The SemiSymmetric Intraclass
Contingency Table
Numbers
in parentheses correspond to the numbered references in my publication
list.
The semisymmetric intraclass
contingency table is a threedimensional (r x r x c) contingency table
that is uppertriangular and a priori symmetric within layers; e.g.,
mijk
= mjik
where mijk
represents the expected cell frequency. Ishii (1960)
solved the maximum likelihood estimation problem of such a table by applying
the maximum likelihood method directly.
In the early 1980s, the loglinear
model was modified to handle this type of data structure, and maximum likelihood
estimation was carried out for the modified loglinear model (1).
This approach leads to an expression of the maximum likelihood estimates
exclusively in terms of the observed cell counts. This analysis is equivalent
to an application of the general loglinear model to an artificially complete
table obtained by splitting the offdiagonal cells in half within layers.
Applications of the semisymmetric
intraclass contingency table appear in social psychology and biology. Examples
include the study of actions of pairs of individuals, the study of amino
acid allele pairs in a protein, the determination of the effect of the
sexlinked dwarfing gene in male chickens on resistance to E. coli infection,
and the association between fingerprint patterns and genetic factors. See
(1) for references, and
for related work see (2),
(4), (5),
(9), (11),
(15), and (16).
Reference
Ishii, G.
(1960). Intraclass contingency tables. Annals of the Institute of Statistical
Mathematics 12: 161207.
