# [Limdep Nlogit List] Krinsky and Robb confidence intervals EC model

maria korjeh maria.korjeh at gmail.com
Tue Dec 7 23:05:54 EST 2010

```Dear all,

I am trying to estimate Krinsky and Robb confidence intervals for WTP ratios
in Nlogit 4.0.1.
It is working perfectly well for a MNL model (I'm including the code below
but omitting the modelling of U since it is lenghty and not relevant to the
problem):

Nlogit
; Lhs = CHOICE;
; choices = alt1, alt2, alt3;
; model:
U(alt1)  = xxx
U(alt2)  = xxx
U(alt3)  = xxx
\$
WALD; Start  = B;Var=VARB
; Labels =
a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15,a16,a17,a18...
; Fn1 = a14/a17
; Fn2 = a18/a17
; Fn3 = a15/a16
; Fn4 = a19/a16
; k&r\$

Which gives the result:

+-----------------------------------------------+
| WALD procedure. Estimates and standard errors |
| for nonlinear functions and joint test of     |
| nonlinear restrictions.                       |
| Wald Statistic             =    186.81428     |
| Prob. from Chi-squared[ 4] =       .00000     |
| Krinsky-Robb method used with 1000 draws      |
+-----------------------------------------------+
+--------+--------------+----------------+--------+--------+
|Variable| Coefficient  | Standard Error |b/St.Er.|P[|Z|>z]|
+--------+--------------+----------------+--------+--------+
Fncn(1) |    -.00975416       .00169695    -5.748   .0000
Fncn(2) |    -.00118653       .00062392    -1.902   .0572
Fncn(3) |    -.00612822       .00109797    -5.581   .0000
Fncn(4) |    -.00126124       .00042306    -2.981   .0029

However when I try with an EC model with additional variability for the
non-status quo alternatives the K&R procedure is unable to calculate the
confidence intervals for the WTP ratios.

Nlogit
; Lhs = CHOICE;
; choices = alt1, alt2, alt3
; rpl
; Halton
; fcn = no_sq (n,*,0)
; pds = 10
; pts = 500
; maxit = 200
; parameters
; model:
U(alt1)  = altsq * ...
U(alt2)  = no_sq * ...
U(alt3)  = no_sq * ...
\$

When, as before, I try to obtain a K&R for the value of time (tid/peng) but
get the following message;

WALD; Start  = B;Var=VARB
; Labels =
a1,a2,tid,peng,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15,a16,a17,...
; Fn1 = tid/peng
; k&r\$

+-----------------------------------------------+
| WALD procedure. Estimates and standard errors |
| for nonlinear functions and joint test of     |
| nonlinear restrictions.                       |
| VC matrix for the functions is singular.      |
| Standard errors are reported, but the         |
| Wald statistic cannot be computed.            |
| Krinsky-Robb method used with 1000 draws      |
+-----------------------------------------------+
+--------+--------------+----------------+--------+--------+
|Variable| Coefficient  | Standard Error |b/St.Er.|P[|Z|>z]|
+--------+--------------+----------------+--------+--------+
Fncn(1) |     .00775481    ......(Fixed Parameter).......

The strange thing is that if I increase the K&R draws to 2000 the message
changes, but the statistic still is not calculated (the standard error is
very very low...).

+-----------------------------------------------+
| WALD procedure. Estimates and standard errors |
| for nonlinear functions and joint test of     |
| nonlinear restrictions.                       |
| Wald Statistic             =*************     |
| Prob. from Chi-squared[ 1] =       .00000     |
| Krinsky-Robb method used with 2000 draws      |
+-----------------------------------------------+
+--------+--------------+----------------+--------+--------+
|Variable| Coefficient  | Standard Error |b/St.Er.|P[|Z|>z]|
+--------+--------------+----------------+--------+--------+
Fncn(1) |     .00775481     .250766D-08  ********   .0000

If I try the delta method the standard error is calculated just fine!

WALD; Start  = B;Var=VARB
; Labels =
a1,a2,tid,peng,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15,a16,a17,...
; Fn1 = tid/peng\$

+-----------------------------------------------+
| WALD procedure. Estimates and standard errors |
| for nonlinear functions and joint test of     |
| nonlinear restrictions.                       |
| Wald Statistic             =     93.16149     |
| Prob. from Chi-squared[ 1] =       .00000     |
+-----------------------------------------------+
+--------+--------------+----------------+--------+--------+
|Variable| Coefficient  | Standard Error |b/St.Er.|P[|Z|>z]|
+--------+--------------+----------------+--------+--------+
Fncn(1) |     .00775481       .00080344     9.652   .0000

I really need to compute a simulated confidence interval to validate the
reliability of the Delta result shown above but can't figure out why the K&R
is only working with the MNL not the EC model.
I would really appreciate advice on how to carry out simulated confidence
intervals. Would it be possible to use boot-strapping for this aim? Would
anyone be willing to give me some hints on how to write the code for this?

Best regards
-Maria
```