Help with Disallowed Combinations for Categorical factors (JMP 15)

Question

Hello,

I have the following factors and levels that I am trying to create a D-Optimal Design for:

Factor A - Categorical two level (Jolt, Triad)

Factor B - Categorical two level (Blunt, Suction Cup)

Factor C - Continuous  (10,25)

Factor D - Categorical two level (Standing, Seated)

Factor E - Categorical three level (Stationary, Evading, Running)

Factor F - Categorical two level (Novice, Expert)

I am attempting to create an example for students to use to teach them how to generate optimal designs with disallowed combinations. The disallowed combination I am trying to make is Factor D (Seated) and Factor F (Expert). I am also trying to build a design with main effects AND two-factor interactions. However, I keep getting the error message (Optimal designer failed to converge). I have tried everything I could in order to generate a design that converges with disallowed combinations between categorical factors to no avail. I have tried adding factors, adding more levels to these factors. I can however get the designer to converge when adding a disallowed combination between a categorical factor and continuous factor. The second I add in a disallowed combination between categorical factors the algorithm will not converge. Any help is appreciated!

Victor_G · Answer

If you need to estimate this interaction effect, you need to test all possible combinations of levels for these two factors : Standing+Novice, Standing+Expert, Seated+Novice, Seated+Expert.

If an experiment is missing (in your case Seated+Expert), you can't estimate the interaction term in your model.
I joined a toy datatable to demonstrate this, if row 4 is hidden and excluded, then on the graph script, you'll not see the line between the two levels for factor D when Factor F is set on "Expert" level, so how can you know there is an interaction ?

And in the model script, interaction effect is not estimable (there is a singularity in your model with the intercept), so once again, you won't have access to this interaction effect term.

I hope this demo will be clear enough,

Interaction_demonstration.jmp

FaceStatistics6 · Answer

Lets say however, that I NEED to estimate the effects of factor D and factor F for the combinations that are allowed to exist. Ex. Factor D Standing - Factor F Novice and Factor D Seated - Factor F Novice. If a set to if possible, then I am potnetially creating a design that will not allow me to include this interaction in the analysis.

Victor_G · Answer

Hi @FaceStatistics6,

I reproduce the same settings and face similar error message.

The problem may be in your combination of disallowed combination and terms in your model : if you block the combination of "Seated" from Factor D (2-level categorical) with "Expert" from Factor F (2-level categorical), that means you can't estimate the interaction term of these two factors since a constraint is preventing you from testing all possible combinations of levels for these two factors.

You can either :

* Remove the 2 factors interaction term "Factor D*Factor F" and use this script to generate the DoE table (or use the attached data table "Custom Design_Remove2FI"):

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ),
	Add Factor( Categorical, {"Jolt", "Triad"}, "Factor A", 0 ),
	Add Factor( Categorical, {"Blunt", "Suction Cup"}, "Factor B", 0 ),
	Add Factor( Categorical, {"Standing", "Seated"}, "Factor D", 0 ),
	Add Factor( Categorical, {"Novice", "Expert"}, "Factor F", 0 ),
	Add Factor( Continuous, 10, 25, "Factor C", 0 ),
	Add Factor( Categorical, {"Stationary", "Evading", "Running"}, "Factor E", 0 ),
	Set Random Seed( 80459262 ), Number of Starts( 2161 ), Add Term( {1, 0} ),
	Add Term( {1, 1} ), Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {4, 1} ),
	Add Term( {5, 1} ), Add Term( {6, 1} ), Add Term( {1, 1}, {2, 1} ),
	Add Term( {1, 1}, {3, 1} ), Add Term( {1, 1}, {4, 1} ),
	Add Term( {1, 1}, {5, 1} ), Add Term( {1, 1}, {6, 1} ),
	Add Term( {2, 1}, {3, 1} ), Add Term( {2, 1}, {4, 1} ),
	Add Term( {2, 1}, {5, 1} ), Add Term( {2, 1}, {6, 1} ),
	Add Term( {3, 1}, {5, 1} ), Add Term( {3, 1}, {6, 1} ),
	Add Term( {4, 1}, {5, 1} ), Add Term( {4, 1}, {6, 1} ),
	Add Term( {5, 1}, {6, 1} ), Set Sample Size( 36 ),
	Disallowed Combinations( Factor D == "Seated" & Factor F == "Expert" ),
	Simulate Responses( 0 ), Save X Matrix( 0 ), Make Design}
);

* Or set estimability of the 2 factors interaction "Factor D*Factor F" as "If Possible" and use this script to generate the DoE table (or use the attached data table "Custom Design_IfPossible"):

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ),
	Add Factor( Categorical, {"Jolt", "Triad"}, "Factor A", 0 ),
	Add Factor( Categorical, {"Blunt", "Suction Cup"}, "Factor B", 0 ),
	Add Factor( Categorical, {"Standing", "Seated"}, "Factor D", 0 ),
	Add Factor( Categorical, {"Novice", "Expert"}, "Factor F", 0 ),
	Add Factor( Continuous, 10, 25, "Factor C", 0 ),
	Add Factor( Categorical, {"Stationary", "Evading", "Running"}, "Factor E", 0 ),
	Set Random Seed( 349202301 ), Number of Starts( 2106 ), Add Term( {1, 0} ),
	Add Term( {1, 1} ), Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {4, 1} ),
	Add Term( {5, 1} ), Add Term( {6, 1} ), Add Term( {1, 1}, {2, 1} ),
	Add Term( {1, 1}, {3, 1} ), Add Term( {1, 1}, {4, 1} ),
	Add Term( {1, 1}, {5, 1} ), Add Term( {1, 1}, {6, 1} ),
	Add Term( {2, 1}, {3, 1} ), Add Term( {2, 1}, {4, 1} ),
	Add Term( {2, 1}, {5, 1} ), Add Term( {2, 1}, {6, 1} ),
	Add Term( {3, 1}, {5, 1} ), Add Term( {3, 1}, {6, 1} ),
	Add Term( {4, 1}, {5, 1} ), Add Term( {4, 1}, {6, 1} ),
	Add Term( {5, 1}, {6, 1} ), Add Potential Term( {3, 1}, {4, 1} ),
	Set Sample Size( 36 ), Disallowed Combinations(
		Factor D == "Seated" & Factor F == "Expert"
	), Simulate Responses( 0 ), Save X Matrix( 0 ), Make Design}
);

Hope this answer will help you,

Custom Design_Remove2FI.jmp

Custom Design_IfPossible.jmp