On the Application of Conditional Independence to Ordinal Data

A special log linear parameterization is described for contingency tables which exploits prior knowledge that an ordinal scale of the variables is involved. It is helpful, in particular, in guiding the possible merging of adjacent levels of variables and may simplify interpretation if higher-order interactions are present. Several sets of data are discussed to illustrate the types of interpretation that can be achieved. The simple structure of the maximum likelihood estimates is derived by use of Lagrange multipliers.