[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]

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
>