Browsing by Author "Fonseca, Miguel"
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- Balanced prime basis factorial fixed effects model with random number of observationsPublication . 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.
- Chisquared and related inducing pivot variables: an application to orthogonal mixed modelsPublication . Ferreira, Dário; Ferreira, Sandra S.; Nunes, Célia; Fonseca, Miguel; Mexia, João T.We use chi-squared and related pivot variables to induce probability measures for model parameters, obtaining some results that will be useful on the induced densities. As illustration we considered mixed models with balanced cross nesting and used the algebraic structure to derive confidence intervals for the variance components. A numerical application is presented.
- Estimation and incommutativity in mixed modelsPublication . Ferreira, Dário; Ferreira, Sandra S.; Nunes, Célia; Fonseca, Miguel; Silva, Adilson; Mexia, João T.In this paper we present a treatment for the estimation of variance components and estimable vectors in linear mixed models in which the relation matrices may not commute. To overcome this difficulty, we partition the mixed model in sub-models using orthogonal matrices. In addition, we obtain confidence regions and derive tests of hypothesis for the variance components. A numerical example is included. There we illustrate the estimation of the variance components using our treatment and compare the obtained estimates with the ones obtained by the ANOVA method. Besides this, we also present the restricted and unrestricted maximum likelihood estimates.