Maximize nonlinear regression function in R

Question

Given a linear model obtained from the function call reg = lm(...) , how can you find the coefficients that maximize the obtained regression function?

I'm aware of the function optim(...) , but it requires a function as an input. I haven't figured out how to extract this from the regression model.

It should be noted that I'm using non-linear terms in my regression analysis (squared variables, to be precise).

In other words, by regression function looks like

y_hat = kx_11*x_1+kx_12*x_1^2 + kx_21*x_2+kx_22*x_2^2 + ...

Answer 1

Here is a quick example to demonstrate 1 way. Use predict() on the lm object to create your function. fxn() is a little messy since I don't have your exact data, but you should get the idea.

#set up dummy data
x1 = -10:10
x2 = runif(21)
y = -x1^2 + x1 - 10*x2^2 + runif(21)*.1 
data = data.frame(y= y, x1=x1, x2=x2)

#fit model
m = lm(data=data, y ~ x1 + I(x1^2) + I(x2^2))

#define function that returns predicted value
fxn = function(z){
    z = as.data.frame( t(z) )
    colnames(z) = colnames(data)[-1]
    predict(m, newdata=z)
}

optim(c(0,0), fxn, control=list(fnscale=-1)) #maximizes fxn

$par
[1]  4.991601e-01 -3.337561e-06

$value
[1] 0.3153461

$counts
function gradient 
      65       NA 

$convergence
[1] 0

$message
NULL