Center for Mathematics and Applications

Funder

Organizational Unit

Publications

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

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

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.

2019Journal article

Restricted access

Considering the sample sizes as truncated Poisson random variables in mixed effects models

Publication . Nunes, Célia; Moreira, Elsa E.; Ferreira, Sandra S.; Ferreira, Dário; Mexia, João T.

When applying analysis of variance, the sample sizes may not be previously known, so it is more appropriate to consider them as realizations of random variables. A motivating example is the collection of observations during a fixed time span in a study comparing, for example, several pathologies of patients arriving at a hospital. This paper extends the theory of analysis of variance to those situations considering mixed effects models. We will assume that the occurrences of observations correspond to a counting process and the sample dimensions have Poisson distribution. The proposed approach is applied to a study of cancer patients.

2019Journal article

Open access

Random sample sizes in orthogonal mixed models with stability

Publication . Nunes, Célia; Mário, Anacleto César Xavier; Ferreira, Dário; Ferreira, Sandra S.; Mexia, João T.

In this work, we presente a new approach that considers orthogonal mixed models, under situations of stability, when the sample dimensions are not known in advande. In this case, samples are considered realizations of independente rendom variables. We apply this methodology to the case where there is na upper bound for the sample dimensions, which may not be attained since failures may occur. Based on this, we assume that sample sizes are binomially distributed. We consider na application on the incidence of unemployed persons in the European Union to illustrate the proposed methodology. A simulation study is also conduced. The obtained results show the relevance of the proposed approach in avoiding false rejections.

2019Journal article

Restricted access