**Date:** Tue, 16 Nov 2010 12:16:03 -0800
**Reply-To:** Dale McLerran <stringplayer_2@YAHOO.COM>
**Sender:** "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
**From:** Dale McLerran <stringplayer_2@YAHOO.COM>
**Subject:** Re: NLMIXED Output combinations
**In-Reply-To:** <5B1372272ABB7B4DB178622784D52BC109C32AB32A@MOR-EXMBPRD01.bvnet.bv>
**Content-Type:** text/plain; charset=iso-8859-1
Rick,

I don't understand the first part of your problem. You indicate
that you want a table of "every parameter estimates, i.e. for
every Y". Can you provide a small example of the output that you
would like to obtain?

Also, I have to ask about your simulated data. The value of Y
does not depend on any other terms (rho, D1, D2, D3, N1, N2, N3).
What is your simulated data supposed to show? Would you please
clarify?

As far as constructing parameters P, Q, and R such that
0<=P<=Q<=R<=1, I don't believe that you can do so with a BOUNDS
statement. I dislike BOUNDS statements anyway because
derivatives are not defined on the boundary. You could construct
P, Q, and R subject to the constraints that you have specified,
but you have to get a little tricky to do so.

Let's start with the parameter P. We will construct P as a
function of a parameter _P where _P is a real valued parameter
whose range is -infinity to infinity.

P = (1 + (exp(_P) - 1)/(exp(_P) + 1) ) / 2;

Note that when _P -> -infinity, exp(_P) -> 0 and

P = (1 + (0-1)/(0+1) ) / 2 = (1 + -1)/2 = 0, _P -> -infinity

When _P -> infinity, the ratio (exp(_P) - 1)/(exp(_P) + 1) -> 1
and

P = (1 + 1) / 2 = 1, _P -> infinity

So, the range of P is (0,1) for our parameter _P which has domain
(-infinity, infinity).

A similar function can be employed to construct Q and R such that
P<=Q and Q<=R. If we add a non-negative term Q' to _P, such that
we have Q* = _P + Q', and if we compute

Q = (1 + (exp(Q*) - 1)/(exp(Q*) + 1) ) / 2;

then Q will have range (P,1). Let Q'=exp(_Q). Without restriction
on the parameter space, _Q has domain -infinity to infinity, but
Q' has range (0,infinity). Programatically, we could write

Qstar = _P + exp(_Q);
Q = (1 + (exp(Qstar) - 1)/(exp(Qstar) + 1) ) / 2;

The extension to constructing R satisfying the conditions stated
above would be to let R* = _P + Q' + R' with R'>0 provided by
letting R'=exp(_R). Thus, we would have

Rstar = _P + exp(_Q) + exp(_R);
R = (1 + (exp(Rstar) - 1)/(exp(Rstar) + 1) ) / 2;

HTH,

Dale

---------------------------------------
Dale McLerran
Fred Hutchinson Cancer Research Center
mailto: dmclerra@NO_SPAMfhcrc.org
Ph: (206) 667-2926
Fax: (206) 667-5977
---------------------------------------

--- On Tue, 11/16/10, Ricardo Gonçalves da Silva <rgs.rsilva@BANCOVOTORANTIM.COM.BR> wrote:

> From: Ricardo Gonçalves da Silva <rgs.rsilva@BANCOVOTORANTIM.COM.BR>
> Subject: NLMIXED Output combinations
> To: SAS-L@LISTSERV.UGA.EDU
> Date: Tuesday, November 16, 2010, 9:14 AM
> Hi,
>
> In the following code, how I ask SAS to give me a table
> with every parameters estimates, i.e., for every Y?
> In fact, I want to restrict the parameters in order P le Q
> le R.
>
> DATA CORP_09;
> DO I=1 TO 100000;
> Y=RANNOR(125);
> OUTPUT;
> RHO=0.12;
> N1=20;
> D1=1;
> N2=52;
> D2=1;
> N3=151;
> D3=5;
> END;
> RUN;
> PROC NLMIXED DATA=CORP_09;
> BOUNDS 0 <= P Q R <=1;
> PARMS P=0.0000005 Q=0.0000005 R=0.0000005;
> NUM1 = (PROBIT(P)+Y*SQRT(RHO))/SQRT(1-RHO);
> NUM2 = (PROBIT(Q)+Y*SQRT(RHO))/SQRT(1-RHO);
> NUM3 = (PROBIT(R)+Y*SQRT(RHO))/SQRT(1-RHO);
> LOGLIKE = D1*LOG(PROBNORM(NUM1)) +
> (N1-D1)*LOG(1-PROBNORM(NUM1))
> + D2*LOG(PROBNORM(NUM2)) + (N2-D2)*LOG(1-PROBNORM(NUM2))
> + D3*LOG(PROBNORM(NUM3)) + (N3-D3)*LOG(1-PROBNORM(NUM3));
> MODEL Y~GENERAL(LOGLIKE) ;
> RUN;
>
> Thanks
>
> Rick
>
>
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