[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?
William Greene
wgreene at stern.nyu.edu
Sat Feb 17 01:29:14 AEDT 2018
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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