[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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