An Approximate Log-Linear Model for Predicting Magazine Audiences

Abstract

In 1988 Danaher showed a log-linear model to be accurate for predicting magazine exposure distributions. However, the model was expensive on computer time and stored array space when the number of magazines and insertions was large. An approximation to that model is developed that is of comparable accuracy yet takes less than one quarter of the computation time and eliminates the need for a large stored array. The approximate log-linear model is compared empirically with Danaher's previous log-linear model and one of Leckenby and Kishi's Dirichlet-multinomial models for equal-insertion schedules. For unequal-insertion schedules, the approximate log-linear model is compared with the log-linear model and the popular Metheringham beta-binomial model. The results show that in accuracy, the approximate log-linear model is between the log-linear and Leckenby and Kishi's model for equal insertions and is about the same as the log-linear for unequal-insertion schedules, but is significantly more accurate than Metheringham's model.