Balanced prime basis factorial fixed effects model with random number of observations

Sandra Oliveira; Célia Nunes; Elsa Moreira; Miguel Fonseca; João T Mexia

doi:10.1080/02664763.2019.1679097

Balanced prime basis factorial fixed effects model with random number of observations

J Appl Stat. 2019 Oct 16;47(13-15):2737-2748. doi: 10.1080/02664763.2019.1679097. eCollection 2020.

Authors

Sandra Oliveira^{1

2}, Célia Nunes³, Elsa Moreira^{2

4}, Miguel Fonseca^{2

4}, João T Mexia^{2

4}

Affiliations

¹ Department of Economics and Management, Polytechnic Institute of Setúbal, Setúbal, Portugal.
² CMA - Center of Mathematics and its Applications, Faculty of Science and Technology, Nova University of Lisbon, Lisbon, Portugal.
³ Department of Mathematics and Center of Mathematics and Applications (CMA-UBI), University of Beira Interior, Covilha, Portugal.
⁴ Department of Mathematics, Faculty of Science and Technology, Nova University of Lisbon, Lisbon, Portugal.

Abstract

Factorial designs are in general more efficient for experiments that involve the study of the effects of two or more factors. In this paper we consider a $p^{U}$ factorial model with U factors, each one having a p prime number of levels. We consider a balanced (r replicates per treatment) prime factorial with fixed effects. Our goal is to extend these models to the case where it is not possible to known in advance the number of treatments replicates, r. In these situations is more appropriate to consider r as a realization of a random variable R, which will be assumed to be geometrically distributed. The proposed approach is illustrated through an application considering simulated data.

Keywords: F distribution; Geometric distribution; Random number of replicates; factorial designs; fixed effects model; simulation study.

Grants and funding

This work was partially supported by national founds of FCT-Foundation for Science and Technology [grant numbers UID/MAT/00212/2019 and UID/MAT/00297/2019].