The Semi-Symmetric Intraclass
in parentheses correspond to the numbered references in my publication
The semi-symmetric intraclass
contingency table is a three-dimensional (r x r x c) contingency table
that is upper-triangular and a priori symmetric within layers; e.g.,
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 off-diagonal cells in half within layers.
Applications of the semi-symmetric
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
sex-linked 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),
(15), and (16).
(1960). Intraclass contingency tables. Annals of the Institute of Statistical
Mathematics 12: 161-207.