# [Limdep Nlogit List] Error 185 using Krinsky and Robb bootstrapping method

Nathan P. Kemper nkemper at uark.edu
Thu Apr 7 12:50:31 AEST 2016

```Professor Hensher,

The example you suggested helped me a great deal. Thank you. I was able to generate Wald functions using K&R with 1000 draws.  The code below gives me the means of the variables and the z, C.I.  However, because I would like the take the next step of using the combinatorial test, I need to be able to save the distribution of the 1000 MWTPs so that I can then apply the Poe test in order to test treatment effects across my 5 treatments. Is there a way in the Wald command to save the bootstraps? I have placed the WALD codes I used which uses b and varb as the starting points and calculates the mean WTP using 1000 K&R but only reports the mean.

When I use my old code which works flawlessly for some of my treatments, I get that pesky error:

Error    185: MATRIX - GINV,SINV,CHOL  singular, not P.D. if SINV or CHOL

I searched on the internet a solution to this problem, but without success. I believe it is related to the fact that I'm dividing coefficients by coefficients which is resulting in some values that cause the "not P.D." error and shut down the routine. I am wondering whether it is a coding or data issue.  Or if I can use the new Wald command to generate a distribution of 1,000 WTPs?

Sorry for bothering again. Here is my ECLOGIT code for treatment 5 and the Wald functions below. Also, I placed the Wald proc output at the end.  A sincere thank you in advance for any further advice.

sample; all\$
ECLOGIT; IF [cell=5];
Lhs=CHOICE;
Choices=PRODA, PRODB, NONE;
RPL;
Pts= 250;
halton;
FCN= bng(n),bgm(n),blo(n),bmd(n),bhi(n),blc(n);
Correlated;
PDS = 8;
PARAMETERS;
MODEL:
U (PRODA)=bprice*price+bng*ng+bgm*gm+blo*lo+bmd*md+bhi*hi+blc*lc/
U (PRODB)=bprice*price+bng*ng+bgm*gm+blo*lo+bmd*md+bhi*hi+blc*lc/
U (NONE)=bnone*none;
ECM = (PRODA,PRODB)\$
matrix
;v_varb = part(varb,1,36,1,36)
;b_b    = part(b,1,36,1,1)
\$
WALD; Labels = a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15,a16,a17,a18,
a19,a20,a21,a22,a23,a24,a25,a26,a27,a28,a29,a30,a31,a32,a33,a34,a35,a36
; Start  = b_b
; Var    = v_varb
; Fn1 = wtpng = a1/-a7
; Fn2 = wtpgm = a2/-a7
; Fn3 = wtplo = a3/-a7
; Fn4 = wtpmd = a4/-a7
; Fn5 = wtphi = a5/-a7
; Fn6 = wtplc = a6/-a7
; Fn7 = wtpno = a8/-a7
; k&r ; pts=1000\$

-----------------------------------------------------------------------------
WALD procedure. Estimates and standard errors
for nonlinear functions and joint test of
nonlinear restrictions.
Wald Statistic             =    464.47987
Prob. from Chi-squared[ 7] =       .00000
Krinsky-Robb method used with 1000 draws
Functions are computed at means of variables
--------+--------------------------------------------------------------------
|                  Standard            Prob.      95% Confidence
WaldFcns|  Coefficient       Error       z    |z|>Z*         Interval
--------+--------------------------------------------------------------------
WTPNG|    3.14315***      .61879     5.08  .0000     1.93034   4.35595
WTPGM|   -1.76899***      .29734    -5.95  .0000    -2.35176  -1.18622
WTPLO|     .87775**       .37497     2.34  .0192      .14281   1.61268
WTPMD|     .35289         .33414     1.06  .2909     -.30202   1.00779
WTPHI|     .71558**       .28931     2.47  .0134      .14853   1.28263
WTPLC|    1.60495***      .24355     6.59  .0000     1.12760   2.08230
WTPNO|   -8.23527***      .49023   -16.80  .0000    -9.19610  -7.27445
--------+--------------------------------------------------------------------
Note: ***, **, * ==>  Significance at 1%, 5%, 10% level.
-----------------------------------------------------------------------------

Nathan Kemper
Dept. of Agricultural Economics and Agribusiness
University of Arkansas - Fayetteville

```