dt << Time Series( X( :Name( "Time (s)" ) ), Y( :Name( "Response" ) ), "Save Spectral Density" , "Invisible" );
In your example above the "Invisible" is associated with the Time Series platform, not the data table that results from your "Save Spectral Density".
Unfortunately, there's no option on "Save Spectral Density" to create it invisibly. Instead you'll have to hide it immediately after it's created.
Here's an example for JMP 12:
dt = Open( "$SAMPLE_DATA/Time Series/Steel Shipments.jmp" );
ts = Time Series( Y( :steel shipments ) );
dtSpec=ts << Save Spectral Density();
dtSpec << Show Window( 0 );
The Save Spectral Density message in JMP 12 will return a reference to the data table that's created. Earlier versions of JMP don't do that so you'll have get that reference yourself.
So, here's an example that works in JMP 11:
dt = Open( "$SAMPLE_DATA/Time Series/Steel Shipments.jmp" );
ts = Time Series( Y( :steel shipments ) );
ts << Save Spectral Density();
dtSpec = Data Table( 1 );
Wait( 0 );
dtSpec << Show Window( 0 );
h/t to WK for the examples.
-Jeff