[Limdep Nlogit List] WTP- space model: Confidence interval of WTP distribution using Delta method
Thao Thai
Thao.T.Thai at monash.edu
Mon Apr 26 15:20:54 AEST 2021
Dear Nlogit users,
Please help if you can! Your help is much appreciated!
I ran a WTP-space model of which the results are below. Please help me
clarify some of my confusions:
(1) Is the confidence interval of the random parameters reported in the
model output, for example of the HOS variable, the confidence interval of
the mean WTP estimate for HOS variable?
(2) Does that mean the WTP distribution for HOS variable depends on the *mean
*WTP and its *standard error *(i.e. confidence interval of the mean WTP)
and the *standard deviation* (i.e. the estimated coefficients and standard
error for NsHOS) of the distribution for the WTP of HOS variables?
Please help:
(3) How can I compute the confidence intervals of WTPs distribution using
Delta method?
(4) How can I compute the confidence interval of the mean WTP using Delta
method? Is it the confidence interval reported in the WTP-space model
output?
Suppose the Delta method Wald syntax is
*Wald; Parameters = b; Covariance = varb*
*;Labels = hos, pri, ind, gov, non, rlh1, rlh2, fl, cr1, cr2, lo1, sa,
rlc1, rlc2, lo2, rlp1, rli1, rli2, rlg1, rln1;Fn1 = ? ;Fn2 = ?*
*$*
I got confused about what to put in the function to get confidence
intervals of WTPs where the coefficients are already WTPs values?
I really look forward to your answers! Thank you in advance!
Best regards,
Thao
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Generalized Mixed (RP) Logit Model
Dependent variable CHO
Log likelihood function -6513.18857
Restricted log likelihood -12150.65191
Chi squared [ 39](P= .000) 11274.92669
Significance level .00000
McFadden Pseudo R-squared .4639639
Estimation based on N = 5530, K = 39
Inf.Cr.AIC = 13104.4 AIC/N = 2.370
---------------------------------------
Log likelihood R-sqrd R2Adj
No coefficients ********** .4640 .4628
Constants only can be computed directly
Use NLOGIT ;...;RHS=ONE$
At start values -7718.0848 .1561 .1543
Note: R-sqrd = 1 - logL/Logl(constants)
Warning: Model does not contain a full
set of ASCs. R-sqrd is problematic. Use
model setup with ;RHS=one to get LogL0.
---------------------------------------
Response data are given as ind. choices
Replications for simulated probs. = 50
Used Halton sequences in simulations.
RPL model with panel has 790 groups
Fixed number of obsrvs./group= 7
BHHH estimator used for asymp. variance
Number of obs.= 5530, skipped 0 obs
--------+--------------------------------------------------------------------
| Standard Prob. 95% Confidence
CHO| Coefficient Error z |z|>Z* Interval
--------+--------------------------------------------------------------------
|Random parameters in utility
functions..............................
HOS| 5.92660 8.03544 .74 .4608 -9.82257 21.67578
PRI| 30.0879*** 6.82100 4.41 .0000 16.7190 43.4568
IND| -74.2164*** 8.56240 -8.67 .0000 -90.9984 -57.4344
GOV| -1.41410 7.62304 -.19 .8528 -16.35499 13.52679
NON| -.55721 7.71549 -.07 .9424 -15.67928 14.56486
RLH1| -4.88831 9.96395 -.49 .6237 -24.41730 14.64068
RLH2| 15.4004** 7.46852 2.06 .0392 .7624 30.0385
FL| 15.1360*** 3.00154 5.04 .0000 9.2531 21.0189
CR1| 33.4554*** 3.29616 10.15 .0000 26.9950 39.9158
CR2| 17.2478*** 4.98946 3.46 .0005 7.4687 27.0270
LO1| -56.0650*** 3.79442 -14.78 .0000 -63.5019 -48.6280
SA| 1.0 .....(Fixed Parameter).....
RLC1| 11.6994 9.01142 1.30 .1942 -5.9627 29.3614
RLC2| 21.9054** 8.76364 2.50 .0124 4.7290 39.0818
LO2| -76.1803*** 5.08817 -14.97 .0000 -86.1529 -66.2077
RLP1| -21.7674*** 6.31574 -3.45 .0006 -34.1460 -9.3887
RLI1| 36.7621*** 9.08386 4.05 .0001 18.9581 54.5662
RLI2| 48.4521*** 6.98327 6.94 .0000 34.7651 62.1390
RLG1| -15.8780** 6.61678 -2.40 .0164 -28.8467 -2.9094
RLN1| -32.0373*** 8.21917 -3.90 .0001 -48.1465 -15.9280
|Distns. of RPs. Std.Devs or limits of
triangular....................
NsHOS| 61.2749*** 5.69437 10.76 .0000 50.1141 72.4356
NsPRI| 52.0645*** 5.48074 9.50 .0000 41.3224 62.8065
NsIND| 81.7682*** 6.32951 12.92 .0000 69.3626 94.1738
NsGOV| 70.6895*** 5.40187 13.09 .0000 60.1021 81.2770
NsNON| 58.2880*** 6.73963 8.65 .0000 45.0786 71.4975
NsRLH1| 38.4853** 16.01183 2.40 .0162 7.1027 69.8679
NsRLH2| 15.0987 14.26854 1.06 .2900 -12.8671 43.0645
NsFL| 27.3007*** 5.52125 4.94 .0000 16.4792 38.1221
NsCR1| 1.25925 7.01920 .18 .8576 -12.49812 15.01662
NsCR2| 9.06253 9.13084 .99 .3209 -8.83358 26.95864
NsLO1| 58.1808*** 4.70198 12.37 .0000 48.9651 67.3965
CsSA| 0.0 .....(Fixed Parameter).....
NsRLC1| 61.6887*** 9.56351 6.45 .0000 42.9445 80.4328
NsRLC2| 8.02381 13.69708 .59 .5580 -18.82197 34.86959
NsLO2| 33.7236*** 7.81182 4.32 .0000 18.4128 49.0345
NsRLP1| 3.64345 12.20383 .30 .7653 -20.27562 27.56251
NsRLI1| 52.0114*** 13.12794 3.96 .0001 26.2811 77.7417
NsRLI2| 7.20127 13.87235 .52 .6037 -19.98804 34.39057
NsRLG1| 14.7726 11.03772 1.34 .1808 -6.8609 36.4061
NsRLN1| 51.6333*** 9.86131 5.24 .0000 32.3055 70.9611
|Variance parameter tau in GMX scale
parameter.......................
TauScale| 0.0 .....(Fixed Parameter).....
|Weighting parameter gamma in GMX
model..............................
GammaMXL| 0.0 .....(Fixed Parameter).....
|Coefficient on SA in preference space
form....................
Beta0WTP| .01539*** .00043 35.64 .0000 .01454 .01623
S_b0_WTP| 0.0 .....(Fixed Parameter).....
| Sample Mean Sample
Std.Dev.....................................
Sigma(i)| 1.0*** .1322D-05 ******** .0000 .10000D+01 .10000D+01
--------+--------------------------------------------------------------------
nnnnn.D-xx or D+xx => multiply by 10 to -xx or +xx.
***, **, * ==> Significance at 1%, 5%, 10% level.
Fixed parameter ... is constrained to equal the value or
had a nonpositive st.error because of an earlier problem.
Model was estimated on Apr 23, 2021 at 08:10:02 PM
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