Orthogonal mixed models and prime basis factorials. (4th January 2022)

• Record Type: Journal Article
• Authors: Ferreira, Dário; Ferreira, Sandra S.; Nunes, Célia; Mexia, João T.
• Other Names: Tosun Murat guestEditor.; Kara Emrah Evren guestEditor.; Usta Fuat guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 18(2023)
• Page Start: 12196
• Page End: 12205
• Publication Date: 2022-01-04
• Subjects: ANOVA -- inference -- mixed models -- prime basis factorial models; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7970
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.