The Background
I recently ran a pilot study with 5 different food samples that have varied "Starch," "Sugar," and "Salt" as continuous factors. Each of the 5 food samples was tasted by 150 panelists each, who either accepted or rejected the sample. The percentage of rejecting panelists is what I would like to model as a function of my three continuous factors.
My pilot study yielded some interesting insights that align with what I expect, but due to only having 5 different samples, my modeling was limited to just using the "Sugar" and "Sugar*Sugar" term. I used a GLM --> Normal --> Logit model, as I know there is curvature and I want my output to be limited to 0 - 1 since it is a percentage. I have attached my data table with the saved GLM ("Pilot Data SSS-Prej_Sugar Logit Model"). It is based on an approach Mark Bailey had recommended in a prior post for proportion data.
Next Steps
My next steps are to test more food samples that have varied "Starch," "Sugar," and "Salt" levels so that I can produce an accurate and precise multivariate model (instead of just "Sugar" and "Sugar*Sugar" terms) for estimating percentage of rejecting panelists. I would like to capture both main effects and crossed effects. To that end, I used the DOE --> Custom Design platform and set the following parameters:
Responses: Percentage Rejection, Goal to minimize, Lower limit = 0, Upper Limit = 1
Factors: "Starch" (38 - 55), "Sugar" (15 - 36), "Salt" (23 - 50) as continuous easy factors, and then I used the RSM to get crossed terms. I removed some terms such that I had 1 intercept, the 3 main effects, and 4 crossed terms.
Replicates: 5
Centerpoints: 0
Number of runs: 40 (we have the budget for that)
Random Blocks: 8
The design/table is attached as "Custom Design SSS-Prej Example"
My Questions
1. Once I run my experiments and get my data, I once again have the option of trying different models. To recap, my goal is to be able to predict how my three factors would influence the proportion of rejectors, and potentially to find minima and maxima for proportion of rejectors. I expect there to be curvature in at least two of the terms ("Sugar" and "Salt"). Are there any issues with again going with GLM --> Normal --> Logit?
2. The reason I ask is because I was following through an exercise in the "JMP Start Statistics" book using the "Reactor 20 Custom" data set for a screening experiment (to look at Percent Reacted), but the exercise used the "Standard Least Squares" + Effects Screening approach even though the output (Percent Reacted) is theoretically constrained from 0 to 1. This page describes this exercise as a homework assignment.
3. In practice I can't exactly follow the custom design levels, but I do have a library of samples that I can pick from that have varying levels of "Starch" "Sugar" "Salt" for testing. It turns out that "Sugar" and "Salt" are also moderately collinear (I don't have much control over this). See the following table ("Example Candidates for SSS-Prej Model"). Should I be concerned about the quality of my DOE and approach given the above concerns?
Thank you for any help you can provide.