[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 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