Applied results of Institute of Sociology of the Academy of Sciences of the Czech Republic

Software MIDIA

Kostelecký, Tomáš – Vajda, Igor – Vrbenský, Karel

Purpose of Program

Given a contingency table K = (Kij ) with dimensions I x J and marginals ai = Qi1 + … + QiJ and bj = Q1j + … + QIj, the program tries to find contingency table Q = (Qij) of equal dimensions having  marginals ai, and bj. In the math sense, this problem for given table K and marginals ai, and bj can have infinitely many solutions, one solution or no solution. The particularity of the table Q, provided by program is as follows: 
(a) If there is only one solution, then the program will provide this one. 
(b) If there are infinitely many solutions, then the program will provide a solution for Q, which is statistically the most difficult to differentiate from the table (in terms of minimum discrimination information between the Q and K). 
(c) If there is no solution, then the program will provide a contingency table Q with the required marginals a, b, which is most difficult to statistically distinguish from a table that only slightly differs from K (not more than 1% for each item).

Details of the methods can be found in:

Vajda I., van der Meulen E. C. (2005): On minimum divergence adaptation of discrete bivariate distributions to given marginals, IEEE Transactions on Information Theory 51 (1): 313-320.