Error in nonlinear regression

Question

Keegan Carvalho 2018-10-10

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/423273-error-in-nonlinear-regression

评论： Keegan Carvalho 2018-10-27

采纳的回答： Star Strider

ban1.csv

在 MATLAB Online 中打开

I am trying to make a nonlinear regression model of the attached csv file. I used the following code:

if true
data=readtable('ban1.csv')
sea=data(:,1)
sst=data(:,2)
at=data(:,3)
X = [sst,at];
y = sea;
modelfun = @(b,x)b(1) + b(2)*x(:,1).^b(3) + ...
  b(4)*x(:,2).^b(5)
beta0 = [100 100 100 100 100];
mdl = fitnlm(X,y,modelfun,beta0)
  % code
end

I am getting the following errors:

Error using internal.stats.parseArgs (line 42) Wrong number of arguments.

Error in NonLinearModel.fit (line 1385) internal.stats.parseArgs(paramNames, paramDflts, otherArgs{:});

Error in fitnlm (line 99) model = NonLinearModel.fit(X,varargin{:});

Would be grateful if someone can help me, if possible with code. I would also like to know where I am going wrong.

Thank you

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Image Analyst 2018-10-12

Which is x and which is y? Why are you having 2 x but only 1 corresponding y? What do you want along the x/horizontal/independent axis and what do you want along the y/vertical/dependent axis?

Keegan Carvalho 2018-10-13

@Image Analyst I wanted to develop a nonlinear relationship between sea level with sea surface temp (sst) and air temp (at). So I wanted to get an equation like sea ~ b1 + b2(sst)^b3 +b4(at)^b5

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Answer 1

Star Strider 2018-10-10

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在 MATLAB Online 中打开

You are not extracting your table variables correctly.

This works (extracting the data from your table):

X = [data.sst, data.at];
y = data.sea;
modelfun = @(b,x)b(1) + b(2)*x(:,1).^b(3) + ...
  b(4)*x(:,2).^b(5)
beta0 = [100 100 100 100 100];
mdl = fitnlm(X,y,modelfun,beta0)

and so does this (using your table, and simply rearranging its columns to be compatible with what fitnlm expects):

new_table = data(:, [2 3 1]);
modelfun = @(b,x)b(1) + b(2).*x(:,1).^b(3) + ...
  b(4).*x(:,2).^b(5)
beta0 = [100 100 100 100 100];
mdl = fitnlm(new_table,modelfun,beta0)

The ‘carbig’ model is likely not appropriate for your sea level and temperature data, so I am not surprised that the model fails, even though the code now runs without error.

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Keegan Carvalho 2018-10-12

在 MATLAB Online 中打开

Hi @Star Strider I tried the code but I get several warnings:

Warning: Rank deficient, rank = 4, tol = 1.431811e+133. > In nlinfit>LMfit (line 587) In nlinfit (line 284) In NonLinearModel/fitter (line 1127) In classreg.regr.FitObject/doFit (line 94) In NonLinearModel.fit (line 1434) In fitnlm (line 99)

Warning: Rank deficient, rank = 2, tol = 4.455183e+132. > In nlinfit>LMfit (line 587) In nlinfit (line 284) In NonLinearModel/fitter (line 1127) In classreg.regr.FitObject/doFit (line 94) In NonLinearModel.fit (line 1434) In fitnlm (line 99)

Warning: Rank deficient, rank = 2, tol = 1.351145e+132. > In nlinfit>LMfit (line 587) In nlinfit (line 284) In NonLinearModel/fitter (line 1127) In classreg.regr.FitObject/doFit (line 94) In NonLinearModel.fit (line 1434) In fitnlm (line 99)

Warning: Rank deficient, rank = 2, tol = 4.068247e+131. > In nlinfit>LMfit (line 587) In nlinfit (line 284) In NonLinearModel/fitter (line 1127) In classreg.regr.FitObject/doFit (line 94) In NonLinearModel.fit (line 1434) In fitnlm (line 99)

Warning: Rank deficient, rank = 2, tol = 1.143089e+131. > In nlinfit>LMfit (line 587) In nlinfit (line 284) In NonLinearModel/fitter (line 1127) In classreg.regr.FitObject/doFit (line 94) In NonLinearModel.fit (line 1434) In fitnlm (line 99)

Warning: Rank deficient, rank = 2, tol = 1.842881e+130. > In nlinfit>LMfit (line 587) In nlinfit (line 284) In NonLinearModel/fitter (line 1127) In classreg.regr.FitObject/doFit (line 94) In NonLinearModel.fit (line 1434) In fitnlm (line 99)

Warning: Rank deficient, rank = 2, tol = 5.038164e+129. > In nlinfit>LMfit (line 587) In nlinfit (line 284) In NonLinearModel/fitter (line 1127) In classreg.regr.FitObject/doFit (line 94) In NonLinearModel.fit (line 1434) In fitnlm (line 99)

Warning: Rank deficient, rank = 2, tol = 5.022077e+129. > In nlinfit>LMfit (line 587) In nlinfit (line 284) In NonLinearModel/fitter (line 1127) In classreg.regr.FitObject/doFit (line 94) In NonLinearModel.fit (line 1434) In fitnlm (line 99)

Warning: Rank deficient, rank = 2, tol = 5.020462e+129. > In nlinfit>LMfit (line 587) In nlinfit (line 284) In NonLinearModel/fitter (line 1127) In classreg.regr.FitObject/doFit (line 94) In NonLinearModel.fit (line 1434) In fitnlm (line 99)

Warning: Some columns of the Jacobian are effectively zero at the solution, indicating that the model is insensitive to some of its parameters. That may be because those parameters are not present in the model, or otherwise do not affect the predicted values. It may also be due to numerical underflow in the model function, which can sometimes be avoided by choosing better initial parameter values, or by rescaling or recentering. Parameter estimates may be unreliable. > In nlinfit (line 381) In NonLinearModel/fitter (line 1127) In classreg.regr.FitObject/doFit (line 94) In NonLinearModel.fit (line 1434) In fitnlm (line 99)

Also my results are a bit odd:

Nonlinear regression model: sea ~ b1 + b2*sst^b3 + b4*at^b5

Estimated Coefficients: Estimate SE tStat pValue _______ ___ ____

    b1          100    0      Inf       0   
    b2    1.071e-12    0      Inf       0   
    b3       99.356    0      Inf       0   
    b4      -4376.3    0     -Inf       0   
    b5       86.292    0      Inf       0

Number of observations: 19, Error degrees of freedom: 19 Root Mean Squared Error: 2.31e+131 R-Squared: -4.46e+258, Adjusted R-Squared -4.22e+258 F-statistic vs. zero model: NaN, p-value = NaN

Keegan Carvalho 2018-10-13

Thank you for your advice @Star Strider. If that is the case, then is there any other way to determine a relationship between the variables with sea level? Or should I do a one-on-one relationship instead? i.e. sea~sst and sea~at?

Star Strider 2018-10-13

My pleasure.

This is not my area of expertise. I suggest you do an Interweb search for an appropriate model.

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Answer 2

Image Analyst 2018-10-13

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/423273-error-in-nonlinear-regression#answer_341229

You should use scatteredInterpolant(). Write back if you can't figure it out.

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Star Strider 2018-10-13

Keegan Carvalho has a complete data set, so interpolation would likely not gain anything.

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Answer 3

Image Analyst 2018-10-13

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/423273-error-in-nonlinear-regression#answer_341238

在 MATLAB Online 中打开

ban1.csv

Try using scatteredInterpolant(). Below is a complete demo:

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
format bank
% Read in data.
data=importdata('ban1.csv')
data = data.data;
% Extract various components.
sea=data(:,1)
sst=data(:,2)
at=data(:,3)
%================================ MAIN PART RIGHT HERE ==============================================
% Make the scattered interpolant.
F = scatteredInterpolant(sst, at, sea)
% Get a grid of points at every pixel location in the RGB image.
resolution = 300; % Number of points across that you want ot evaluate it at.
x = linspace(min(sst), max(sst), resolution);
y = linspace(min(at), max(at), resolution);
[xGrid, yGrid] = meshgrid(x, y);
xq = xGrid(:);
yq = yGrid(:);
% Evaluate the interpolant at query locations (xq,yq).
vq = F(xq, yq);
fittedImage = reshape(vq, resolution, resolution);
%================================ END OF MAIN PART ==============================================
imshow(fittedImage, [], 'XData', x, 'YData', y);
axis on;
xlabel('sst', 'FontSize', fontSize);
ylabel('at', 'FontSize', fontSize);
title('sea as a function of sst and at', 'FontSize', fontSize);
colorbar;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
% For fun, overlay the known points.
hold on;
plot(sst, at, 'r*', 'MarkerSize', 20, 'LineWidth', 2);