[Limdep Nlogit List] Random parameters logit unconditional probabilities

[Iain Pardoe]

I've saved the unconditional probabilities for a random parameters logit
model using "list."  I've also attempted to calculate these
probabilities from scratch to ensure I understand exactly what they are,
but I've been unable to match the results.  For example, I tried fitting
an RPL model to the transportation data:

CALC ; Ran(12345) $

NLOGIT ; Lhs=MODE
       ; Choices=Air,Train,Bus,Car
       ; Rhs=TTME,GC
       ; Rh2=ONE
       ; RPL
       ; Pts=25
       ; list
       ; Fcn=gc(N),ttme(N) $

The four transport choice probabilties for the first respondent are
given as:

PREDICTED PROBABILITIES (* marks actual, + marks prediction.)
Indiv    AIR       TRAIN     BUS       CAR
    1   .0823     .4361 +   .1481     .3335*

Then I tried calculating these probabilties from scratch using the
fitted model results (please forgive the clunky code):

CALC   ; gc1=gc(1)
       ; gc2=gc(2) 
       ; gc3=gc(3) 
       ; gc4=gc(4) 
       ; ttme1=ttme(1) 
       ; ttme2=ttme(2) 
       ; ttme3=ttme(3) 
       ; ttme4=ttme(4) $

CALC ; Ran(12345) $

CREATE ; re1=b(1)+b(6)*Rnn(0,1) ? Simulate 840 random effects for gc
       ; re2=b(2)+b(7)*Rnn(0,1) ? Simulate 840 random effects for ttme
       ; elp1=exp(re1*gc1+re2*ttme1+b(3))
       ; elp2=exp(re1*gc2+re2*ttme2+b(4))
       ; elp3=exp(re1*gc3+re2*ttme3+b(5))
       ; elp4=exp(re1*gc4+re2*ttme4)
       ; selp=elp1+elp2+elp3+elp4
       ; p1=elp1/selp 
       ; p2=elp2/selp 
       ; p3=elp3/selp 
       ; p4=elp4/selp $

DSTAT  ; Rhs=p1,p2,p3,p4 $

The four transport choice probabilities for the first respondent from
these 840 simulations have means of:

.108607, .383156, .129932, .378305

The values seem too far off to be a result of simulation error (and
repeating the process using more simulations doesn't seem to get me any
closer), so I think I must be doing something wrong.  I would greatly
appreciate any enlightenment.

Best wishes, Iain

Iain Pardoe <ipardoe at lcbmail.uoregon.edu>
Assistant Professor of Decision Sciences
Charles H. Lundquist College of Business
1208 University of Oregon
Eugene, OR 97403-1208, USA
Ph: 541-346-3250, Fax: 541-346-3341
http://lcb1.uoregon.edu/ipardoe