[Help-gsl] Maximizing likelihood functions - GSL vs. Matlab

[AJ Bostian]

I recently programmed up some probit and logit routines in GSL and in 
Matlab.  (The Matlab machine is an i386 and the GSL machine is an 
x86_64, both running linux)  I then compared the output from each of 
these to the output from some commercial statistical packages like SAS 
and Stata.

The output from the Matlab code matches up with the commercial output 
exactly -- the parameter estimates, maximizing value of the likelihood 
function, etc. are identical.  However, the GSL output tends to show a 
slight improvement in the maximizing value of the likelihood function. 
The improvement is not large, say a 0.1% difference, but the parameter 
estimates are noticeably different (5-10%) due to the nonlinearity of 
the function.

Just to check, I plugged the GSL parameter estimates into the Matlab 
objective function.  The value of the Matlab objective using the GSL 
parameter estimates is indeed very slightly worse.

I thought that this might be due to differences in precision, but 
Matlab/SAS/Stata all seem to do calculations in double, which is what I 
used.  I also thought that the choice of GSL minimizer might make a 
difference, but the result holds under all GSL minimizers.

Obviously, I would like to think that the improvement in the maximizing 
value of the likelihood function using GSL is real, but it's hard to go 
up against Matlab/SAS/Stata.  Anyone have any thoughts about why this 
difference might exist, and whether the improvement is legit?

Regards,
AJ Bostian


PS: Can't beat GSL for speed, though.  I blew through 20 iterations of a 
probit problem in about 0.25 sec using GSL, compared to about 3 sec for 
Matlab.


AJ Bostian
Dept. of Economics
University of Virginia
Rouss Hall 114
Charlottesville, VA  22904
Email: address@hidden