In reply to Rick Wicklin.

Dear Rick, I don't think that there is a mixture of distributions underlying the model. Indeed, the problem is that there are two raters: the first assigns a value from an ordinal scale (absent, moderate and severe) or nominal scale (depression, anxiety, schizophrenia) the subjects according to the marginal probabilitis of the rows of a contingency table.
The same applies for the second rater which assigns the subjects according to the marginal probabilities of the columns of a contingency table.
Of course, the marginal probabilities do not have to be the same.
If there is no agreement the two multinomial / multicategorical distributions are not correlated, but in the case of an agreement, the two distributions are correlated.
The following papers are very useful for illustrating the problem. In addition, the second shows a SAS IML Macro for generating correlated data, but in the context of longitudinal studies.
1)-A.J. Lee Some simple methods for generating correlated categorical variates Computational Statistics & Data Analysis 26 (1997) 133-148
2)-Noor Akma Ibrahim, Suliadi Suliadi Generating correlated discrete ordinal data using
R and SAS IML computer methods and programs in biomedicine 104 ( 2011 ) e122–e132
Many thanks for your help in having the IML code for obtaining two correlated multinomial / categorical distributions