Star Strider asked . 2022-07-23

Which statistical test for change in a nonlinear regression model?

% Define model function (BOLTZMANN);
f = @(beta0,conds)beta0(1) + ((beta0(2)-beta0(1)) ./ (1+exp((beta0(3) - conds) ./ beta0(4))));

% Find initialization parameters:
resp50 = (max(resp) + min(resp))/2;
x50 = 5000; %Educated guess

inidat = [0,max(resp),resp50,x50];

% Estimate the fitted function:
[beta,res,jac,covb] = nlinfit(conds',fliplr(resp),f,inidat);

% Fit the function:
xfit = linspace(min(conds),max(conds),100);
[yfit,delta,n,df,varpred] = nlpredci(f,xfit,beta,res,'Covar',covb,'PredOpt','observation'); %Function edited, see below
yfit = fliplr(yfit);
delta = fliplr(delta');
varpred = fliplr(varpred');

alpha = 0.05;

for i=2:length(yfit)
     testdiff = yfit(1) - yfit(i);

     %Common MSE is mean of both estimated variances (s. ONLINESTATBOOK p.376):
     mse = (varpred(1) + varpred(i))/2;

     %Common SE:
     testse = sqrt(2*mse/n); %Correct?

     %Compute t-value:
     t = testdiff/testse;

     %Common df:
     testdf = (n-1) + (n-1); %Correct?

     p = tpdf(t,testdf);

     if p < (alpha/(i-1)) %With BONFERRONI correction (correct?)
        m = i;
        break;
     end
  end

data analysis , t-test , nonlinear regression , AI, Data Science, and Statistics , Statistics and Ma