Conditional symmetry model as a better alternative to Symmetry Model for rater agreement measure

In almost all life or social science researches, subjects are
classified into categories by raters, interviewers or observers.
Many approaches have been proposed by various authors for analyzing
the data or the results obtained from these raters. Symmetry and
conditional symmetry models are models designed for square tables
like the one arising from the raters results. Conditional symmetry
model which possessed an extra parameter for the off-diagonal cells
is a special case to symmetry. In this research work, we examined
the effect of the extra parameter introduced by conditional
symmetry model over that of symmetry on structure of agreement as
well as their fittings. Generalized linear model (GLM) approach was
used to model the loglinear model forms of these models with
empirical examples. We observed that conditional symmetry based on
it extra parameter gave a tremendous improvement to the significant
level of the test statistics over that of its symmetry model
counterpart, hence conditional symmetry model is better for raters
agreement modelling which require symmetric table.