Fit nonlinear regression model
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I am trying the fit the eclosed data,
for the X-Axis:
x = 0:1:248;
I enclosed the data for the Y-axis. (Each row is a curve, there are 5 row = 5 curves)
with the following objective function:
here is my code:
DF = load('Inter_cubic.mat');
Data = DF.Inter_cubic(:,1:230);
Data1 = array2table(Data);
x = 1:size(Data,2);
Sig = @(p,x) p(4)./(1 + exp(-p(1).*x + p(7))) + p(5)./(1 + exp(-p(2).*x + p(8))) + p(6)./(1 + exp(-p(3).*x + p(9))) + p(10);
beta0 = [Data(1,1) Data(2,1) Data(3,1) Data(4,1) Data(5,1)];
for k = 1:size(Data1,1)
mdl(1,:) = fitnlm(Data1(k,:),Sig,beta0(1,k));
end
I am getting error message regarding using the function "fitnlm", and regarding the initial value beta0 are they the intial values of the data?
Accepted Answer
Answering your main question: beta0 is the initial guess at the coefficients of the fit. In your case, MATLAB is expecting a vector of length 10, because you have 10 parameters to fit.
There are lots of problems with both your MATLAB syntax, and how you are trying to fit your curves. In the code below, I have fixed the syntax problems, by
- fixing the beta0 problem you asked about
- creating separate tables for each fit
- storing the resulting models in a cell array
But, I did not try to fix the equation you are trying to fit to.
load Data
x = (1:size(Data,2))';
% Define the fitting function
Sig = @(p,x) p(4)./(1 + exp(-p(1).*x + p(7))) + p(5)./(1 + exp(-p(2).*x + p(8))) + p(6)./(1 + exp(-p(3).*x + p(9))) + p(10);
% Initial guess of coefficients
beta0 = ones(1,10);
for k = 1:size(Data,1)
% Put the data for this curve into a table
y = Data(k,:)';
tbl = table(x,y);
% Fit the model
mdl{k} = fitnlm(tbl,Sig,beta0);
% Plot the fit against the data
figure
hold on
plot(x,Data(k,:),'o')
plot(x,predict(mdl{k},x))
end
5 Comments
Hidd_1
on 19 May 2023
the cyclist
on 19 May 2023
As I mentioned, I only fixed your syntax, not your fitting problem. Given your equation, and a very naive initial guess, MATLAB cannot do better.
Note the warning that MATLAB is giving: The model is insensitive to some of the parameters. If you look at the results of one of the fits, you'll see
Nonlinear regression model:
y ~ F(p,x)
Estimated Coefficients:
Estimate SE tStat pValue
________ __________ __________ ___________
b1 9407 0 Inf 0
b2 9407 4.1233e-17 2.2814e+20 0
b3 9406 0 Inf 0
b4 3.3047 0.046424 71.183 3.4629e-158
b5 3.3047 0.046424 71.183 3.4629e-158
b6 3.3047 0.046424 71.183 3.4629e-158
b7 8681.2 0 Inf 0
b8 8681.2 0 Inf 0
b9 8681.4 0 Inf 0
b10 3.3403 0.046424 71.951 3.2946e-159
with redundant info where you have the exact same functional term three times. Unless you give much closer initial guesses for each of those terms, I don't think MATLAB is going to be able to figure it out (even if this is a good function to try to fit the curve with).
Hidd_1
on 19 May 2023
I think a simplified model can still do a pretty good fit, if you choose better initial guesses. And you may need different initial guesses for each curve. For example, looking only at the 5th set of data ...
load Data
x = (1:size(Data,2))';
% Define the fitting function
% Sig = @(p,x) p(4)./(1 + exp(-p(1).*x + p(7))) + p(5)./(1 + exp(-p(2).*x + p(8))) + p(6)./(1 + exp(-p(3).*x + p(9))) + p(10);
Sig = @(p,x) p(2)./(1 + exp(-p(1).*x + p(3))) + p(4); % <----- I used only one non-linear function here, not all three
% Initial guess of coefficients
beta0 = [0.01 1 0 19] % <------- I changed these
for k = 5 % <------- I am ONLY looking at 5th curve
% Put the data for this curve into a table
y = Data(k,:)';
tbl = table(x,y);
% Fit the model
mdl{k} = fitnlm(tbl,Sig,beta0);
% Plot the fit against the data
figure
hold on
plot(x,Data(k,:),'o')
plot(x,predict(mdl{k},x))
end
Hidd_1
on 19 May 2023
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