Most importantly, we appear to have figured out the answer to my original question: no, it is not easy. :P

And inadvertently provided an object lesson for anyone watching about the value of researchers providing code...

The value of the smart fraction cutoff appears to have a huge impact on the napping from smart fraction to gdp, but doesn't appear to have a significant effect on the goodness of fit, which troubles me somewhat. I'm also surprised that deleting the outliers seems to have improved the performance of the exponential fit more than the smart fraction fit, which is not what I would have expected from the graphs.

My intuition so far is that La Griffe found a convoluted way of regressing on a sigmoid, and the gain is coming from the part which looks like an exponential. I'm a little troubled that his stuff is so hard to reproduce sanely and that he doesn't compare against the exponential fit: the exponent is obvious, has a reasonable empirical justification. Granting that Dickerson published in 2006 and he wrote the smart fraction essay in 2002 he could at least have updated.

[edit] Sorry, it looks like the formatting for my code is totally ugly.

You need to delete any trailing whitespace in your indented R terminal output. (Little known feature of LW/Reddit Markdown code blocks: one or more trailing spaces causes the newline to be ignored and the next line glommed on. I filed an R bug to fix some cases of it but I guess it doesn't cover nls or you don't have an updated version.)

I don't understand your definition

egdp <- function(iq,iq0,m,b) (m*sf(iq,iq0)+b)

sf(iq,iq0) makes sense, of course, and m presumably is the multiplicative scale constant LG found to be 69k, but what is this b here and why is it being added? I don't see how this tunes how big a smart fraction is necessary since shouldn't it then be on the inside of sf somehow?

But using that formula and running your code (using the full dataset I posted originally, with outliers):

R> erf <- function(x) 2 * pnorm(x * sqrt(2)) - 1
R> sf <- function(iq,iq0) ((1+erf((iq-iq0)/(15*sqrt(2))))/2)
R> egdp <- function(iq,iq0,m,b) (m*sf(iq,iq0)+b)
R> summary(nls(rGDPpc ~ egdp(IQ,iq0,m,b), lynn, start=list(iq0=110,m=40000,b=0)))
Formula: rGDPpc ~ egdp(IQ, iq0, m, b)
Parameters:
Estimate Std. Error t value Pr(>|t|)
iq0 102.08 4.89 20.88 < 2e-16
m 37108.87 9107.73 4.07 0.00011
b 1140.94 1445.76 0.79 0.43241
Residual standard error: 5320 on 78 degrees of freedom
Number of iterations to convergence: 7
Achieved convergence tolerance: 5.09e-06