Jens Henrik Badsberg
More complex graph computations for undirected graphical models
by the CoCo bundle for R
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CoCo is a program for estimation, test and model search among hierarchical
interaction models for large complete contingency tables. The name CoCo is
derivated of "Co"mplete "Co"ntingency tables, since the initial program
could only handle complete contingency tables, but the program has been
enhanced to handle also incomplete tables and latest also graphical models
with continuous variables.

CoCo works especially efficiently on graphical models, and some of the
commands are designed to handle graphical models.

Graphical models are log-linear interaction models for contingency tables
that can be represented by a simple undirected graph with as many vertices
as the table has dimension. Further all these models can be given an
interpretation in terms of conditional independence and the interpretation
can be read directly off the graph in the form of a Markov property. The
class of graphical model is a proper subclass of the hierarchical models,
but the class strictly contains the decomposable models, e.g.,
Haberman (19772). See Darroch, Lauritzen and Speed (1980) for how graphical
models are defined by the close connection between the theory of Markov
fields and that of log-linear interaction models for contingency tables.

CoCo is a program designed to perform estimation and tests in large
contingency tables. By using graph-theoretical results the hierarchical
mixed interaction models are decomposed. The iterative algorithm is not
used on the full table, but only on the non-decomposable irreducible
components. Furthermore, the optimized version of the IPS-algorithm of
Jirouvsek (1991) is used on these non-decomposable discrete atoms.

Besides incomplete tables also tables with incomplete observations
can be handled in CoCo, e.g. by the EM algorithm.  Exact tests between
any two nested decomposable discrete models can be computed.

The CoCo bundle for R is available from
http://www.jbs.agrsci.dk/Biometry/Software-Datasets/CoCo/CoCo.1.5/.
The package for handling models with both discrete and continuous
variables are currently called CoCoCg. This module will be included
in the next version of the CoCo bundle made available later this year.
Some of the function names used in the example section this version
of the paper might be changed in later versions of the CoCo bundle.