Get relative prediction variance values

dp30

Hello,

I would like to make ternary plots showing the relative prediction variance of 3-component mixture DOEs.

To do that, I would need to extract a high number of values (let's say 20,000) from the Prediction Variance Profile graph, and make a datatable with these values. This datatable would have 20,000 rows and 4 columns: X1, X2, X3 and the Relative Prediction Variance.

Perhaps another way to do that, would be to use the Column Formula Editor and implement the relative prediction variance formula, but I am not familiar with matrix functions in the Formula Editor.

Thanks a lot.

By the way, this would be a nice feature for next JMP updates

 

Mark_Bailey

This script illustrates an approach for three components, X1, X2, X3, and the quadratic Scheffe model.

 

Names Default to Here( 1 );

// make design
doe = DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ), Add Factor( Mixture, 0, 1, "X1", 0 ),
	Add Factor( Mixture, 0, 1, "X2", 0 ), Add Factor( Mixture, 0, 1, "X3", 0 ),
	Set Random Seed( 27513 ), Number of Starts( 10000 ), Add Term( {1, 1} ),
	Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {1, 1}, {2, 1} ),
	Add Term( {1, 1}, {3, 1} ), Add Term( {2, 1}, {3, 1} ), Set Sample Size( 12 ),
	Simulate Responses( 0 ), Save X Matrix( 1 ), Make Design,
	Set Run Order( Randomize )}
);

// make design data table
doe dt = doe << Make Table;
doe << Close Window;

// get model matrix, X
model matrix expr = doe dt << Get Script( "Model Matrix" );
X = Arg( Arg( model matrix expr, 1 ), 2 );
inv x prime x = Inverse( X` * X );

// make expression for prediction variance
pv expr = Substitute(
	Expr(
		xi = Matrix( List( :X1, :X2, :X3, :X1*:X2, :X1*:X3, :X2*:X3 ) );
		xi` * iii * xi;
	),
	Expr( iii ), inv x prime x
);

// add data column with prediction variance formula
Eval(
	Substitute(
		Expr(
			doe dt << New Column( "Prediction Variance", Numeric, Continuous,
				Formula( fff )
			);
		),
		Expr( fff ), Name Expr( pv expr )
	)
);

// plot prediction variance
mp = doe dt << Mixture Profiler(
	Y( :Prediction Variance ),
	Mixture Profiler(
		1,
		Term Value(
			X1( 0.333333333333335, Lock( 0 ), Show( 1 ) ),
			X2( 0.333333333333336, Lock( 0 ), Show( 1 ) ),
			X3( 0.333333333333335, Lock( 0 ), Show( 1 ) )
		),
		Contour Value(
			Prediction Variance(
				0.5,
				Min( 0 ),
				Max( 1 )
			)
		),
		Top Factor( X1 ),
		Left Factor( X2 ),
		Right Factor( X3 )
	)
);
mp << Contour Grid( 0, 1, 0.1, :Prediction Variance );