For equations such as the one you're looking to typeset, it's usually best not to rely on any automatic sizing of "fences" (i.e., round parentheses, square brackets, curly braces, etc). Instead, use the TeX/LaTeX \big
, \Big
, \bigg
, and \Bigg
directives to size the fences. For the equation at hand, \bigg
for both the outermost curly braces and for the inner fences seems OK.
I would further recommend (i) splitting the equation (a log-likelihood function, right?) across three lines instead of just two so give it a chance of fitting inside the text block, and (ii) using different fence symbols for the inner fences -- which enclose the arguments of the various logarithm terms -- and the outer fences. In the example below, I use round parentheses for the inner fences. Oh, and you also seem to be inserting "thin spaces" (\,
) between some summation symbols but not between others; I wouldn't insert any such thin-spaces.

\documentclass{article}
\usepackage[margin=1in]{geometry} % choose whatever margins suit you best
\usepackage{amsmath} % amsmath package provides 'split' environment
\begin{document}
\begin{equation}
\begin{split}
G^{2} = -2 \bigg\{&
\sum_i\sum_j\sum_k z_{ijk111}\log \biggl( \frac{m_{ijk}}{z_{ijk111}}\biggr) +
\sum_j\sum_k z_{+jk211}\log \biggl( \frac{\sum_i m_{ijk}a_{ijk}}{z_{+jk211}}\biggr)\\
&+ \sum_k\sum_i z_{i+k121}\log \biggl( \frac{\sum_j m_{ijk}b_{ijk}}{z_{i+k121}} \biggr)
+ \sum_j\sum_i z_{ij+112}\log \biggl( \frac{\sum_km_{ijk}b_{ijk}}{z_{ij+112}} \biggr) \\
&+ z_{+++222} \log \biggl( \frac{m_{ijk}a_{ijk}b_{ijk}c_{ijk}\theta_{M_{(I)}}\theta_{M_{(J)}}\theta_{M_{(K)}}}{z_{+++222}} \biggr)
\bigg\}
\end{split}
\end{equation}
\end{document}
\{
and\}
by\left\{
and\right\}
respectively. That allows the bracket to vary their size accordingly to the context – Dox Aug 22 '13 at 16:36\{
..\}
needs to cover more than one alignment cell. – David Carlisle Aug 22 '13 at 16:38\big\{
,\Big\{
,\bigg\{
or\Bigg\{
(also allowed for closing the bracket by replacing{
for}
– Dox Aug 22 '13 at 16:44