[Limdep Nlogit List] Re: Limdep Digest, Vol 14, Issue 4

William Greene wgreene at stern.nyu.edu
Tue May 22 13:29:30 EST 2007


Mr. Choi.  You are attempting to compute the log likelihood function as if your panel
were a cross section.  You cannot compute it that way.  The log likelihood is built up
from the joint probabilities for the T (5 for you), observations.  The probabilities that
are kept in the variable Prob_SD are computed after estimation so that you can have
a set of probabilities computed from the model parameters, but they are computed
by turning off the panel data switch.  After the model is estimated, the model parameters
are used to compute those probabilities one choice situation at a time.  But, that is 
not how the log likelihood is computed.
Sincerely,
Bill Greene

************************************************
Professor William Greene
Department of Economics
Stern School of Business
New York University
44 West 4th St., Rm. 7-78
New York, NY   10012
Ph. 212.998.0876
Fax. 212.995.4218
URL. http://www.stern.nyu.edu/~wgreene
Email. wgreene at stern.nyu.edu
************************************************

----- Original Message -----
From: Andy Sungnok Choi <Andy.Choi at anu.edu.au>
Date: Sunday, May 20, 2007 9:54 am
Subject: [Limdep Nlogit List] Re: Limdep Digest, Vol 14, Issue 4

> Dear Dr. Greene,
> 
> Andy again. Regarding LL values, sorry! I should have been more 
> elaborated.
> You are absolutely right when MNL models are applied. However, I 
> am using 
> mixed logit models. As the following outputs show, the manually 
> calculated 
> LL value (at the end) is not close to both LL values of MNL and ML 
> estimates. That is what I tried to ask. Any idea?
> 
> Best wishes,
> 
> Andy S. Choi
> 
> PhD Candidate
> Australian National University
> 
> 
> --> sample ;all$
> --> Nlogit
>     ;lhs=choice, cset, alti
>     ;choices=1, 2, 3
>     ;rpl=old,gen,uni,inc
>     ;fcn=c2(n),cnpg(n),ctem(n),cint(n),cfac(n),ctax(n)
>     ;Prob=prob_SD
>     ;pts=100
>     ;halton
>     ;pds=5
>     ;maxit=100
>     ;Model:
>     
> U(1)=crep*rep+cnpg*npg+ctem*tem+cint*int+cexh*exh+ceve*eve+cfac*fac+ctax*...     U(2)=c2+crep*rep+cnpg*npg+ctem*tem+cint*int+cexh*exh+ceve*eve+cfac*fac+ct...
>     
> U(3)=c2+crep*rep+cnpg*npg+ctem*tem+cint*int+cexh*exh+ceve*eve+cfac*fac+ct...Normal exit from iterations. Exit status=0.
> 
> +---------------------------------------------+
> | Start values obtained using nonnested model |
> | Maximum Likelihood Estimates                |
> | Model estimated: May 20, 2007 at 06:36:09PM.|
> | Dependent variable               Choice     |
> | Weighting variable                 None     |
> | Number of observations             3925     |
> | Iterations completed                  5     |
> | Log likelihood function       -3948.085     |
> | Log-L for Choice   model =  -3948.08540     |
> | R2=1-LogL/LogL*  Log-L fncn  R-sqrd  RsqAdj |
> | Constants only.  Must be computed directly. |
> |                  Use NLOGIT ;...; RHS=ONE $ |
> | Response data are given as ind. choice.     |
> | Number of obs.=  3925, skipped   0 bad obs. |
> +---------------------------------------------+
> +---------+--------------+----------------+--------+---------+
> |Variable | Coefficient  | Standard Error |b/St.Er.|P[|Z|>z] |
> +---------+--------------+----------------+--------+---------+
>  C2          -.2663306962       .12268521   -2.171   .0299
>  CNPG     -.5192644722E-01  .55200724E-01    -.941   .3469
>  CTEM      .9543844085E-01  .20985588E-01    4.548   .0000
>  CINT         .2564211502   .57130348E-01    4.488   .0000
>  CFAC         .2010000283   .30400071E-01    6.612   .0000
>  CTAX     -.2421919430E-01  .10958630E-01   -2.210   .0271
>  CREP         .1965589530       .18169612    1.082   .2793
>  CEXH      .8434991488E-01  .69121601E-01    1.220   .2223
>  CEVE      .9754254919E-01  .55469769E-01    1.758   .0787
>  (Note: E+nn or E-nn means multiply by 10 to + or -nn power.)
> 
> 
> Normal exit from iterations. Exit status=0.
> +---------------------------------------------+
> | Random Parameters Logit Model               |
> | Maximum Likelihood Estimates                |
> | Model estimated: May 21, 2007 at 00:12:44AM.|
> | Dependent variable               CHOICE     |
> | Weighting variable                 None     |
> | Number of observations            11775     |
> | Iterations completed                 87     |
> | Log likelihood function       -2999.925     |
> | Restricted log likelihood     -4312.053     |
> | Chi squared                    2624.257     |
> | Degrees of freedom                   39     |
> | Prob[ChiSqd > value] =         .0000000     |
> | R2=1-LogL/LogL*  Log-L fncn  R-sqrd  RsqAdj |
> | No coefficients  -4312.0532  .30429  .30082 |
> | Constants only.  Must be computed directly. |
> |                  Use NLOGIT ;...; RHS=ONE $ |
> | At start values  -3948.0854  .24016  .23636 |
> | Response data are given as ind. choice.     |
> +---------------------------------------------+
> 
> +---------------------------------------------+
> | Random Parameters Logit Model               |
> | Replications for simulated probs. = 100     |
> | Halton sequences used for simulations       |
> | ------------------------------------------- |
> | RPL model with panel has  785 groups.       |
> | Fixed number of obsrvs./group=        5     |
> | Random effects model was specified          |
> | ------------------------------------------- |
> | Hessian was not PD. Using BHHH estimator.   |
> | Number of obs.=  3925, skipped   0 bad obs. |
> +---------------------------------------------+
> +---------+--------------+----------------+--------+---------+
> |Variable | Coefficient  | Standard Error |b/St.Er.|P[|Z|>z] |
> +---------+--------------+----------------+--------+---------+
>           Random parameters in utility functions
>  C2           1.075217537       1.2441197     .864   .3875
>  CNPG         .2720569803       .31342523     .868   .3854
>  CTEM         .2843338080       .12117424    2.346   .0190
>  CINT         .3929863233       .37191855    1.057   .2907
>  CFAC         .5622360369       .19532371    2.878   .0040
>  CTAX        -.1727720247   .87521371E-01   -1.974   .0484
>           Nonrandom parameters in utility functions
>  CREP         .4431833560       .24476960    1.811   .0702
>  CEXH         .2055225877   .90316183E-01    2.276   .0229
>  CEVE      .3342026667E-02  .75659190E-01     .044   .9648
>           Heterogeneity in mean, Parameter:Variable
>  C2:OLD   -.3942854455E-01  .16609177E-01   -2.374   .0176
>  C2:GEN      -.1085920005       .48927588    -.222   .8244
>  C2:UNI       .6564092435       .49696646    1.321   .1866
>  C2:INC    .1226827228E-04  .81746597E-05    1.501   .1334
>  CNPG:OLD -.4951551004E-02  .43622492E-02   -1.135   .2563
>  CNPG:GEN -.8628792321E-01      .12957477    -.666   .5055
>  CNPG:UNI -.5875244064E-01      .13395609    -.439   .6610
>  CNPG:INC -.5862173776E-06  .21029477E-05    -.279   .7804
>  CTEM:OLD -.2798302276E-02  .16941507E-02   -1.652   .0986
>  CTEM:GEN -.1016663631E-01  .48672625E-01    -.209   .8345
>  CTEM:UNI -.9508708540E-02  .51551647E-01    -.184   .8537
>  CTEM:INC  .8759373514E-06  .80704690E-06    1.085   .2778
>  CINT:OLD -.3227159342E-02  .50865164E-02    -.634   .5258
>  CINT:GEN     .2371150816       .15674834    1.513   .1304
>  CINT:UNI -.7893586621E-01      .16537162    -.477   .6331
>  CINT:INC -.1900121273E-05  .24989246E-05    -.760   .4470
>  CFAC:OLD -.5237950787E-02  .27175897E-02   -1.927   .0539
>  CFAC:GEN -.9116722591E-01  .77305532E-01   -1.179   .2383
>  CFAC:UNI  .4048481528E-02  .79532293E-01     .051   .9594
>  CFAC:INC  .7875725277E-06  .12739218E-05     .618   .5364
>  CTAX:OLD  .1539969693E-03  .12211236E-02     .126   .8996
>  CTAX:GEN  .1622910026E-01  .37443357E-01     .433   .6647
>  CTAX:UNI  .4625877590E-01  .38479590E-01    1.202   .2293
>  CTAX:INC  .6640594438E-06  .62969174E-06    1.055   .2916
>           Derived standard deviations of parameter distributions
>  NsC2         4.017164742       .24138858   16.642   .0000
>  NsCNPG       .3210807778       .15041239    2.135   .0328
>  NsCTEM    .5380942876E-01  .88241729E-01     .610   .5420
>  NsCINT       .6355227859       .12125596    5.241   .0000
>  NsCFAC    .4276296049E-01      .19602661     .218   .8273
>  NsCTAX       .1020525972   .39258483E-01    2.600   .0093
>  (Note: E+nn or E-nn means multiply by 10 to + or -nn power.)
> 
> 
> --> Create ;LL_SD=log(prob_sd)*choice$    ?choice is 0 or 1 (the 
> indicator 
> for the chosen options)
> --> Calc ;list ;sum(LL_SD)$
>     Result  = -.39096698358844520D+04
> 
> 
> 
> At 12:00 PM 18/05/2007 +1000, you wrote:
> >Message: 2
> >Date: Thu, 17 May 2007 05:04:00 -0500
> >From: William Greene <wgreene at stern.nyu.edu>
> >Subject: Re: [Limdep Nlogit List] LL values in LIMDEP
> >To: Limdep and Nlogit Mailing List <limdep at limdep.itls.usyd.edu.au>
> >Message-ID: <e62ac445628a.464be240 at stern.nyu.edu>
> >Content-Type: text/plain; charset=us-ascii
> >
> >Dear Andy:  In the output below, the NLOGIT routine reports a log 
> likelihood>value of -199.9766.  At the bottom of the listing, the 
> program segment that
> >replicates the calculation of the log likelihood reports a value 
> of 
> >-199.976623.
> >There is no discrepancy.  This is how NLOGIT computes the log 
> likelihood>function for a multinomial logit model.  I do not know 
> what your routine does.
> >You sent me the algorithm, but you did not send me the actual 
> commands.>The discrepancy, if there is one, must be in the code 
> you used..
> >/B. Greene
> >
> >--> RESET
> >Initializing NLOGIT Version 4.0.1 (January 1, 2007).
> >--> RESET
> >Initializing NLOGIT Version 4.0.1 (January 1, 2007).
> >--> LOAD;file="C:\limdepwsrc\clogit.lpj"$
> >.LPJ save file contained     840 observations.
> >--> nlog;lhs=mode;rhs=one,gc,ttme;prob=pri;choices=air,train,bus,car$
> >+---------------------------------------------+
> >| Discrete choice and multinomial logit models|
> >+---------------------------------------------+
> >Normal exit from iterations. Exit status=0.
> >+---------------------------------------------+
> >| Discrete choice (multinomial logit) model   |
> >| Maximum Likelihood Estimates                |
> >| Model estimated: May 17, 2007 at 05:56:36AM.|
> >| Dependent variable               Choice     |
> >| Weighting variable                 None     |
> >| Number of observations              210     |
> >| Iterations completed                  6     |
> >| Log likelihood function       -199.9766     |
> >| Number of parameters                  5     |
> >| Info. Criterion: AIC =          1.95216     |
> >|   Finite Sample: AIC =          1.95356     |
> >| Info. Criterion: BIC =          2.03185     |
> >| Info. Criterion:HQIC =          1.98438     |
> >| R2=1-LogL/LogL*  Log-L fncn  R-sqrd  RsqAdj |
> >| Constants only    -283.7588  .29526  .28962 |
> >| Chi-squared[ 2]          =    167.56429     |
> >| Prob [ chi squared > value ] =   .00000     |
> >| Response data are given as ind. choice.     |
> >| Number of obs.=   210, skipped   0 bad obs. |
> >+---------------------------------------------+
> >
> >+---------------------------------------------+
> >| Notes No coefficients=> P(i,j)=1/J(i).      |
> >|       Constants only => P(i,j) uses ASCs    |
> >|         only. N(j)/N if fixed choice set.   |
> >|         N(j) = total sample frequency for j |
> >|         N    = total sample frequency.      |
> >|       These 2 models are simple MNL models. |
> >|       R-sqrd = 1 - LogL(model)/logL(other)  |
> >|       RsqAdj=1-[nJ/(nJ-nparm)]*(1-R-sqrd)   |
> >|         nJ   = sum over i, choice set sizes |
> >+---------------------------------------------+
> >+--------+--------------+----------------+--------+--------+
> >|Variable| Coefficient  | Standard Error |b/St.Er.|P[|Z|>z]|
> >+--------+--------------+----------------+--------+--------+
> >  GC      |    -.01578375       .00438279    -3.601   .0003
> >  TTME    |    -.09709052       .01043509    -9.304   .0000
> >  A_AIR   |    5.77635888       .65591872     8.807   .0000
> >  A_TRAIN |    3.92300124       .44199360     8.876   .0000
> >  A_BUS   |    3.21073471       .44965283     7.140   .0000
> >
> >--> crea;jpri=mode*pri$
> >--> reje;jpri=0$
> >--> crea;logp=log(jpri)$
> >--> calc;list;sum(logp)$
> >+------------------------------------+
> >| Listed Calculator Results          |
> >+------------------------------------+
> >  Result  =   -199.976623
> >
> >
> >************************************************
> >Professor William Greene
> >Department of Economics
> >Stern School of Business
> >New York University
> >44 West 4th St., Rm. 7-78
> >New York, NY   10012
> >Ph. 212.998.0876
> >Fax. 212.995.4218
> >URL. http://www.stern.nyu.edu/~wgreene
> >Email. wgreene at stern.nyu.edu
> >************************************************
> >
> >----- Original Message -----
> >From: Andy Sungnok Choi <Andy.Choi at anu.edu.au>
> >Date: Wednesday, May 16, 2007 10:58 pm
> >Subject: [Limdep Nlogit List] LL values in LIMDEP
> >
> > > Dear Bill,
> > >
> > > Thanks for the kind explanation. However, the routine you showed
> > > is exactly
> > > the same as mine. And still, I could not have the same LL values
> > > as LIMDEP.
> > > To check, I asked one of my colleague and he told me the same
> > > discrepancy
> > > he has found.
> > >
> > > I wonder whether other LIMDEP users have the similar experience.
> > > Not sure
> > > what's going on.
> > >
> > > Regards,
> > >
> > > Andy
> > >
> > > At 12:00 PM 17/05/2007 +1000, you wrote:
> > > >Message: 4
> > > >Date: Wed, 16 May 2007 13:50:19 -0500
> > > >From: William Greene <wgreene at stern.nyu.edu>
> > > >Subject: Re: [Limdep Nlogit List] Log likelihood values
> > > >To: Limdep and Nlogit Mailing List 
> <limdep at limdep.itls.usyd.edu.au>> > >Message-ID: 
> <d6f583fc6b72.464b0c1b at stern.nyu.edu>> > >Content-Type: 
> text/plain; charset=us-ascii
> > > >
> > > >Mr. Choi.  No, it is not correct.  You only sum the logs of the
> > > >probabilities for
> > > >the choices actually made.  For example, here's a routine that
> > > does it.
> > > 
> >nlog;lhs=mode;rhs=one,gc,ttme;prob=pri;choices=air,train,bus,car$$> > >crea;jpri=mode*pri$
> > > >reje;jpri=0$
> > > >crea;logp=log(jpri)$
> > > >calc;list;sum(logp)$
> > > >/B. Greene
> > > >************************************************
> > > >Professor William Greene
> > > >Department of Economics
> > > >Stern School of Business
> > > >New York University
> > > >44 West 4th St., Rm. 7-78
> > > >New York, NY   10012
> > > >Fax. 212.995.4218
> > > >URL. http://www.stern.nyu.edu/~wgreene
> > > >Email. wgreene at stern.nyu.edu
> > > >************************************************
> > > >
> > > >----- Original Message -----
> > > >From: Andy Sungnok Choi <Andy.Choi at anu.edu.au>
> > > >Date: Wednesday, May 16, 2007 10:21 am
> > > >Subject: [Limdep Nlogit List] Log likelihood values
> > > >
> > > > > Dear all,
> > > > >
> > > > > I wonder how LIMDEP calculates LL values when MNL or ML 
> models are
> > > > > applied.
> > > > > When I calculated manually, the results did not get close 
> to LL
> > > > > values
> > > > > estimated by LIMDEP.
> > > > >
> > > > > Is the following wrong?
> > > > >
> > > > > 1. use ";prob=prob1" (in the syntax of MNL or ML models) to
> > > > > indicate
> > > > > probabilities of individual alternatives to be chosen
> > > > > 2. use "log(prob1) x choice" for LL values of individual
> > > > > alternatives
> > > > > (choice=0 or 1)
> > > > > 3. sum up all LL values.
> > > > >
> > > > > If this procedure is not right, how can I get 
> probabilities of
> > > > > individual
> > > > > alternatives correctly? FYI, I am carrying out the test 
> for model
> > > > > selection
> > > > > of Vuong (1989), when models are overlapping.
> > > > >
> > > > > Many thanks.
> > > > >
> > > > > Andy S. Choi
> > > > >
> > > > > PhD Candidate
> > > > > Australian National University
> > > _______________________________________________
> _______________________________________________
> Limdep site list
> Limdep at limdep.itls.usyd.edu.au
> http://limdep.itls.usyd.edu.au
> 




More information about the Limdep mailing list