How to add boundary conditions using fitnlm function?

Hello,

I would like to run a nonlinear regression model for the function detailed below (in the code). However, I want to add boundary conditions for my parameters, which include:

b(1) > 0, b(2) > 0, and 0.45 < b(3) < 0.89

I would like to know how I can obtain the full statistical analysis (i.e. SSE, coefficients, t test, confidence intervals) while being able to add the boundary conditions to the model. Right now, I am able to run the model, but without the specified boundaries.

I am aware that if I use lsqcurvefit function, I will be able to include the boundaries that I want. However, my goal is not only to include the boundaries and minimize SSE. I want to evaluate whether it is important to include the parameter b(2) in the model or not. Thank you in advance for the help.

%% Data and Model for the Fit
% Defining experimental data (x,y)

x = [1	2	4	6	8	10	15	20	30	40	60	90	120	150	180]';
y = [0	0	0	0	0.206398349	0.063037496	0.085397317	0.56381149	0.946508428	1.462332301	1.731854145	1.700722394	1.829205366	2.092363261	2.265393877]';

%% Defining function

fitfcn = @(b,x) b(1).*x.^(b(3)) + b(2).*x.^(2*b(3));

start = [0.1,0.01,0.45];
nlm = fitnlm(x,y,fitfcn,start);
xx = linspace(0,180)';
line(xx,predict(nlm,xx),'linestyle','--','color','k');

hold on;

plot(x,y,'ko');
xlabel('Time (min)'); ylabel('Concentration (mg/mL/g');

Answer 1

[Aditya Patil]

This is an known request, and might be implemented in any future release.

As a workaround, you can use the predicted parameters/weights from lsqcurvefit to evaluate the function, and then use various hypothesis tests to evaluate the fit.