Application of Prediction Analysis to Cross Classifications of Ordinal Data

Prediction analysis (PA) of cross classifications is characterized as a method for the analysis of local prediction hypotheses, that is, hypotheses that link particular predictor states to particular states of criteria. To evaluate the success of a prediction, PA compares the observed with an expected frequency distribution. The latter is estimated under the assumption of independence between predictors and criteria. When predictors of criteria have ordinal categories, the success of a prediction hypothesis is overestimated if there is a regression of the cell frequencies on the ranks of the variable categories. Using the method of log‐linear models, it is shown how ordinal categories can be taken into account in PA. Numerical examples are given from the areas of cognitive development and drug research.