[Gretl-users] Constant in log-likelihood and graph of two densities together (Allin Cottrell)

Riccardo (Jack) Lucchetti r.lucchetti at univpm.it
Tue Jul 9 13:45:00 EDT 2013

On Tue, 9 Jul 2013, Alecos Papadopoulos wrote:

> GRAPH OF TWO DENSITIES TOGETHER: Thanks for providing the older link. 
> Although the code there is to plot two densities /consecutively /from left to 
> right, while what I need to do is to /superimpose/ them - and this I realize 
> now has the problem of having two different abscissaes series. Still, I 
> learned something new about handling plots in Gretl.

Really? Have you seen this?


> The basic code *without the constant in the log-l *is (omitting the initial 
> part where OLS executes to obtain initial values)


> *COMMENT: **slope coefficients are again comparable and the value of the 
> likelihood is close to what it should have been if its constant term was 
> added afterwards. But the estimates of the three variance terms v0 v1 v2 are 
> totally different, the one reaching the specified boundary of the parameter 
> space (zero). *

This is very strange indeed. It *may* have something to do with the 
machine epsilon of your computer, but still it's very strange. Basically, 
models 1 and 2 converge to the same maximum (with negligible differences); 
model 3 really doesn't converge at all: BFGS gives you a spurious 
convergence message, but you're not on the maximum. Weird.

Here's a couple of things you may try just to see what happens:

* try using "set bfgs_richardson on"; this uses a different algorithm for 
computing numerical derivatives. Slower, but much more accurate.

* re-parametrise your model so to avoid estimating quantities, such as 
variances, which have a lower bound. Try logarithms instead, for example.

   Riccardo (Jack) Lucchetti
   Dipartimento di Scienze Economiche e Sociali (DiSES)

   Università Politecnica delle Marche
   (formerly known as Università di Ancona)

   r.lucchetti at univpm.it

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