Rasch Models with Exchangeable Rows and Columns
Steffen Lilholt Lauritzen · 2003
Abstract The article studies distributions of doubly infinite binary matrices with exchangeable rows and columns which satisfy the further property that the probability of any m x n submatrix is a function of the row and column sums of that matrix. We show that any such distribution is a (unique) mixture of random Rasch distributions. The non-degenerate elements of these distributions were introduced by Rasch (1960). We investigate the relationship between these random Rasch distributions and a problem in visual perception, the characters of a certain Abelian semigroup, and the problem of existence of measures with given marginals.