nav[aria-label="Primary Navigation"] { padding: 0; & ul { list-style: none; width: 100%; display: flex; flex-direction: row; justify-content: start; align-items: start; gap: 30px; padding: 0; & li { margin: 0; } & ul li { list-style: none; } } }

Parameter bound for Nonlinear curve fitting

eugur

I'm trying to fit to data points for 1000+ samples. I've found out that Biexponential 5P function gives the best fitting results. However, same samples with one or two data points slightly outside of the trend makes the fitting really strange. For typical population, decay rate parameters are around 0.2 and for those samples fitting provides results in the range of 10. "Parameter bound" and increased iteration limit options in nonlinear fitting resolves the issue. However, doing this manually through GUI is impossible.

Is there a way to set parameter bounds and iteration number "globally" (for all samples)?

I also tried script option, but I'm not familiar with JSL scripting and I couldn't achieve to show fit results with the script below.

<JSL>

Names Default To Here( 1 );

dt = Current Data Table();


obj = Nonlinear( Y( :data ), X( :data Predictor ), By( :ID ) );
obj << Go;
obj << Parameter Bounds(
	asympt( 14, 22 ),
	scale1( 0, 100 ),
	decayrate1( -0.2, 0.1 ),
	scale2( -100, 0 ),
	decayrate2( -0.2, 0.1 )
);
obj << Iteration Limit( 10000 );
obj << Finish;
G = obj << Get Estimates;
Show( G );
obj << Report View( "Summary" );

obj << get estimates;

Note: Original JSL moved into JSL display box by txnelson
<JSL>

Accepted answers

All comments

Ben_BarrIngh

Hi @eugur ,

I'm going to show you how to achieve this without using JSL just so you understand how the process works (apart from the starting section). So you should start by generating a formula column that is going to provide the blank parameter values that can then be changed to find the best fit for your data in the Non-linear platform. First off you want to create the formula column (i've added a brief script here for this, but you can also do it by hand):

dt=current data table();
dt<<New Column("BExp 5P Formula",Formula(
			Parameter(
				{a = 0, b = 0, c = 0, d = 0, f = 0},
				a + b * Exp( -c * :Day ) + d * Exp( -(f * :Day) )
			)
		));

When that's ready, open up the non-linear platform, put your formula column in the "X, Predictor Formula" role, and your Y of interest in the Y section, hit Run. When the platform has booted up, click the red button and select 'parameter bounds' and put in the limits that you wish to use -

You can then run the Non-linear platform with 'Go' to get the paramaters estimated with those bounds.

Hope that helps!

Thanks,

Ben

eugur

Hi Ben,

Thank you for your response, but I can already do this and this is not what I'm asking for. As I mentioned in my post, I'm trying to fit to data points for 1000+ samples, which means 1000+ curves fitted. Therefore, in non-linear platform, I would also need to use "ID" column in "By" section. (Somehow "Group" option doesn't work here while it works for Fit Curve).

When you have multiple samples, you need to do what you explained (click the red button and select 'parameter bounds' and put in the limits that you wish to use) manually for each sample. This might be fine if you have a couple samples, but not for 1000+. What I'm asking is to be able to set parameter bounds and number of iterations for all 1000+ samples at once.

Ben_BarrIngh

Hi @eugur ,

If you're not using the group term, then the parameter bounds that are set are being set globally for all 1000+ samples, (also the reason grouping doesn't work in Non-linear is because the group itself has to be integrated into the prediction formula you are feeding NL with). The script you have should work, but you don't need to run 'Go' on the second line, that's why the parameter bounds aren't being added because the platform is running before anything can be changed. Here's an example which then uses the 'combined data table' tool to get a singular report to easily see how the values have changed in each sample

dt=current data table();

id_no=N Items(Associative Array(dt:Batch)<<get keys;);//grab how many samples exist that you want to individually run NL on

dt<<New Column("BExp 5P Formula",Formula(
			Parameter(
				{a = 0, b = 0, c = 0, d = 0, f = 0},
				a + b * Exp( -c * :Day ) + d * Exp( -(f * :Day) )
			)
		));
		

NLplatform=DT<<Non Linear(
	Y (:Rel Potency),
	X (:"BExp 5P Formula"n),
	By (:Batch)
	);
NLplatform<<iteration limit(1000);
NLplatform<<
	Parameter Bounds( a( 10, 30 ), b(1,9), c(4,10), d(10,200),f(6,1000) );

NLPlatform<<Go;
NLPlatform<<Finish;

//Instead of using Get Estimates, have a combined table appear that is more organised
Estimate_dt=report(NLPlatform[1])["Solution",Tablebox(2)]<<make combined data table; //use this to grab all of the estimates into one data table, you need to refer to any of the sub-reports created with the 'by' variable for NLPlatform [x] where x is the number of a report

christian-z

Fit Curve works best for cases with many curve ID's, but if your fitting function is not included in Fit Curve's library of pre-programmed functions, then Fit Nonlinear is needed.

As you noticed, "Group" works differently in Fit Nonlinear and is not what you want to use in this case. I recommend grouping the curves using "By".

I prefer using the following syntax for this. Could you try this and let us know if it works:</CODE></P> <PRE><CODE class=" language-jsl">Nonlinear( Y( :data ), X( :data predictor), By( :ID ), Parameter Bounds( asympt( 14, 22 ), scale1( 0, 100 ), decayrate1( -0.2, 0.1 ), scale2( -100, 0 ), decayrate2( -0.2, 0.1 ) ), Iteration Limit( 10000 ) );

eugur

Thanks Ben,
This functionally works. But I think nonlinear platform uses a different solver. Almost 50% of the fit results are not acceptable.

eugur

Hi Christian,

Thank you very much for your response. You are right, Fit Curve seems to work much better. The fitting function I'm using (Biexponential 5P) is included in Fit Curve's library of pre-programmed functions. However, as I mentioned previously, for same samples (5%) the fitting results is really strange and that's the reason I wanted to try Fit Nonlinear option. But even with the boundaries, Fit Nonlinear can only fit around 50% of the samples accurately.

So my questions are:
- Is it possible to add Parameter Bounds for Fit Curve?
- If not, is it possible to use same solvers and settings for Fit Nonlinear as in Fit Curve?