How to perform nonlinear regression accross multiple datasets

Question

Jack Nolan 2021-2-19

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/750764-how-to-perform-nonlinear-regression-accross-multiple-datasets

评论： Jack Nolan 2021-2-25

regression.zip

Appolgies in advance as I am new to MATLAB.

I am trying to fit a model to mutiple data sets at once using non linear regression. I have found similiar examples but I am unable to modify them to suit my needs.

The model contains 3 unkown paramaters that must be tuned to satsifty (or give best model fit) accross 4 data sets at once.However, the model also contains 1 known paramater which is different for each of the 4 datasets.

Model to fit:

ΔRon/Ron are the data set y values
t is the data set x values
A1, A2, γ are unkown paramaters (common to all data sets) which must be found
tau is a kown paramaer whcih differs accross all data sets

I have attached an m-file with relevant data and information. If sombody could provide guidance or a commented solution I would be very grateful. Thanks.

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Jack Nolan 2021-2-20

@Alex Sha, can you recommend a free/more afordable software package please.

Alex Sha 2021-2-21

Matlab should be OK, but need you to do more work.

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Answer 1

Deepak Meena 2021-2-24

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https://ww2.mathworks.cn/matlabcentral/answers/750764-how-to-perform-nonlinear-regression-accross-multiple-datasets#answer_631989

在 MATLAB Online 中打开

Hi Jack,

The following post on MATLAB Answers discusses a similar case:

http://www.mathworks.com/matlabcentral/answers/1056-nonlinear-fit-to-multiple-data-sets-with-shared-parameters.

In that question , there were 2 unknown shared parameters and 1 parameter was different for all the dataset but was also unknown. In this question we have 3 unknown shared parameters and 1 known parameters whose value will be different for each dataset.So I modified that to illustrate that :

function sharedparams
t = (0:10)';
T = [t; t; t;t];
Y = 3 + [exp(-t/2); 2*exp(-t/2); 3*exp(-t/2);4*exp(-t/2)] + randn(44,1)/10;
dsid = [ones(11,1); 2*ones(11,1); 3*ones(11,1);4*ones(11,1)];
gscatter(T,Y,dsid)
X = [T dsid];
A3 = [-5;1;3;4];
b = nlinfit(X,Y,@subfun,ones(1,3))
 line(t,b(1)+b(2)+b(3)*t+A3(1),'color','r');
 line(t,b(1)+b(2)+b(3)*t+A3(2),'color','g');
 line(t,b(1)+b(2)+b(3)*t+A3(3),'color','b');
 line(t,b(1)+b(2)+b(3)*t+A3(4),'color','c');
function yfit = subfun(param,X)
T = X(:,1);        % time
dsid = X(:,2);     % dataset id
A0 = param(1);
A1 = param(2);
A2 = param(3);
A3 = [-5;1;3;4]; %known paramter 
yfit = A0 + A1+ A2*T + A3(dsid);

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Jack Nolan 2021-2-25

在 MATLAB Online 中打开

regression.zip

Hi @Deepak Meena,

Unfortuanely I am still getting erros.

Error using nlinfit (line 219)
MODELFUN must be a function that returns a vector of fitted values the same size as Y (160-by-1).  The model function you provided returned a result that was 160-by-4.
One common reason for a size mismatch is using matrix operators (*, /, ^) in your function instead of the corresponding elementwise operators (.*, ./, .^).
Error in sharedparams (line 18)
b = nlinfit(X,Y,@subfun,ones(1,4))
Error in regression (line 17)
sharedparams

See attached for m files and data. Heres what I've done so far.

I presume I should create a main m file to call the functions shararedparams & subfun (which are each contained in seperate function files).

MAIN .m file:

clc
clear all
close all
d1 = xlsread('data.xlsx', 'Sheet1', 'G4:G43'); % y data 1
d2 = xlsread('data.xlsx', 'Sheet1', 'M4:M43'); % y data 1
d3 = xlsread('data.xlsx', 'Sheet1', 'AG4:AG43'); % y data 1
d4 = xlsread('data.xlsx', 'Sheet1', 'AM4:AM43'); % y data 1
T = [d1 ;d2; d3;d4];% d1 , d2 ,d3 ,d4 are your data sets 
dsid = [ones(40,1); 2*ones(40,1); 3*ones(40,1);4*ones(40,1)]; % 40 data points in each data set (hence, ones(40,1)
X = [T dsid];
%%%% FUNCTION CALL TO sharedparams
sharedparams
param = [0.01, 1, 900]; % intial estimates of A1, A2 and tau
%%%% Function call to subfun
yfit = subfun(param,X)

sharedparams function:

function sharedparams
t = xlsread('data.xlsx', 'Sheet1', 'F4:F43'); % x data
y1 = xlsread('data.xlsx', 'Sheet1', 'G4:G43'); % y data 1
y2 = xlsread('data.xlsx', 'Sheet1', 'M4:M43'); % y data 1
y3 = xlsread('data.xlsx', 'Sheet1', 'AG4:AG43'); % y data 1
y4 = xlsread('data.xlsx', 'Sheet1', 'AM4:AM43'); % y data 1
% t = (0:10)';
T = [t; t; t;t];
Y = [y1; y2; y3; y4];
% Y = 3 + [exp(-t/2); 2*exp(-t/2); 3*exp(-t/2);4*exp(-t/2)] + randn(44,1)/10
dsid = [ones(40,1); 2*ones(40,1); 3*ones(40,1);4*ones(40,1)];
gscatter(T,Y,dsid)
X = [T dsid];
tau = [63085.05; 1525.3; 1601.8; 62465.28756];
b = nlinfit(X,Y,@subfun,ones(1,4))
 line(t,b(1)+b(2)+b(3)*t+tau(1),'color','r');
 line(t,b(1)+b(2)+b(3)*t+tau(2),'color','g');
 line(t,b(1)+b(2)+b(3)*t+tau(3),'color','b');
 line(t,b(1)+b(2)+b(3)*t+tau(4),'color','c');
 

subfun function:

 function yfit = subfun(param,X)
T = X(:,1);        % time
dsid = X(:,2);     % dataset id
A1 = param(1);
A2 = param(2);
gamma = param(3);
tau = [63085.05; 1525.3; 1601.8; 62465.28756]; %known paramter 
% yfit = A0 + A1+ A2*T + A3(dsid);
yfit = A1 * log(1 + T/tau) + A2 * log(1 + (T/tau)*(1/gamma))

Jack Nolan 2021-2-25

在 MATLAB Online 中打开

regresson.zip

Hi @Deepak Meena, Thankyou for all your help so far.

I have corrected all of the mistakes that you pointed out. I also now understand the purpose of dsid (its like and ID for each dataset, identifying it as 1,2,3, or 4). I have gone through every line of my code and your code running each line individualy so I understand its purpose.

Unfortuanately I am still getting an error (something to do with deviations between matrix dimiension of Y and the model function I provided). See below error. I don't see where I'm going wrong as I have followed your methodology exactly and have debugged each line without finding a solution. If you could point out my mistake I would realy appreciate it. Thanks.

ERROR:

Error using nlinfit (line 219)
MODELFUN must be a function that returns a vector of fitted values the same size as Y (160-by-1).  The model function you provided returned a result that was 160-by-160.
One common reason for a size mismatch is using matrix operators (*, /, ^) in your function instead of the corresponding elementwise operators (.*, ./, .^).
Error in untitled (line 18)
b = nlinfit(X,Y,@subfun,ones(1,3))

CODE:

clc
clear all
close all
t = xlsread('data.xlsx', 'Sheet1', 'F4:F43'); % x data
y1 = xlsread('data.xlsx', 'Sheet1', 'G4:G43'); % y data 1
y2 = xlsread('data.xlsx', 'Sheet1', 'M4:M43'); % y data 1
y3 = xlsread('data.xlsx', 'Sheet1', 'AG4:AG43'); % y data 1
y4 = xlsread('data.xlsx', 'Sheet1', 'AM4:AM43'); % y data 1
T = [t; t; t; t] % vector of x data sets
Y = [y1; y2; y3; y4] % vector of y data sets
dsid = [ones(40,1); 2*ones(40,1); 3*ones(40,1);4*ones(40,1)] % ones(40,1) is a 40 x 1 array of 1's
gscatter(T,Y,dsid)
X = [T dsid] %%%%%%%%
tau = [63085.05; 1525.3; 1601.8; 62465.3]
b = nlinfit(X,Y,@subfun,ones(1,3))
 line(t,b(1) * log(1 + t/tau(1)) + b(2) * log(1 + (t/tau(1))*(1/b(3))), 'color', 'r');
 line(t,b(1) * log(1 + t/tau(2)) + b(2) * log(1 + (t/tau(2))*(1/b(3))), 'color', 'g');
 line(t,b(1) * log(1 + t/tau(3)) + b(2) * log(1 + (t/tau(3))*(1/b(3))), 'color', 'b');
 line(t,b(1) * log(1 + t/tau(4)) + b(2) * log(1 + (t/tau(4))*(1/b(3))), 'color', 'c');
 function yfit = subfun(param,X)
T = X(:,1)        % time
dsid = X(:,2);     % dataset id
A1 = param(1);
A2 = param(2);
gamma = param(3);
tau = [63085.05; 1525.3; 1601.8; 62465.28756]; %known paramter 
yfit = A1 * log(1 + T/tau(dsid)) + A2 * log(1 + (T/tau(dsid))*(1/gamma));
 end

Tom Lane 2021-2-25

在 MATLAB Online 中打开

You have:

yfit = A1 * log(1 + T/tau(dsid)) + A2 * log(1 + (T/tau(dsid))*(1/gamma));

You should have:

yfit = A1 * log(1 + T./tau(dsid)) + A2 * log(1 + (T./tau(dsid))*(1/gamma));

You want element-by-element division, not vector division in the sense of a matrix operation.

Jack Nolan 2021-2-25

Thanks alot @Tom Lane, it's working now

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How to perform nonlinear regression accross multiple datasets

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