# Boost Trap for multivariant model

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Faizan Lali il 9 Mar 2023
Risposto: Shivansh il 12 Set 2023
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.
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
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### Risposte (1)

Shivansh il 12 Set 2023
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!
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