# [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?

http://lists.wfu.edu/pipermail/gretl-users/2013-April/008747.html

> CONSTANT IN LOG-LIKELIHOOD
> 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
http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------
```