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rnon-linear-regression

Nonlinear LAD regression in R

I would like to estimate the parameters of a nonlinear regression model with LAD regression. In essence the LAD estimator is an M-estimator. As far as I know it is not possible to use the robustbase package to do this. How could I use R to do LAD regression? Could I use a standard package?

Solution

  • You could do this with the built-in optim() function

    Make up some data (make sure x is positive, so that a*x^b makes sense - raising negative numbers to fractional powers is problematic):

    set.seed(101)
a <- 1; b <- 2
dd <- data.frame(x=rnorm(1000,mean=7))
dd$y <- a*dd$x^b + rnorm(1000,mean=0,sd=0.1)

    Define objective function:

    objfun <- function(p) {
  pred <- p[1]*dd$x^p[2]   ## a*x^b
  sum(abs(pred-dd$y))      ## least-absolute-deviation criterion
}

    Test objective function:

    objfun(c(0,0))
objfun(c(-1,-1))
objfun(c(1,2))

    Optimize:

    o1 <- optim(fn=objfun, par=c(0,0), hessian=TRUE)

    You do need to specify starting values, and deal with any numerical/computational issues yourself ...

    I'm not sure I know how to compute standard errors: you can use sqrt(diag(solve(o1$hessian))), but I don't know if the standard theory on which this is based still applies ...