Deal with hierachical (nested) factors in DOE custom design platorm

[#1]

Hello,

I'm trying to build a design using the DOE custom design platform. I have three categorical factors (G, L, and Z) to consider, with one nested within another. Ultimately, the model I want to run is Y = G + L[Z] + Z + e. However, my primary goal is to ensure that the number of replications of G is balanced within Z, and that the number of runs is balanced across my L factor.

By using the "Disallowed Combinations" option, I managed to get something close to my desired outcome. For example, this script produces results that are fairly close to what I want:

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ),
	Add Factor(
		Categorical,
		{"L1", "L2", "L3", "L4", "L5", "L6", "L7", "L8", "L9", "L10"},
		"L",
		0
	), Add Factor(
		Categorical,
		{"V1", "V2", "V3", "V4", "V5", "V6",
		"V7", "V8", "V9", "V10", "V11", "V12",
		"V13", "V14", "V15", "V16", "V17", "V18",
		"V19", "V20", "V21", "V22", "V23", "V24",
		"V25", "V26", "V27", "V28", "V29", "V30",
		"V31", "V32"},
		"G",
		0
	), Add Factor( Categorical, {"Z1", "Z2"}, "Z", 0 ),
	Set Random Seed( 1289561612 ), Number of Starts( 360 ), Add Term( {1, 0} ),
	Add Term( {1, 1} ), Add Term( {2, 1} ), Add Potential Term( {3, 1} ),
	Set Sample Size( 360), Disallowed Combinations(
		Z == "Z1" & (L == "L6" | L == "L7" |
		L == "L8" | L == "L9" | L == "L10") |
		Z == "Z2" & (L == "L1" | L == "L2" |
		L == "L3" | L == "L4" | L == "L5")
	), Simulate Responses( 0 ), Save X Matrix( 0 ), Make Design}
);

Nevertheless, this is far from perfect because the number of levels for L, Z, and G can vary significantly depanding on the designs I have to create and and I have many!  This approach is not straightforward to automate through scripting.

Moreover, the number of replications per Z level for my G factor is not perfectly balanced, as shown in the following summary of my results table:

Any thought is welcome  

I'm using JMP16 

[#2]

Hi @johanna_younous,

I may not answer directly your questions but I have some remarks/comments :

• What is your objective ? Pick a winner or an understanding and modelization of the link between factors and response(s) ?
  In the second case, I'm wondering if you couldn't get an understanding of this link with fewer levels for factor G for example (32 levels are a lot !). Also, depending on what the factors represent, could you use one or several numerical factors related to the categorical factors ? For example, using measurements of the specific categorical levels of the factors as numerical covariates in the design ?
  Some options and inspiration for this idea : Re: Increase efficiency and model applicability...  
• About the imbalance of your design, I don't see any specific imbalance in factors levels when launching the same script as you have :
  

  (I attached the design datatable generated for comparison if needed).
  What is exactly the problem you're seeing ?

• For automation, I'm wondering if it wouldn't be easier to use a Candidate Set approach :
  1. Create automatically a dataset with all combinations (Classical Full Factorial DoE),
  2. Remove infeasible combinations by scripting rules,
  3. Use this candidate set to create a design.

More info about the Candidate set approach here : Candidate Set Designs: Tailoring DOE Constraints to the Problem (2021-EU-30MP-784) 

Hope this answer may help you,

[#3]

Hello, thank you for this answer. 

in fact the purpose is to order properly all my levels of G , and in the end to select the better ones. 32 levels is quite a low number of level to me in fact ! There is no direct nor easy way to associate numbers to those factors.

I tryed to illustrate the ubalancing with the picture but I may not be clear, sorry about that. 

Here is what I get as with another run where I increased the number of runs .

Problem of balance comes from the number of replication fo my G levels within Z. Here is what I have :  

and this is what I would like 

Thanks for the candidate approach, I'll dig on that .

I though this problematic would be easier to solve to be fair  

[#4]

Hi @johanna_younous,

What is the need behind exact balancing between levels ? Did you try to create the design manually ? How does it compare to your scripted design ?

I'm not sure the slight unbalance here is something to worry about, you can do the designs comparison with the Compare Designs platform.

Anyway, the use of the Candidate approach could be a nice alternative here, so that the constraints are already in the points choice, instead of specyfying the constraints in design generation.