Date: Sun, 21 Jun 2009 15:40:09 -0700 Dale McLerran "SAS(r) Discussion" Dale McLerran Re: Log likelihood Specification text/plain; charset=iso-8859-1

--- On Thu, 6/18/09, clyde013 <clyde013@YAHOO.COM> wrote:

> From: clyde013 <clyde013@YAHOO.COM> > Subject: Log likelihood Specification > To: SAS-L@LISTSERV.UGA.EDU > Date: Thursday, June 18, 2009, 7:28 AM > I'm trying to do estimate parameters > for the following log likelihood > by ML. Can anyone help me with this. In > addition I need to write > that u~Normal(resmean,resstd). Can I do that with a > model statement > (model u ~ n(resmean,resstd))? > > proc nlmixed data=alright; > parms > gamma1=.37169079, > gamma2=.24768216286, > gamma3= .13767485639, > gamma4= .17399481039, > gamma0= .068957371574, > resmean=-.000068063, > resstd=14.329124207, > u=.93104262843, > > l=log(gamma1*u*.5*res+ > gamma1*u*(1/8)*res+gamma2*u*.25*res+gamma1*u* > (1/16)*res+ > gamma2*u*(1/8)*res+gamma3*u*.25*res+gamma1*u*(1/16)*res+gamma2*u*(1/8) > *res > +gamma3*u*.25*res+gamma4*2*.5*res +gamma0*(1-u)*res); > model l ~ general(l);run; > > > Any help is greatly appreciated! >

Clyde,

Your likelihood model is written in a rather peculiar way. You wrote the likelihood (with a little editing to show how the parameters enter the model) as:

l=log(gamma1*u*.5*res + gamma1*u*(1/8)*res + gamma2*u*.25*res + gamma1*u*(1/16)*res + gamma2*u*(1/8)*res + gamma3*u*.25*res + gamma1*u*(1/16)*res + gamma2*u*(1/8)*res + gamma3*u*.25*res + gamma4*2*.5*res + gamma0*(1-u)*res);

which can be written more simply as

l=log(gamma1*u*(0.5 + 1/8 + 1/16 + 1/16)*res + gamma2*u*(0.25 + 1/8 + 1/8)*res + gamma3*u*(0.25 + 0.25)*res + gamma4*2*(0.5)*res + gamma0*(1-u)*res);

or, after collecting like terms,

l=log(gamma1*u*(0.75)*res + gamma2*u*(0.5)*res + gamma3*u*(0.5)*res + gamma4*2*(0.5)*res + gamma0*(1-u)*res;

Now, a few observations about this model would seem to be in order. FIRST, gamma2 and gamma3 enter identically and are not separately identifiable. SECOND, gamma1 enters the model simply as a scaled version of gamma2 and gamma3 which means that gamma1, gamma2, and gamma3 are not separately identifiable. THIRD, my guess is that the portion of your likelihood which is written as

gamma4*2*(0.5)*res +

really should have been written as

gamma4*u*(0.5)*res +

in which case gamma4 would enter the model identically to gamma2 and gamma3 (and as a scaled version of gamma1).

This likelihood does not have separately identifiable parameters. You need to review your model and come up with a likelihood which has identifiable parameters.

Dale

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

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