Custom Designer and Random Effects / Desingn Evaluation and Random Effects

[#1]

Hello,  I tried to reproduce a nice Design in Chapter 4 of Elizabeth A. Claassens book "JMP for Mixed Models" using JMP DOE Custom designer. But I failed and don’t know why/how to solve it.

The design itself is straight forward: There are 6 cages. Each cage can be divided into two areas. An area can be set to one of 4 condition. Each of the areas is big enough to hold space for 3 different nests. Inside a nest the mice will be attributed to one of 3 different diets. 

The experiment is set up to learn how the mice gain weight depending on condition and diet. These are the fixed effects.

The interesting part is the fact that cage*condition shall be treated as a random effect as it is the  actual experimental unit. I added two pictures to show the evaluation.

I also attached two different handmade Designs to show the idea. The first one is from Elizabeth's book. The second considers a larger cage.

How would I produce such designs with Custom Designer taking the random nature of the experimental unit into account? (And of course get some randomisation.)

Which runs would i drop/add if i could afford fewer/more runs keeping the balance in mind? Is the lager one worth while?

How can I compare the two designs including the random effects?

Best Olaf

[#2 · Accepted solution]

Hi @Olaf,

Looking at the use case, the design seems to be a split-split plot design (since "Condition" is nested into factor "Cage"), with :

• categorical factor "Cage" set as "Very hard to change" (with 6 levels)
• categorical factor "Condition" set as "Hard to change" (with 4 levels)
• categorical factor "Diet" set as "Easy to change" (with 3 levels).

More infos here : Designs with Randomization Restrictions (jmp.com)

Specifying 6 whole plots and 12 subplots for 36 runs, you should get the same kind of table as the one you have shared (see table "Custom-Designer-and-Random-Effects-Desingn-Evaluation-and-Random").
The script to generate the DoE table is here :

DOE(
Custom Design,
{Add Response( Maximize, "Gain", ., ., . ),
Add Factor( Categorical, {"C1", "C2", "C3", "C4", "C5", "C6"}, "Cage", 2 ),
Add Factor( Categorical, {"A1", "A2", "A3", "A4"}, "Condition", 1 ),
Add Factor( Categorical, {"Restrict", "Normal", "Supplementary"}, "Diet", 0 ),
Set Random Seed( 641607656 ), Number of Starts( 1562 ), Add Term( {1, 0} ),
Add Term( {1, 1} ), Add Term( {2, 1} ), Add Term( {3, 1} ),
Add Alias Term( {1, 1}, {3, 1} ), Set N Whole Plots( 6 ), Set N Subplots( 12 ),
Set Sample Size( 36 ), Simulate Responses( 0 ), Save X Matrix( 0 ), Make Design}
)

However, there will be some redundant columns in the analysis and model, as the whole plots correspond to the "Cage" factor, and subplots correspond to the "Condition" factor.

So when launching the analysis, you may have to specify the model manually in order to correspond to the analysis you have :

• Fixed effects : Condition, Diet, Condition x Diet
• Random effects : Cage, Cage x Condition

I have saved the script to launch this model in the "Fit Mixed Model" script in the datatable.

The JSL code is :

Fit Model(
	Y( :Gain ),
	Effects( :Condition, :Diet, :Condition * :Diet ),
	Random Effects( :Cage, :Cage * :Condition ),
	Personality( "Mixed Model" )
)

Concerning the runs to drop/add, in the design generation the minimum number of runs is 13 and by default JMP recommends 36 runs (the number you have in your case study). There is no maximum number of runs, but you can try with 48 runs for example (to have a multiple of 6 and 12, for the whole plot and subplot respectively).

So you could compare 3 designs with 24, 36 and 48 runs and see what is the best design for a good compromise between accuracy and experimental budget. The evaluation of the designs may not be very "accurate", as some columns are redundant in the analysis (and you won't use all your factors as fixed effects). But it can still provide an interesting and comparative view on power analysis (lower power for hard/very hard to change factors compared to easy-to-change factor), prediction variance, and aliases in the design. 

I hope this answer will help you,

[#3]

Hello Victor,

You perfectly answered the generation question. Sometimes we just overlook the most obvious in favour of something much more complicated 

Thank you very much. 

Olaf