Date: Sun, 30 Jan 2005 19:02:53 -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: Estimate odds ratio in proc NLMIXED
Content-Type: text/plain; charset=us-ascii
LogSDu is the log of the square root of your parameter s2u. For
a single random effect, you could parameterize the model in terms
LogS2U and convergence would be obtained just as easily. But if
you have two or more random effects which have a nonzero covariance
structure, then it is better to parameterize the model as I
indicated previously. The reason is that the random effect
covariance structure can then be expressed as
cov(u1, u2) = | exp(2*LogSDu1) rho*exp(LogSDu1 + LogSDu2) |
| rho*exp(LogSDu1 + LogSDu2) exp(2*LogSDu2) |
We can also reparameterize the correlation employing the functional
relationship Z = 0.5*log((1 + rho) / (1 - rho)). Note that this
is the Fisher Z statistic. For rho from -1 to 1, the Fisher Z
statistic ranges from -infinity to infinity. We can invert the
Fisher Z statistic to get the correlation. When we parameterize
the model in terms of the Fisher Z statistic, then we do not
need to worry about any boundary conditions for the correlation.
The inverse transformation which returns rho from the Fisher Z
rho = (exp(2*Z) - 1) / (exp(2*Z) + 1)
That is, you could replace rho in the covariance matrix presented
above by a function of the Fisher Z statistic. Then the estimation
process can operate on an unrestricted parameter space. This can
greatly help the estimation process.
It is for this same reason that we might prefer to work with
reparameterized variance function where the parameter LogSDu
is completely unrestricted, but the function exp(2*LogSDu)
returns a positive variance estimate.
Sorry that I don't have time to go into more details now. You
can look for more of my posts about the NLMIXED procedure in the
SAS-L archives. I have previously posted on these topics.
--- "adel F." <email@example.com> wrote:
> Hi Dale,
> Sorry I did not see your present email, I agree with you, we do not
> need a test for the odds ratio, since we have already a test for the
> parameter, but let me ask you what is the quantity LogSDu, it is the
> log of the parameter s2u, that I consider in starting parameter?
> Dale McLerran <firstname.lastname@example.org> wrote:
> You are correct that the test of exp(beta1)=0 is almost surely
> non=informative, and that we really are interested in the test
> of exp(beta1)=1. But we really don't need a test for the odds
> ratio since we have an equivalent test (H0: beta1=0) for the
> log odds.
> You indicate that the variance estimate for your random effect
> is going negative and you are not getting convergence. A
> reparameterization of your variance estimation process can be
> a big help in such situations. In place of the RANDOM statement
> random u ~ normal(0, s2u) subject=region;
> try fitting the model with
> random u ~ normal(0, exp(2*LogSDu)) subject=region;
> Since exp(x)>0, the reparameterization will avoid a negative
> variance estimate. Note that you can obtain an estimate of the
> variance in NLMIXED through an estimate statement - just as you
> obtain an estimate of the odds ratio through an estimate statement.
> Thus, you can code
> estimate "Variance(u)" exp(2*LogSDu);
Fred Hutchinson Cancer Research Center
Ph: (206) 667-2926
Fax: (206) 667-5977
Do you Yahoo!?
Yahoo! Mail - Find what you need with new enhanced search.