[Lme4-commits] r1838 - www/JSS

[noreply at r-forge.r-project.org]

Author: walker
Date: 2013-08-18 00:56:29 +0200 (Sun, 18 Aug 2013)
New Revision: 1838

Modified:
   www/JSS/glmerAppendix.tex
Log:
adjusted log-likelihood to be a real log-likelihood

Modified: www/JSS/glmerAppendix.tex
===================================================================
--- www/JSS/glmerAppendix.tex	2013-08-17 21:56:09 UTC (rev 1837)
+++ www/JSS/glmerAppendix.tex	2013-08-17 22:56:29 UTC (rev 1838)
@@ -112,13 +112,16 @@
 \begin{equation}
 L(\bm\beta, \bm\theta | \bm y, \bm u) = 
 \bm\psi^\top \bm A \bm y - 
-\bm a^\top \bm \phi -
+\bm a^\top \bm \phi  + 
+\bm c -
 \frac{1}{2}\bm u^\top \bm u
 \end{equation}
-where $\bm\psi$ is the $n$-by-$1$ natural parameter of an exponential family,
-$\bm\phi$ is the $n$-by-$1$ vector of cumulant functions, and $\bm A$ is an $n$-by-$n$ diagonal
-matrix of prior weights, $\bm a$, which could depend on a dispersion
-parameter although we ignore this possibility for now.
+where $\bm\psi$ is the $n$-by-$1$ canonical parameter of an exponential family,
+$\bm\phi$ is the $n$-by-$1$ vector of cumulant functions, $\bm c$ an
+$n$-by-$1$ vector required for the log-likelihood to be based on a
+true probability distribution, and $\bm A$ is an $n$-by-$n$ diagonal
+matrix of prior weights, $\bm a$. Both $\bm a$ and $\bm c$ could depend on a dispersion
+parameter, although we ignore this possibility for now.
 
 The natural parameter, $\bm\psi$, and cumulant function, $\bm\phi$,
 depend on a linear predictor,