*
* Example 17.4 on page 482
*
open data tablefd-1[1].txt
data(format=prn,org=columns) 1 20 id y e
*
* There's one free parameter, which we'll call b
*
nonlin b
*
* We create a FRML which evaluates the log likelihood element for each
* observation.
*
frml logl = -log(b+e)-y/(b+e)
*
* This estimates the model using the BHHH procedure. This is used not just for
* computing the covariance matrix at the end, but is also used to estimate the
* curvature at all iterations.
*
maximize(method=bhhh) logl
compute bhhhvar=%stderrs(1)**2
*
* This estimates the model using the BFGS procedure, which does computes an
* estimate to the inverse of 2nd derivative of the log likelihood. This cannot be
* started from a converged or almost converged settings for the parameters, as it
* makes its estimate by seeing how the gradient changes from one iteration to
* the next. If the gradient starts out at zero, this isn't possible.
*
compute b=0
maximize(method=bfgs) logl
compute bfgsvar=%stderrs(1)**2
*
* Computing the expected value of the 2nd derivative directly.
*
set logl2diff = 1.0/(b+e)**2-2*(b+e)/(b+e)**3
compute infovar=-1.0/%sum(logl2diff)
*
* And using the sample mean rather than the theoretical mean
*
set logl2diff = 1.0/(b+e)**2-2*y/(b+e)**3
compute ainfovar=-1.0/%sum(logl2diff)
*
report(action=define,hlabels=||"Method","Est. Variance"||)
report(row=new,atcol=1) "BHHH" bhhhvar
report(row=new,atcol=1) "BFGS" bfgsvar
report(row=new,atcol=1) "Info" infovar
report(row=new,atcol=1) "Sample Info" ainfovar
report(action=show)