I had to change one of the solvents, resulting in a change in three of the selected parameters (I tried to select a solvent with properties as close as possible to the one it replaced). I figured, thinking about how George Box viewed it, that it then became a botched design - it would work, but not give me the best results. For a screening experiment, I could probably accept this.

Now, as I try to fit the model, I have some issues interpreting the JMP output:

1) I have something called 'Singularity Details'. I guess it is because the botched design now has some collinearities?

2) In parameter estimates, many are 'biased' and the rest are zeroed. Is this because of the botched design - or the aliasing of the second order interactions?

3) No effects at all seem significant in the Effect Summary - or rather, they don't appear.

4) The actual vs predicted plot is perfectly linear, with R^2 = 1. That can't be true.

5) The intercept is negative - so heavily biased?

So, all in all...can I do much more than look at the fitted model and use extrastatistical knowledge to select the few important main effects?

Accepted answers

cwillden

Unless you are only attempting to fit main effects, you would expect singularities with such a sparse design. However, if you are getting a singularity with just main effects, you’re in a bit more trouble.

If your factors all have 2 levels, you should be able to use the Fit Two Level Screening platform to ID significant factors and potentially a few interactions. I don’t think it will be able to properly test your hard to change factor, but it’s probably good enough to make general conclusions.

All comments

cwillden

doechemist

Thanks for you input!

The model I try to fit is main effects + interactions. If I understand the customized DoE properly, setting the interactions to 'if possible' and the main effects to 'required' lets me find a design with main effects estimable and (some of) the interactions aliased (which the alias table did show me when I made the original design).

I didn't know about the Fit Two Level Screening platform - thanks! I shouldn't include Whole Plots with that, should I?

Including Whole Plots or not, no factors are significant (even main effects!) by looking at the p-values/Pareto charts, but some deviate from the half normal plot.

So, to sum up:

I have no degrees of freedom left to analyse the data as usual, and I should expect singularities with the design I have. I intend to make some experiments in the center of the design to get an idea of the variance, though.

The Fit Two Level Screening platform is not helpful looking at the p-values/Pareto chart, but a few factors deviate significantly from the half normal plot - and hence I will focus on these in the next iteration. And keep the hard to change factor for good measure.

Is that correctly understood?

cwillden

Yes, you understood correctly.

When you set interactions to "if possible", you are basically telling JMP "you can confound this term with other 'if possible' terms, but don't confound it with any 'Necessary' terms." It implies that you will need use something like a half-normal plot to identify important factors and use principles of effect heredity and effect hierarchy to make an educated guess about which of an interactions aliases are most likely the active factor based on which main effects were significant. JMP does that for you in Fit Two Level Screening. You cannot attempt the full model right off the bat in Fit Model because you already know you have aliased model terms that will cause singularities.

Don't worry about Whole Plot in Fit Two Level Screening. That needs to be included as a random effect, and Fit Two Level Screening can't handle random effects as far as I know. This means the analysis will not be exactly correct, but I am confident it will still serve its purpose to highlight the strong effects. The half-normal plot is the primary output you should use to make your decisions. Once you have that, you can use Fit Model to fit just the selected model terms.

doechemist

Thanks! It makes sense - and I'm beginnning to make sense of the data already!