Predicting from Unbalanced Linear or Generalized Linear Models

Abstract

The formation of predictions to summarize the fit of a model is an important stage of practical analysis. In unbalanced linear models, and in generalized linear models, choices have to be made about the basis of standardization of subsidiary effects so that primary effects can be summarized. Two problems in the formation of predictive summaries are discussed and solutions are proposed. First, the large storage requirement of calculations for relatively modest models can be greatly reduced by modifying the algorithm to take account of the structure of the intermediate matrices. Second, the presence of non-estimable parameters can be dealt with satisfactorily by a further modification to keep track of ‘unset’ values throughout the calculations.