User Input List for Regression Report with Interactions

[#1]

I have an input box where users can select columns to be run in a regression report. This part works great. I then insert the list of columns into a list. I would like to take the list of columns and make different interactions that can be inserted into a regression report. Specifically, I am interested in slightly more complicated interactions (i.e. Column 1 * Column 2 ^2) When I try to put anything but just the generic list in the regression report, it doesn’t run the report. What do I do to create these interactions in the report?

The user input list readout looks like this: {"Column 1", "Column 2", "Column 3"}

platform = dt << Fit Model(
    Y( :Char( variable ) ),
    Effects(
           // What should go here?????
          ),
    Personality( "Generalized Regression" ),
    Generalized Distribution( "Normal" ),
    Run(
        Fit(
            Estimation Method( Two Stage Forward Selection ),
            Validation Method( AICc ),
            Enforce Heredity
        )
    )
);

[#2]

The Scripting Index has an example for Effects - copied in below. 

Names Default To Here( 1 );
dt = Open( "$SAMPLE_DATA/Dogs.jmp" );
obj = Fit Model(
	Y( :LogHist0, :LogHist1, :LogHist3, :LogHist5 ),
	Effects( :drug, :dep1, :drug * :dep1 ),
	Personality( Manova ),
	Run( Response Function( Sum ) )
);

[#3 · Accepted solution]

Here is one way to handle this

names default to here(1);
dt=data table("big class");
variable = "Age";
// If you build your list as expressions the code below works
effectsList = {height, weight, weight * height};

Fit Model(
	Y( :char(variable) ),
	Effects( eval(effectsList) ),
	Personality( "Standard Least Squares" ),
	Emphasis( "Effect Leverage" ),
	Run(
		:char(variable) << {Summary of Fit( 1 ), Analysis of Variance( 1 ),
		Parameter Estimates( 1 ), Scaled Estimates( 0 ),
		Plot Actual by Predicted( 1 ), Plot Regression( 0 ),
		Plot Residual by Predicted( 1 ), Plot Studentized Residuals( 0 ),
		Plot Effect Leverage( 1 ), Plot Residual by Normal Quantiles( 0 ),
		Box Cox Y Transformation( 0 )}
	)
);

/*
// If you build your list using strings
effectsList = {"height", "weight", "weight * height"};
// You can convert the elements back to expressions by
// using the Parse() function
For( i = 1, i <= N Items( effectsList ), i++,
	effectsList[i] = Parse( effectsList[i] );
);

[#4]

Here is another way using expressions. There are more solutions based on expressions than just this example.

Names Default To Here( 1 );

dt = Open( "$SAMPLE_DATA/Dogs.jmp" );

predictor = { :drug, :dep1 };
n = N Items( predictor );

effectExpr = Expr( Effects() );
For( x1 = 1, x1 < n, x1++,
	Insert Into( effectExpr, predictor[x1] );
	For( x2 = 2, x2 <= n, x2++,
		Eval(
			Substitute(
				Expr( Insert Into( effectExpr, Expr( xxx1 * xxx2 ) ) ),
				Expr( xxx1 ), predictor[x1],
				Expr( xxx2 ), predictor[x2]
			)
		)
	);
);
Show( Name Expr( effectExpr) );

Eval(
	Substitute(
		Expr(
			obj = dt << Fit Model(
				Y( :LogHist0, :LogHist1, :LogHist3, :LogHist5 ),
				eee,
				Personality( Manova ),
				Run( Response Function( Sum ) )
			);
		),
		Expr( eee ), Name Expr( effectExpr )
	)
);

[#5]

This solution seems like it could be really flexible. I am unfamiliar with expressions, so please bear with me. 

I tried to have both the basic interactions (a * b) and more complex interactions (a * b^2) work at the same time and I can't seem to figure out how to make it work. Can you provide a little more guidance on this?

[#6]

JMP does not represent a higher order term in a linear predictor that way (e.g., X^2). It represents it as X*X, so your term would be A * B * B.