[Limdep Nlogit List] Interpretation of RPL coefficients when using lognormal distribution: why results from direct estimation and from estimated parameters are not giving the same results?

Damien Jourdain djourdain at ait.asia
Tue Feb 20 18:45:31 AEDT 2018


Dear Pr. Greene, 

Thank you for this tip. It is easier to operate indeed!

Damien

-----Message d'origine-----
De : Limdep [mailto:limdep-bounces at mailman.sydney.edu.au] De la part de William Greene
Envoyé : Friday, February 16, 2018 4:29 PM
À : Limdep and Nlogit Mailing List
Objet : Re: [Limdep Nlogit List] Interpretation of RPL coefficients when using lognormal distribution: why results from direct estimation and from estimated parameters are not giving the same results?

Damien.  That looks even better.
Note, you can use DSTAT with matrices directly - the statistics are computed for the columns of the matrices.  Note the example in my previous note.
Cheers
Bill Greene

On Thu, Feb 15, 2018 at 9:33 AM, Damien Jourdain <djourdain at ait.asia> wrote:

> Dear Mik,
>
> Thank you.
> I've looked again, and I think found the  mistake I made.
> When creating the variables from the matrix, I forgot to add the 
> "Sample; 1-1400". By failing to do so, I suppose the calculation of 
> the average include all the zeros for the variable BNPR (from 1401 to 
> 13500 ... since I have 13500 rows). This result in an average that is 
> much smaller than the reality!
>
> I am now adding the following line    Sample ; 1-1400$  before getting the
> parameters from the matrix
>
> When I tried again with this statement, I find the calculated from 
> direct estimation being quite close to the average of posterior 
> individual-specific estimates. If that is correct, there is no need to 
> use the exponential of the coefficients.
>
> |-> CALC; List; XBR(BNPR)$
> [CALC]         =         .3199974
>
> |-> create; expBNPR = exp(BNPR)$
> |-> calc; list; xbr(expBNPR)$
> [CALC]         =        1.6429415
>
> |-> CALC; LIST; exp(-1.95961 + (1.31682^2)/2)$
> [CALC]         =         .3353426
>
> Again, thank you for your  help and interest.
>
> Damien
>
>
> -----Message d'origine-----
> De : Mikołaj Czajkowski [mailto:mc at uw.edu.pl] Envoyé : Thursday, 
> February 15, 2018 3:21 PM À : Damien Jourdain Objet : Re: [Limdep 
> Nlogit List] Interpretation of RPL coefficients when using lognormal 
> distribution: why results from direct estimation and from estimated 
> parameters are not giving the same results?
>
>
> Dear Damien,
>
> This is what I would expect - direct estimation using coefficients is 
> likely always better than the one based on posterior 
> individual-specific estimates (even though asymptotically they should be equivalent).
>
> Best regards,
> Mik
>
>
> On 2018-02-15 12:41, Damien Jourdain wrote:
> > Dear Mik,
> >
> > Thank you for the suggestion.
> >
> > I tried that but there is still an important difference between the two.
> >
> > |-> create; expBNPR = exp(BNPR)$
> > |-> calc; list; xbr(expBNPR)$
> > [CALC]         =        1.0329355
> >
> > As the direct estimation from the coefficients is giving :
> >> |-> CALC; LIST; EXP(-1.61991 + (0.99479^2)/2)$
> >> [CALC]         =         .3246179
> > By the way, the more 'realistic' calculation is the direct 
> > estimation from the coefficients (at least it is of the same 
> > magnitude than the MNL coefficient for price)
> >
> >
> > Damien
> >
> >
> > -----Message d'origine-----
> >
> > De : Mikołaj Czajkowski [mailto:mc at uw.edu.pl] Envoyé : Thursday, 
> > February 15, 2018 12:34 PM À : Damien Jourdain Objet : Re: [Limdep 
> > Nlogit List] Interpretation of RPL coefficients when using lognormal
> distribution: why results from direct estimation and from estimated 
> parameters are not giving the same results?
> >
> >
> > Dear Damien,
> >
> > Shoulnd't you have something like:
> >
> > create; expBNPR = exp(BNPR)$
> >
> > first?
> >
> > Then
> > calc; list; xbr(expBNPR)$
> >
> > Cheers,
> > Mik
> >
> >
> >
> >
> > On 2018-02-15 11:26, Damien Jourdain wrote:
> >> Dear All,
> >>
> >>
> >>
> >> I developing a RPL model using choice experiment data
> >>
> >>
> >>
> >> The model is as followed:
> >>
> >>
> >>
> >> Calc; Ran(1234567)$
> >>
> >> RPLOGIT
> >>
> >>         ; Choices = 1,2,3
> >>
> >>         ; Lhs = CHOICE, CSET, ALT
> >>
> >>         ; Rhs = L_IMP, L_RAU, L_GAP, L_PGS,
> >>
> >>                     FRESH, O_SUPE, O_SPEC, NPRICE
> >>
> >>         ; Fcn = L_IMP(n), L_RAU(n), L_GAP(n),
> >>
> >>               L_PGS(n), FRESH(n), O_SUPE(n), O_SPEC(n), NPRICE(l)
> >>
> >>         ; Halton
> >>
> >>         ; Pds = csi
> >>
> >>         ; Pts = 20
> >>
> >>         ; Parameters
> >>
> >>         ; Maxit = 150$
> >>
> >>
> >>
> >> I have changed the price attribute to negative values, so I can use 
> >> a lognormal distribution of for the price attribute.
> >>
> >> I am getting the following results
> >>
> >>
> >>
> >> --------+----------------------------------------------------------
> >> --------+--
> >> --------+-
> >> --------+------
> >> -
> >>
> >>           |                  Standard            Prob.      95%
> Confidence
> >>
> >>     CHOICE|  Coefficient       Error       z    |z|>Z*         Interval
> >>
> >> --------+----------------------------------------------------------
> >> --------+--
> >> --------+-
> >> --------+------
> >> -
> >>
> >>           |Random parameters in utility 
> >> functions..............................
> >>
> >>      L_IMP|   -1.11608***      .29152    -3.83  .0001    -1.68745
>  -.54470
> >>
> >>      L_RAU|    1.49941***      .09880    15.18  .0000     1.30577
>  1.69304
> >>
> >>      L_GAP|    1.82794***      .10487    17.43  .0000     1.62239
>  2.03349
> >>
> >>      L_PGS|     .63730**       .25734     2.48  .0133      .13291
>  1.14168
> >>
> >>      FRESH|    -.61318***      .05496   -11.16  .0000     -.72089
>  -.50546
> >>
> >>     O_SUPE|     .43891***      .07567     5.80  .0000      .29060
> .58721
> >>
> >>     O_SPEC|    -.76256***      .17329    -4.40  .0000    -1.10221
>  -.42291
> >>
> >>     NPRICE|   -1.61991***      .33228    -4.88  .0000    -2.27117
>  -.96865
> >>
> >>           |Distns. of RPs. Std.Devs or limits of 
> >> triangular....................
> >>
> >> NsL_IMP|    1.52346***      .31666     4.81  .0000      .90281   2.14410
> >>
> >> NsL_RAU|     .69380***      .13439     5.16  .0000      .43040    .95721
> >>
> >> NsL_GAP|     .01744         .24287      .07  .9427     -.45858    .49346
> >>
> >> NsL_PGS|     .95598***      .21017     4.55  .0000      .54405   1.36790
> >>
> >> NsFRESH|     .48681***      .05657     8.60  .0000      .37593    .59770
> >>
> >> NsO_SUPE|    1.65455***      .11307    14.63  .0000     1.43293
>  1.87616
> >>
> >> NsO_SPEC|    1.08890***      .12068     9.02  .0000      .85237
>  1.32544
> >>
> >> LsNPRICE|     .99479***      .18655     5.33  .0000      .62917
>  1.36041
> >>
> >>
> >>
> >> If I am not wrong, I can calculate the population mean of the price
> >> E(beta) =  exp(beta + sigma^2/2)
> >>
> >> |-> CALC; LIST; EXP(-1.61991 + (0.99479^2)/2)$
> >>
> >> [CALC]         =         .3246179
> >>
> >>
> >>
> >> Then, I am using the procedure described in section N29.8.2 of the 
> >> Nlogit manual to examine the distribution of the parameters.
> >>
> >> Matrix; bn = beta_i; sn =sdbeta_i $
> >>
> >> CREATE; BIMP=0; BRAU=0; BGAP=0; BPGS=0; BFRE =0; BSUP=0; BSPE=0;
> >> BNPR=0 $
> >>
> >> CREATE ;SIMP=0; SRAU=0; SGAP=0; SPGS=0; SFRE =0; SSUP=0; SSPE=0;
> >> SNPR=0 $
> >>
> >> NAMELIST; betan = BIMP,BRAU, BGAP, BPGS, BFRE, BSUP, BSPE, BNPR$
> >>
> >> NAMELIST; sbetan = SIMP,SRAU, SGAP, SPGS, SFRE, SSUP, SSPE, SNPR$
> >>
> >> CREATE ; betan =bn$
> >>
> >> CREATE ; sbetan = sn$
> >>
> >>
> >>
> >> CALC; List; XBR(BNPR)$ ? calculate the average of the beta for 
> >> nprice
> >>
> >>
> >>
> >> |-> CALC; List; XBR(BNPR)$
> >>
> >> [CALC]         =         .0257560
> >>
> >>
> >>
> >> My understanding is that these two figures should be close to one
> another.
> >> Is there anything that could explain such difference between these 
> >> two ways to estimate the results?
> >>
> >>
> >>
> >> Any help is welcomed?
> >>
> >>
> >>
> >> Best,
> >>
> >>
> >>
> >> Damien
> >>
> >>
> >>
> >> _______________________________________________
> >> Limdep site list
> >> Limdep at mailman.sydney.edu.au
> >> http://limdep.itls.usyd.edu.au
> >>
>
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--
William Greene
Department of Economics
Stern School of Business, New York University
44 West 4 St., 7-90
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Email: wgreene at stern.nyu.edu
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Editor in Chief: Journal of Productivity Analysis Editor in Chief: Foundations and Trends in Econometrics Associate Editor: Economics Letters Associate Editor: Journal of Business and Economic Statistics Associate Editor: Journal of Choice Modeling _______________________________________________
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