In recent years, harmonic regression models have been applied to implement quality control for educational assessment data consisting of multiple administrations and displaying seasonality. As with other types of regression models, it is imperative that model adequacy checking and model fit be appropriately conducted. However, there has been no…

Criteria for prediction of multinomial responses are examined in terms of estimation bias. Logarithmic penalty and least squares are quite similar in behavior but quite different from maximum probability. The differences ultimately reflect deficiencies in the behavior of the criterion of maximum probability.