[Limdep Nlogit List] Log normally distributed cost parameter

Tienhaara Annika (LUKE) annika.tienhaara at luke.fi
Wed Jan 26 00:38:00 AEDT 2022


Dear all,

We are estimating random parameters (mixed) logit models with environmental attributes following a normal distribution and the cost parameter lognormal distribution. How can we calculate the means and standard errors of the marginal WTPs for the attributes using Nlogit, based on the unconditional estimates? We have looked into simulating the WTP values for the population, but have not found instructions or examples on how to do this when the cost is lognormal. Estimation in WTP space is not possible, as there we have problems with model convergence.
Here is our model and results:

|-> NLOGIT;Lhs=CHOICE
           ;Choices=BAU,ALT1,ALT2
           ;Halton
           ;rpl
           ;pts=2000
           ;pds=6
    ;Fcn=a2(n),a3(n),b1(n),b2(n),b3(n),b4(n),b5(n),b6(n),b7(n),b8(n),b9(n),b10(n),b11(l)
           ;parameters
           ;Model:
    U(BAU)=b1*p30+b2*p60+b3*e2+b4*e3+b5*k4+b6*k5+b7*i10+b8*i30+b9*v70+b10*v80+b11*mpc/
    U(ALT1)=a2+b1*p30+b2*p60+b3*e2+b4*e3+b5*k4+b6*k5+b7*i10+b8*i30+b9*v70+b10*v80+b11*mpc/
    U(ALT2)=a3+b1*p30+b2*p60+b3*e2+b4*e3+b5*k4+b6*k5+b7*i10+b8*i30+b9*v70+b10*v80+b11*mpc$


---------------------------------------------------------------------------
Random Parameters Multinom. Logit Model
Dependent variable               CHOICE
Log likelihood function     -2462.16944
Restricted log likelihood   -3401.30365
Chi squared [ 26](P= .000)   1878.26841
Significance level               .00000
McFadden Pseudo R-squared      .2761101
Estimation based on N =   3096, K =  26
Inf.Cr.AIC  =   4976.3 AIC/N =    1.607
---------------------------------------
            Log likelihood R-sqrd R2Adj
No coefficients -3401.3036  .2761 .2731
Constants only  -3228.5985  .2374 .2342
At start values -3003.1598  .1801 .1767
Note: R-sqrd = 1 - logL/Logl(constants)
---------------------------------------
Response data are given as ind. choices
Replications for simulated probs. =2000
Used Halton sequences in simulations.
RPL model with panel has     516 groups
Fixed number of obsrvs./group=        6
BHHH estimator used for asymp. variance
Number of obs.=  3096, skipped    0 obs
--------+------------------------------------------------------------------
        |                  Standard            Prob.      95% Confidence
  CHOICE|  Coefficient       Error       z    |z|>Z*         Interval
--------+------------------------------------------------------------------
        |Random parameters in utility functions..............................
      A2|    2.13805***      .38031     5.62  .0000     1.39265   2.88344
      A3|    1.34720***      .36737     3.67  .0002      .62718   2.06723
      B1|     .70033***      .16475     4.25  .0000      .37743   1.02323
      B2|     .73475***      .16741     4.39  .0000      .40663   1.06288
      B3|     .20620         .15004     1.37  .1694     -.08788    .50028
      B4|     .73427***      .16651     4.41  .0000      .40792   1.06062
      B5|    -.19350         .14221    -1.36  .1736     -.47223    .08523
      B6|     .08965         .13512      .66  .5070     -.17519    .35448
      B7|     .69951***      .17191     4.07  .0000      .36256   1.03645
      B8|     .64813***      .17595     3.68  .0002      .30329    .99298
      B9|     .31783*        .16785     1.89  .0583     -.01116    .64681
     B10|     .68545***      .17767     3.86  .0001      .33723   1.03367
     B11|   -4.10386***      .14879   -27.58  .0000    -4.39548  -3.81224
        |Distns. of RPs. Std.Devs or limits of triangular....................
    NsA2|     .80219***      .22657     3.54  .0004      .35811   1.24627
    NsA3|    1.29128***      .18269     7.07  .0000      .93322   1.64934
    NsB1|    1.18243***      .19424     6.09  .0000      .80172   1.56314
    NsB2|    1.16108***      .25288     4.59  .0000      .66544   1.65672
    NsB3|     .93324***      .23092     4.04  .0001      .48064   1.38584
    NsB4|     .95523***      .23226     4.11  .0000      .50001   1.41046
    NsB5|     .51003*        .30579     1.67  .0953     -.08931   1.10936
    NsB6|     .88595***      .20339     4.36  .0000      .48731   1.28458
    NsB7|     .72713***      .24920     2.92  .0035      .23871   1.21555
    NsB8|    1.33430***      .19572     6.82  .0000      .95070   1.71790
    NsB9|     .93112***      .24078     3.87  .0001      .45919   1.40305
   NsB10|    1.01326***      .21938     4.62  .0000      .58328   1.44324
   LsB11|    2.10463***      .16179    13.01  .0000     1.78753   2.42173
--------+------------------------------------------------------------------

Thank you in advance!

Best regards
Annika


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