[Limdep Nlogit List] Simulating unconditional WTP

Wed Apr 4 01:46:09 AEST 2018

Dear Prof Greene, 

Thank you for your rapid spotting of my mistake!

As a follow-up question, I noticed quite similar correlations when running DSTAT for the conditional and unconditional parameters. (see below)

The simulation now works very well. However, I notice a large difference in terms of correlation for one attribute (LAB) between conditional and un-conditional parameters. 

Should I draw any conclusion from these large difference in correlation for this attribute (model specification, data?) 

Yours respectfully,

Damien

SAMPLE; 1-1000$

create 

; rna1 = rnn(0,1)

; rna2 = rnn(0,1) 

; rna3 = rnn(0,1)

; MUBEN = exp(B(1) + B(8)  * RNA1)   ?? This was a lognormal distribution

; MULAB = B(2) + B(13) * RNA1 + B(9)  * RNA2

; MUCAS = B(3) + B(14) * RNA1 + B(15) * RNA2 + B(10) * RNA3

$

I compared the following three correlation matrices 

The one obtained directly from the NLOGIT output, the one from simulated parameters, 

and the one from conditional parameters

Correlation matrix (model output)

--------+--------------------------------------------

Cor.Mat.|     ONE       LA       CA       RI      FEH

--------+--------------------------------------------

     ONE| 1.00000  -.61706  -.83717   .07331  -.06425

      LA| -.61706  1.00000   .23113  -.52217  -.23501

      CA| -.83717   .23113  1.00000   .09078  -.16867

      RI|  .07331  -.52217   .09078  1.00000   .63762

     FEH| -.06425  -.23501  -.16867   .63762  1.00000

Correlation matrix of the simulated conditional parameters

--------+--------------------------------------------

Cor.Mat.|   MUBEN    MULAB    MUCAS    MURIS    MUFEH

--------+--------------------------------------------

   MUBEN| 1.00000  -.59427  -.79918   .04706  -.07725

   MULAB| -.59427  1.00000   .23176  -.51297  -.23958

   MUCAS| -.79918   .23176  1.00000   .09940  -.18260

   MURIS|  .04706  -.51297   .09940  1.00000   .62600

   MUFEH| -.07725  -.23958  -.18260   .62600  1.00000

Correlation matrix of the conditional parameters

--------+--------------------------------------------

Cor.Mat.|    BBEN     BLAB     BCAS     BRIS      BHI

--------+--------------------------------------------

    BBEN| 1.00000  -.57742  -.83278   .14806  -.07852

    BLAB| -.57742  1.00000   .75064   .56024   .46689

    BCAS| -.83278   .75064  1.00000   .08143  -.11306

    BRIS|  .14806   .56024   .08143  1.00000   .33236

     BHI| -.07852   .46689  -.11306   .33236  1.00000

De : William Greene [mailto:wgreene at stern.nyu.edu] 
Envoyé : Tuesday, April 03, 2018 5:13 PM
À : Limdep and Nlogit Mailing List; djourdain at ait.asia
Objet : Re: [Limdep Nlogit List] Simulating unconditional WTP

Damien. The simulated coefficients are not correlated because you used

independent random draws to create them.  You should be using rna1 in the

first one, rna1,rna2 in the second one and rna1,rna2,rna3 in the third one.

/B, Greene

On Tue, Apr 3, 2018 at 10:56 AM, Damien Jourdain <djourdain at ait.asia> wrote:

Dear All,

I ran the following RPL-EC model. It gives me reasonable results.

? ML-EC Model

Sample; ALL$

Calc; Ran(12345)$

RPLOGIT

      ; Choices = 1,2,3

      ; Lhs = CHOICE, CSET, ALT

      ; Model:

      U(1)   = A1 + BE*BENEF + LA*LAB + CA*CASH +RI*RISK + FEL*FERTLO +FEH*
FERTHI /

      U(2,3) =      BE*BENEF + LA*LAB + CA*CASH +RI*RISK + FEL*FERTLO +FEH*
FERTHI

      ; Fcn =  BE(l), LA(n),  CA(n), RI(n), FEH(n)

      ; Pds = 6

      ; Pts = 20

      ; Shuffled

      ; Correlation

      ; WTP = LA/BE, CA/BE, RI/BE, FEH/BE

      ; ECM = (2,3)

      ; Parameters

      ; Maxit = 300$

I have obtained the conditional WTP (using the WTP command) but in fact I
would like to manipulate simulated un-conditional WTPs. As the coefficients
are correlated, I understand that I have to use the Cholesky decomposition
(provided in the model output) to be able to draw correlated random
coefficients. I have two set of questions:

First, can I use the WALD command to develop these simulations (I know this
can be done with an MNL model, but I do not see any simple manner to use the
B and VARB matrices obtained from the model for a RPL model.

Second, as I assumed that I could not use WALD, I developed the following
commands for simulating the first three random coefficients:

SAMPLE; 1-1000$

create

; rna1 = rnn(0,1)

; rna2 = rnn(0,1)

; rna3 = rnn(0,1)

; rna4 = rnn(0,1)

; rna5 = rnn(0,1)

; rna6 = rnn(0,1)

; MUBEN = B(1) + B(8)  * RNA1

; MULAB = B(2) + B(13) * RNA2 + B(9)  * RNA3

; MUCAS = B(3) + B(14) * RNA4 + B(15) * RNA5 + B(10) * RNA6

$

(the coefficients are correct and correspond to the Cholesky matrix
coefficients )

When checking the simulated coefficients, I can reproduce the coefficients
mean and standard deviation, but they are not correlated as I had expected
given that I used the Cholesky coefficients to reproduce these correlations

I do not understand what I have done wrong?

Any help is welcomed.

Damien

DSTAT; RHS = MUBEN, MULAB, MUCAS; out=2$

--------+-------------------------------------------------------------------
--

        |                  Standard
Missing

Variable|         Mean    Deviation      Minimum      Maximum    Cases
Values

--------+-------------------------------------------------------------------
--

   MUBEN|      -3.7348      .408152    -5.023775    -2.357132     1000
0

   MULAB|      -.02753      .028474     -.117069      .048933     1000
0

   MUCAS|     -.015962      .015583     -.064371      .035926     1000
0

--------+-------------------------------------------------------------------
--

Descriptive Statistics for   3 variables

DSTAT results are matrix LASTDSTA in current project.

Correlations computed for 3 variables.

--------+--------------------------

Cor.Mat.|   MUBEN    MULAB    MUCAS

--------+--------------------------

   MUBEN| 1.00000   .04327  -.04466

   MULAB|  .04327  1.00000  -.01857

   MUCAS| -.04466  -.01857  1.00000

I am really far off the model outputs

--------+--------------------------------------------

Cor.Mat.|     ONE       LA       CA       RI      FEH

--------+--------------------------------------------

     ONE| 1.00000  -.61706  -.83717   .07331  -.06425

      LA| -.61706  1.00000   .23113  -.52217  -.23501

      CA| -.83717   .23113  1.00000   .09078  -.16867

      RI|  .07331  -.52217   .09078  1.00000   .63762

     FEH| -.06425  -.23501  -.16867   .63762  1.00000

Dr. Damien Jourdain

Agricultural and Natural Resources Economist

Visiting Assistant Professor

Asian Institute of Technology / CIRAD G-EAU

Natural Resource Management / Water Engineering and Management

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-- 

William Greene

Department of Economics

Stern School of Business, New York University

44 West 4 St., 7-90

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Email: wgreene at stern.nyu.edu

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