  We introduce an informative probabilistic association matrix to measure a
proportional local-to-global association of categories of one variable with
another categorical variable. Towards a probability based proportional
prediction, the association matrix gives rise to the expected predictive
distribution of the first and second types of errors for a multinomial response
variable. In addition, the normalization of the diagonal of the matrix gives
rise to an association vector, which provides the expected category accuracy
lift rate distribution. A general scheme of global-to-global association
measures with flexible weight vectors is further developed from the matrix. A
hierarchy of equivalence relations defined by the association matrix and vector
is shown. Applications to financial and survey data together with simulations
results are presented.
