Get MaxPro value for any Space-Filling design

Question

Hi dear JMP Users and expert scripters,

I would like to compare several DoEs (Space-Filling type). Some are generated with JMP (with all the column properties needed for the factors and response), some are created with other external tools (so no column properties after file importation in JMP).

Since these designs are Space-Filling types, I would like to compare them based on discrepancy and MaxPro criterion values (example here with a Fast Flexible Filling design for 4 continuous factors) :

These values are available directly for JMP-generated designs in "DOE Dialog" script, but not with external tools.

I have read the Scripting index and the "<< Get MaxPro Values" function, but I don't know how to use it in a script for "external" DoEs ?

Practically, I would like to have a script that can calculate discrepancy and MaxPro values for any design, and provide a datatable with the results.

Ideally (maybe an idea for Wish List), I would like to have a comparison platform like Compare Designs,  where I could match the factors between different tables, and a window will open with the comparison of these two values, discrepancy and MaxPro criterion.

I have attached two datatable for testing, each is a design with 4 continuous factors, one generated externally and one generated with JMP.
Any help is welcome !

Thanks,

Example_Fast Flexible Filling Design-JMP.jmp

Example_external-DoE.jmp

Ryan_Lekivetz · Answer

Sorry for the late (and brief) reply - there is indeed an issue when loading an external design. Note that in particular, that denominator is based on single dimension distances, so if you have any input that has the same value, the denominator is 0 (usually we're looking for the non-collapsing property, which protects against this). From what I recall, that formula can be used on the scaled estimates:

https://www.jmp.com/support/help/en/18.0/index.shtml#page/jmp/fast-flexible-filling-design-details.shtml

For discrepancy, we were discussing about adding that formula directly into the documentation - if you're able to access, in the Hickernell, it’s the bottom of page 317.

Fang, K., Lin, D., Winker, P., and Zhang, Y. (2000). “Uniform Design: Theory and Application.” Technometrics 42:237-248.

Hickernell, F. (1998). “A Generalized Discrepancy and Quadrature Error Bound.” Mathematics of Computation 67:299-322.

Victor_G · Answer

Posted two wish list items on this topic :
Design Explorer for Space-Filling designs

Compare Designs platform for Space-Filling designs

Generating several designs and using distances from Hierarchical Clustering platform already helps assessing the "performance" and points distribution of space-filling designs. Here is a visual comparison of the min, mean and max distance values of 2 designs types with increasing number of factors (dimensionality). The first one see a sharp increase of the distances with increasing dimensionality, whereas the second one seems more "robust" with a linear increase of distance regarding the augmentation of factors.

Looking at the Variance of the distances between points (which seems to be correlated with discrepancy values), design 1 seems to have a more compact way to spread points compared to design 2. Design 2 is able to spread points with the same "variability" when increasing dimensionality :

Victor_G · Answer

Hi @SDF1,

Thanks for the reference.

I might have something to start by reading old posts from the Community, using Hierarchical Clustering platform to get access to Matrix Distance :

A = Current Data Table() <<
	Hierarchical Cluster(
		Y( :X1, :X2, :X3, :X4 ),
		Method( "Ward" ),
		Standardize By( "Columns" ),
		Dendrogram Scale( "Distance Scale" ),
		Number of Clusters( 3 ),
		Set Random Seed( 2088588291 ),
		SendToReport(
			Dispatch( {"Dendrogram"}, "Clust Dendro", FrameBox,
				{Frame Size( 35, 325 )}
			)
		)
	);
	A << Save Distance Matrix;
	A << Close Window;

Then, I'm a bit lost on how to use the Distance Matrix to get the same informations as in the DOE Dialog from Space-Filling Designs : Minimum Distance, Nearest Points, MaxPro value and Discrepancy value.

I have tested using Multidimensional Scaling platform with the Distance Matrix generated previously and defining the number of dimensions as the number of original factors in my design ; I'm able to spot nearest points correctly, but the (minimum) distance seems off compared to calculations done in the DoE Dialog :

Any inputs from @Mark_Bailey, @Ryan_Lekivetz, and other JMP experts ?

EDIT: Using "Unstandardized" in the options of Hierarchical Clustering for the data format give me the right distances... I'm getting closer !

I can now compare designs depending on the min, mean, max distance values, and variability in the distances between points (range, StdDev/Variance, ...). Still no MaxPro calculations, but a better insight about distribution of points in Space-Filling designs. 
Also using the platform Distributions and comparing the distributions of factors values to Uniform distributions (Beta with alpha and beta values set to 1) help me getting closer of this "discrepancy" values. There might be something to do with the p-values, log-likelihood, chi-square values that seem correlated to discrepancy :