How do i use the nlinfit function when there are two independent variables?

v0=b(1).*A.*B/((b(2).*b(3))+(b(3).*A)+(A.*B))

This is my model. I have two independent variables A and B.v0 is the dependent variable. Now can you please help me with writing the line code for this in matlab where i have to use a nlinfit function.

For one independent variable the following code worked:

model=@(b,x) b(1).*substrate./(b(2)+substrate); 
 initialguess=[1 1]; 
 [beta,R,J,CovB,MSE] = nlinfit(substrate,vo,model, initialguess);

I want to do the same thing for my above equation.Please suggest.

THANK YOU.

Answer 1

[Star Strider]

You have to pass your independent variable as a single value. If you have two independent variables, simply create a matrix from them, and make corresponding changes in your function:

AB = [A B];     % Assumes A and B are COLUMN vectors
v0=b(1).*AB(:,1).*AB(:,2)/((b(2).*b(3))+(b(3).*AB(:,1))+(AB(:,1).*AB(:,2)))

Make appropriate changes if they are row vectors, or simply transpose the row vectors to column vectors. (The nlinfit function doesn’t care. It just wants your function to return a vector that matches your dependent variable vector dimensions.)

Your call to nlinfit then becomes:

[beta,R,J,CovB,MSE] = nlinfit(AB, ...

Answer 2

[Himaja]

hello, I have tried using the syntax but im a bit confused.I will post my code here can u suggest as to where im going wrong?

 % Assign the data vectors 2 
 A=[1.814966667 2.527168776 3.156463768 4.883318386 6.701415385 7.686917647 8.296990476];
 B=[7.661333333 7.060064135 6.528788406 5.070909417 3.536 2.704 2.188952381];
 vo=[25.9 35.6 39.2 27.9 20 10.7 8.5];  
 % Plot the raw data to get a look at the shape 
 figure(1) 
 clf 
 plot(A,vo,'o') 
 xlabel('Substrate Concentration (mM)','FontSize',14) 
 ylabel('Initial rate (mM/s)','FontSize',14) 
 title('Initial Rate vs. Concentration','FontSize',16) 
 print -depsc rawdataplot 
 figure(2) 
 clf 
 plot(B,vo,'o') 
 xlabel('Substrate Concentration (mM)','FontSize',14) 
 ylabel('Initial rate (mM/s)','FontSize',14) 
 title('Initial Rate vs. Concentration','FontSize',16) 
 print -depsc rawdataplot 
 % Calculate unknown coefficients in the model using nlinfit 
 AB=[A B];     % Assumes A and B are COLUMN vectors
 model=@(b,AB)b(1).*AB(:,1).*AB(:,2)/((b(2).*b(3))+(b(3).*AB(:,1))+(AB(:,1).*AB(:,2)));
 initialguess=[1 1]; 
 [beta,R,J,CovB,MSE] = nlinfit(AB,vo,model, initialguess); 
 % 95% CI of coeffieicents 
 betaci = nlparci(beta,R,J); 
 % Plot the nonlinear fit with the raw data 
 figure(3) 
 plot(A,vo,'o') 
 hold on 
 A=0:0.1:10;
 B=0:0.1:10;
 AB=A.*B;
 f=beta(1).*AB(:,1).*AB(:,2)/((beta(2).*beta(3))+(beta(3).*AB(:,1))+(AB(:,1).*AB(:,2))) ; 
 plot(AB,f,'-') 
 xlabel('Substrate Concentration A (mM)','FontSize',14) 
 ylabel('Initial rate (mM/s)','FontSize',14) 
 title('Initial Rate vs. Concentrtaion A','FontSize',16) 
 legend('Data Points','Nonlinear Fit',0) 
 print -depsc rawdatawithfit
 % Make a residual plot 
 figure(4) 
 clf 
 plot(AB,0,'-',A,R,'rp')
 xlabel('Substrate Concentration (mM)','FontSize',14) 
 ylabel('Residuals','FontSize',14) 
 title('Residual Plot','FontSize',16) 
 print -depsc nonlinresiduals 
 % Compute the r^2 value 
 ssresnonlin=sum(R.^2); 
 sstotnonlin=sum((vo-mean(vo)).^2); 
 rsqrnonlin=1-(ssresnonlin/sstotnonlin); 
 disp(beta(1));
 disp(beta(2));
 disp(beta(3));

this is the non linear regression to fit my data into the formula i have sent you before. I would be thankful to u if u would tell me my mistake. Thanks.

[Star Strider]

I just ran the regression part of your code, not the entire script. Note that A and B are row vectors. I transposed them, transposed vo in the argument list, vectorised your model, and expanded your initialguess vector from 2 elements to 3, since you are estimating three parameters.

AB=[A' B'];     % Assumes A and B are COLUMN vectors — TRANSPOSED to make them so
model=@(b,AB)b(1).*AB(:,1).*AB(:,2)./((b(2).*b(3))+(b(3).*AB(:,1))+(AB(:,1).*AB(:,2)));   initialguess=[1 1 1]; 
[beta,R,J,CovB,MSE] = nlinfit(AB,vo',model, initialguess);

Your model appears to have problems in the parameters it estimates. That could be due to an inappropriate initialguess vector that would lead nlinfit to the wrong solution, or you may not have programmed your model correctly. I don’t know what it is, so I can’t help you with that.

[GAGANDEEP KAUR]

May I please get some suggestion for multivariable output case. As I have 1 input variable(say mole fraction x) and 9 outputs e.g. say activity coefficient of 9 species yk1,yk2,yk3.........yk9, are in form of vactors, that are obtained and has to be fitted to obtain unknown parameters

[Star Strider]

GAGANDEEP KAUR —

The nlinfit function cannot (to my knowledge) fit more than 1 dependent variable. However, the lsqcurvefit function can.

Some restrictrions remain with respect to lsqcurvefit however, since confidence intervals on the parameters are possible with more than 1 dependent variable and only with unconstrained parameter estimates with nlparci, although it is not possible to calculate confidence intervals on the fit with more than 1 dependent variable with nlpredci.