I need to do a multivariate nonlinear regression.The regression would be quadratic with three variables (x1, x2, x3) and looks like the following:
y = a0 + a1x1 + a2x1^2 + a3x2 + a4x2^2 + a5x3 + a6x3^2 + a7x1x2 + a8x1x3 + a9x2x3 + a10x1x2x3
As shown above, the model has 11 coefficients to be estimated.If I am correct, the code should look as following:
load mydata
tbl = table(x1,x2,x3,y);
modelfun = @(b,x)b(1) + b(2)*x(:,1) + b(3)*x(:,1)^2 + b(4)*x(:,2) + b(5)*x(:,2)^2 + b(6)*x(:,3) + b(7)*x(:,3)^2 +...
b(8)*x(:,1)*x(:,2) + b(9)*x(:,1)*x(:,3) + b(10)*x(:,2)*x(:,3) + b(11)*x(:,1)*x(:,2)*x(:,3)
beta0 = [b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11];
mdl = fitnlm(tbl,modelfun,beta0)
My question is how to find good starting guess initial values for beta0. I do not want to use random initial values for the coefficients since that might not lead to a solution. I searched Matlab questions/answers and found that I could use functions such as patternsearch (link) or ga (link), but this would require having the Global Optimization Toolbox. Unfortunatelly, I do not have this toolbox.
