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How to Control the number of center points in a Design<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />

I live in a fictional world where my data has no random variation as all of my data is derived from deterministic computer simulations.  My goal is typically to find a model which fits my data that is maximally significant but minimally complex so that I can make predictions about the unknown realms.

Most of the variables in my design are continuous but I often cast them as categorical in the Design because each variable typically represents a sub block in my simulation which can take min, typical and max settings.  I use categorical variables in the Design but then treat them as continuous in the model fit so I can capture the expected quadratic behavior.

With JMP 10 I found that I could start using Discrete Numeric Factor types which has the behavior which I was mimicking as detailed above.  The only problem is when I use discrete numeric I find a much higher occurrence of duplicates of the center points and other replicates.  This occurs even when the 'Number of Center Points:' and 'Number of Replicate Runs' fields are set to zero.

Now, since I live in a world with no random variation the duplicate points are of no worth to me. 

I've attached an example script which has replicate center points.  To detect replicate points just sort the table and browse to the center to see them.

I am using D-optimal designs (which seem to have less center points than I-optimal designs).

Does anyone know of a way to ensure that there are no duplicate data points in a Design?

Re: How to Control the number of center points in a Design

DOE(

  Custom Design,

  {Add Response( Maximize, "Y", ., ., . ),

  Add Factor( Discrete Numeric, {1, 2, 3}, "X1", 0 ),

  Add Factor( Discrete Numeric, {1, 2, 3}, "X2", 0 ),

  Add Factor( Discrete Numeric, {1, 2, 3}, "X3", 0 ),

  Add Factor( Discrete Numeric, {1, 2, 3}, "X4", 0 ),

  Add Factor( Discrete Numeric, {1, 2, 3}, "X5", 0 ),

  Add Factor( Continuous, -1, 1, "X6", 0 ),

  Add Factor( Continuous, -1, 1, "X7", 0 ),

  Add Factor( Continuous, -1, 1, "X8", 0 ), Set Random Seed( 1502480852 ),

  Number of Starts( 200 ), 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( {7, 1} ), Add Term( {8, 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( {1, 1}, {7, 1} ),

  Add Term( {1, 1}, {8, 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( {2, 1}, {7, 1} ),

  Add Term( {2, 1}, {8, 1} ), Add Term( {3, 1}, {4, 1} ),

  Add Term( {3, 1}, {5, 1} ), Add Term( {3, 1}, {6, 1} ),

  Add Term( {3, 1}, {7, 1} ), Add Term( {3, 1}, {8, 1} ),

  Add Term( {4, 1}, {5, 1} ), Add Term( {4, 1}, {6, 1} ),

  Add Term( {4, 1}, {7, 1} ), Add Term( {4, 1}, {8, 1} ),

  Add Term( {5, 1}, {6, 1} ), Add Term( {5, 1}, {7, 1} ),

  Add Term( {5, 1}, {8, 1} ), Add Term( {6, 1}, {7, 1} ),

  Add Term( {6, 1}, {8, 1} ), Add Term( {7, 1}, {8, 1} ), Add Term( {1, 2} ),

  Add Term( {2, 2} ), Add Term( {3, 2} ), Add Term( {4, 2} ), Add Term( {5, 2} ),

  Add Term( {6, 2} ), Add Term( {7, 2} ), Add Term( {8, 2} ),

  Set Sample Size( 48 ), Optimality Criterion( 1 ), Make Design}

)

Re: How to Control the number of center points in a Design

Well, I actually do want the pure quadratic terms in the model since I expect curvature in the data and if I remove it (the quadratic term) then JMP makes a two level design which isn't near what I want. 

The best solution I've found so far is to find and remove the duplicate points manually but this is far from the solution I want/need.

-R

Re: How to Control the number of center points in a Design

I think if you just remove the polynomial terms from your model and just use main effects and interactions that should do what you would like.