```Date: Sun, 30 Jan 2005 19:02:53 -0800 Reply-To: Dale McLerran Sender: "SAS(r) Discussion" Comments: DomainKeys? See http://antispam.yahoo.com/domainkeys From: Dale McLerran Subject: Re: Estimate odds ratio in proc NLMIXED Comments: To: "adel F." In-Reply-To: <20050130191555.92891.qmail@web26402.mail.ukl.yahoo.com> Content-Type: text/plain; charset=us-ascii Adel, 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 statistic is 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. Dale --- "adel F." 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? > Thanks > Adel > > Dale McLerran wrote: > Adel, > > 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); > > Dale ===== --------------------------------------- Dale McLerran Fred Hutchinson Cancer Research Center mailto: dmclerra@NO_SPAMfhcrc.org Ph: (206) 667-2926 Fax: (206) 667-5977 --------------------------------------- __________________________________ Do you Yahoo!? Yahoo! Mail - Find what you need with new enhanced search. http://info.mail.yahoo.com/mail_250 ```

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