Orthogonal mixed models and prime basis factorials

Prime basis factorial models have the advantage of allowing the simultaneous study of a larger number of interactions compared to classical approaches. However, the procedures for obtaining the sums of squares can be somewhat cumbersome. In this work, we present a recurrence method for obtaining the sums of squares in prime basis factorial models. Nevertheless, this recurrence procedure may be applied in cases with any number of factors and levels, even when it is neither a prime nor a power of a prime. We illustrate the method with an application to real data, where the percentage of total deaths due to cancer, diabetes, and any circulatory system disease in three European countries, in 3 years, is compared. We compare the results with the ones obtained using ANOVA.