[Limdep Nlogit List] Allowing for a full correlation matrix in a random parameter error correction model?

[Soren Olsen]

Dear all,

In a recent review of one of my manuscripts I was adviced by a reviewer to allow for a full correlation matrix when estimating my model. 
 
In order to do so, I use a random parameter error correction model in which I estimate 2 out of the 3 possible ASC standard deviations (I have three alternatives in my choice set so I need to normalize one of them) to obtain the diagonal of the correlation matrix. Furthermore, I have specified three error correction terms in order to obtain the three off-diagonal correlation parameters. Here's my model specification in Limdep/NLogit:
 /* Random parameters model with error correction - allowing for full correlation matrix*/
CALC ;ran(12345) $
RPLOGIT ;lhs=choic
;choices=1,2,3
;Model: U(1)=basc1*asc1+bskov*skov+bvaad*vaad+bhede*hede+bpris*pris/
U(2)=basc2*asc2+bskov*skov+bvaad*vaad+bhede*hede+bpris*pris/
U(3)=bskov*skov+bvaad*vaad+bhede*hede+bpris*pris
;Fcn=bskov(n),bvaad(n),bhede(n),basc1(n),basc2(n)
;ECM=(2,3),(1,2),(1,3)
;Parameters
;WTP=bskov/bpris,bvaad/bpris,bhede/bpris
;Maxit=50
;pts=2000
;halton
;pds=6 
;PrintVC
;Utility=util
;Prob=prob
$
The model runs nicely, but here's my problem:
 
When I use 300 halton draws, SigmaE01 is significant (at the 0.05-level) while SigmaE02 and SigmaE03 are not. Furthermore, NsBASC1 and NsBASC2 are both insignificant.
 
When I increase to 500 Halton draws, SigmaE01 suddenly becomes insignificant while the conclusion regarding the other parameters is unchanged.
 
When I further increase to 1000 Halton draws, NsBASC1 now becomes signficant while the conclusion regarding the other parameters is unchanged (SigmaE01 still insignficant).
 
Finally, when I further increase to 2000 Halton draws, NsBASC1 goes back to being insignficant while the conclusion regarding the other parameters is unchanged .
 
Furthermore, the magnitude of the parameter estimates changes quite a lot as I increase the number of draws (e.g. SigmaE01 going from 3.01 to 1.82, and NsBASC1 going from 1.43 to 2.46 when increasing the number of draws from 300 to 2000).
 
So, unfortunately it seems, that my results are very unstable as they depend very much on the chosen number of draws. I my opinion, increasing the number of draws should not have this effect (at least when we are above 300 Halton draws). 
 
Could someone out there please help me out with an explanation? Does it make sense at all to try to estimate the full correlation matrix in a single model, or is it simply over- or mis-specified? And if this is not the way to do it, then what should I do instead?
 
Best regards
 
Søren Bøye Olsen
University of Copenhagen
 
PS. Similar problems arise when I estimate the model in Biogeme, but there I also see apparently random changes in the signs of the parameter estimates as I change the number of draws.


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