RE: MU referencing
There is another theoretical issue - constraining two parameters to have the
same
mean (tvParam) but different etas (ETA(1) and ETA(2)) violates the fundamental
assumption of MCPEM-like method
that the parameters are multivariate normal. The basic update formula for the
fixed effects based
on the means of the posteriors for the random effects is no longer valid. For
example, in a standard formulation the mean of the posteriors over all
subjects must be zero (this is the basic EM first order stationarity condition
for the derivative of the log likelihood function ).
But if you have two different means associated with the same eta, both means in
general cannot both be simultaneously zero..
It is unclear if MCPEM will converge under these conditions, and even if it
does, there is no guarantee that
the point corresponds to maximum likelihood.
Quoted reply history
________________________________________
From: [email protected] [[email protected]] On Behalf Of
Brendan Johnson [[email protected]]
Sent: Sunday, May 26, 2013 2:54 PM
To: [email protected]
Subject: [NMusers] MU referencing
Hi all,
When using MU referencing, how do I code the situation where the typical value
appears to be the same between two groups, but one group is more variable – how
do I give these two groups different ETAs but essentially the same THETA?
Is this legit?
tvParam=THETA(.)
MU_1=tvParam
MU_2=tvParam
Param1=MU_1+ETA(1)
Param2=MU_2+ETA(2)
Param=Param1*G1+Param2*G2
Where G1 and G2 equal 0 or 1 based on which group the subject belongs.
Thanks for the advice,
Brendan