Boost Trap for multivariant model

I am trying to do boost trap for 2 independent variables and I am not sure how to do it. I have already done the boost trap for 1 independent variable by boost trapping the residuals. The code for 1 independent variable is given below. Data sheet "Data.xlsx" is also attached.

data =readmatrix('Data.xlsx');

x1=data(3:42,2);

x2=data(3:42,3);

Cobs=data(3:42,4);

xm=[x1 x2];

%% Initial parameter guesses

C1=1.3585;

C2=0.1749;

beta0(1)=C1; %initial guess yo

beta0(2)=C2; %initial guess kr

n=length(x1);

p=length(beta0);

%% bootstrap CB for beta

fnameFOR = @Project_func;

% use nlinfitcheck to ignore NaN

nlinfitcheck = statset('nlinfit');

nlinfitcheck.FunValCheck='off';

nboot=100;

betab(1,:)=beta;%put beta from original data as first row

ypredb(1,:)=Cpred;%put Cpred from original data as first row

%mm=1;%use x1, y1; x2, y2;... bootstrapping the data

mm=2;%use x1, Ypred1+e1; x2, Ypred2+e2;... bootstrapping the residuals

for j=2:nboot

r=round(1 + (n-1).*rand(n,1));%index of random integers from 1 to n

for i=1:n

if mm==1

tt(i)=t(r(i));%tt(i) is the time for each bootstrapped datum

yboot(i)=Cobs(r(i));%yboot(i) is the y value for each bootstrapped datum

end

if mm==2

tt=t;

yboot(i)=Cpred(i)+resids(r(i));

if i==n

yboot=yboot'; %make yboot a column

end

end

end

[betab(j,:),rr(j,:),J2,COVB2,mse2]= nlinfit(tt,yboot,fname,beta0,nlinfitcheck);%betab are the parameters from the bootstrapping

ypredb(j,:)=fname(betab(j,:),t);%should change "t" to tpred(1000,1) using linspace

clear yboot

end

r2=rr(1,:)';%save the residuals from first bootstrapping

%r2=resids;

for j=2:nboot

r2=[r2; rr(j,:)']; %build a matrix "r2" where each column holds residuals for one bootstrap

end

bsort=sort(betab,1); ysort=sort(ypredb,1); %"1" means sorts along columns

L=round(0.025*nboot); %L is lower 2.5% cutoff

if L==0; L=1; end %if L = 0, switch to L = 1 to avoid MATLAB error

U=round(0.975*nboot); %U is upper 2.5% cutoff

cib(1,1)=bsort(L,1); cib(1,2)=bsort(U,1);%bootstrap 95% CI for first beta

cib(2,1)=bsort(L,2); cib(2,2)=bsort(U,2);%bootstrap 95% CI for second beta

for i=1:n

ybci(i,1)=ysort(L,i); ybci(i,2)=ysort(U,i);%ybci is a n-by-2 matrix with bootstrap CI for y at each time

end

%% compute bootstrap prediction bands

D=rmse*tinv(.975,n-p);

CIwb(:,1)=ybci(:,1)-Cpred; CIwb(:,2)=Cpred-ybci(:,2); %upper (column 1) and lower (column 2) bootstrap CIwidths

PIwb(:,1)=sqrt(CIwb(:,1).^2+D^2); PIwb(:,2)=sqrt(CIwb(:,2).^2+D^2);%upper and lower widths of PI

PIb(:,1)=Cpred+PIwb(:,1); PIb(:,2)=Cpred-PIwb(:,2); %PI values

%% Functions

function y=Project_func(beta0,x1,x2)

c2s=@(x)-2.40874-39.748*(1+x).^-2.856;

y=100./(1+exp(-beta0(1).*c2s(x1)+(beta0(2).*c2s(x1).*log10(100.*x2))));

end

Answer 1

[Shivansh]

Hi Faizan,

I understand that you have a working code for one independent variable. You want to know the way to generalise the above algorithm for the multivariate case.

To generalize the bootstrap approach for a multivariate model with multiple independent variables, you would need to make a few modifications to the code you provided. Here's a general outline of the steps involved:

1. Update the data and independent variables: X = data(3:42, 2:end);
2. Adjust the function definition of the Project_func function. You can change by using the linear combination of independent variables and modifying the model equation.
3. Modify the bootstrap loop to include all independent variables. This is an example code for the changes in your previous code.

    for j = 2:nboot
        r = round(1 + (n - 1) .* rand(n, 1)); % Index of random integers from 1 to n
        for i = 1:n
            if mm == 1
                tt(i) = t(r(i)); % tt(i) is the time for each bootstrapped datum
                yboot(i) = Cobs(r(i)); % yboot(i) is the y value for each bootstrapped datum
            end
            if mm == 2
                tt = t;
                yboot(i) = Cpred(i) + resids(r(i));
                if i == n
                    yboot = yboot'; % Make yboot a column
                end
            end
        end
        [betab(j, :), rr(j, :), J2, COVB2, mse2] = nlinfit(tt, yboot, @(beta) Project_func(beta, X), beta0, nlinfitcheck);
        ypredb(j, :) = Project_func(betab(j, :), X);
        clear yboot
    end

These modifications will enable your code to generalise for multivariate cases. Make sure to adjust the code with respect to the changes.

Hope this helps!