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- 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.
- Exact Estimators for Normal Linear Mixed ModelsPublication . Ferreira, Sandra S.; Ferreira, Dário; Moreira, Elsa; Mexia, João T.
- Discriminant analysis and decision theoryPublication . Ferreira, Sandra Saraiva; Ferreira, Dário; Nunes, Célia; Mexia, João T.A unified approach, based in Statistical Decision Theory, is presented for Discriminant Analysis. Thus optimum allocation rules minimizing the expected costs are derived for the continuous case and for the mixed case. In the first case, the observed variables are continuous, while in the mixed case, there will also be discrete as qualitative variables. The second case has many times been treated using logistic regression. The breaking up of the allocation problem into distinct cases is now overcome.
- Estimation of variance components in normal linear mixed models with additivityPublication . Ferreira, Dário; Ferreira, Sandra S.; Nunes, Célia; Mexia, João T.In this paper we use commutative Jordan Algebras to estimate variance components in linear mixed models. We apply the theory to a model in which three factors cross and one of the factors is additive to the other two.
- Confidence intervals for variance components in gauge capability studiesPublication . Ferreira, Dário; Ferreira, Sandra S.; Nunes, Célia; Oliveira, Teresa A.; Mexia, João T.We present a method, that uses pivot variables, which are functions of statistics and parameters, of constructing confidence intervals for variance components in gauge capability studies. As illustration we will consider a study on repeatability and reproducibility measures. Besides this the paper includes a simulation study demonstrating that in approximately 9500 out of 10000 simulations the 95% confidence interval covers the true value of the parameter.
- Estimation of Variance Components in Linear Mixed Models with Commutative Orthogonal Block StructurePublication . Ferreira, Sandra S.; Ferreira, Dário; Nunes, Célia; Mexia, João T.Segregation and matching are techniques to estimate variance compo- nents in mixed models. A question arising is whether segregation can be applied in situations where matching does not apply. Our motivation for this research relies on the fact that we want an answer to that question and to explore this important class of models that can contribute to the devel- opment of mixed models. That is possible using the algebraic structure of mixed models. We present two examples showing that segregation can be applied in situations where matching does not apply.
- Maximum Likelihood Estimation Methods for Variance Components in Linear Non-Orthogonal Small Size Design ModelsPublication . Ferreira, Dário; Ferreira, Sandra S.; Nunes, Célia; Mexia, João T.We compare four Maximum Likelihood Estimation methods for estimating variance components in normal linear mixed models, in the case of unbalanced small size design models: The Newton-Raphson, the Triple Minimization, the Gradient and a method where the starting points for the Newton-Raphson are the estimates obtained with the Triple Minimization method.
- Random sample sizes in one-way fixed effects modelsPublication . Nunes, Célia; Capistrano, Gilberto; Ferreira, Dário; Ferreira, Sandra S.; Mexia, João T.Analysis of variance (ANOVA) is one of the most frequently used statistical analysis in several research areas, namely in medical research. Despite its wide use, it has been applied assuming that sample dimensions are known. In this work we aim to carry out ANOVA like analysis of one-way fixed effects models, to situations where the samples sizes may not be previously known. Assuming that the samples were generated by Pois- son counting processes we obtain the unconditional distribution of the test statistic, under the assumption that we have random sample sizes. The applicability of the pro- posed approach is illustrated considering a real data example on cancer registries. The results obtained suggested that false rejections may be avoid by applying our approach.
- Exact critical values for one-way fixed effects models with random sample sizesPublication . Nunes, Célia; Capistrano, Gilberto; Ferreira, Dário; Ferreira, Sandra S.; Mexia, João T.Analysis of variance (ANOVA) is one of the most frequently used statistical analyses in several research areas, namely in medical research. Despite its wide use, it has been applied assuming that sample dimensions are known. In this work we aim to carry out ANOVA like analysis of one-way fixed effects models, to situations where the samples sizes may not be previously known. In these situations it is more appropriate to consider the sample sizes as realizations of independent random variables. This approach must be based on an adequate choice of the distributions of the samples sizes. We assume the Poisson distribution when the occurrence of observations corresponds to a counting process. The Binomial distribution is the proper choice if we have observations failures and there exist an upper bound for the sample sizes. We also show how to carry out our main goal by computing correct critical values. The applicability of the proposed approach is illustrated considering a real data example on cancer registries. The results obtained suggested that false rejections may be avoided by applying our approach.
- The relative age effect among elite youth competitive swimmersPublication . Costa, Aldo M.; Marques, Mário C; Louro, Hugo; Ferreira, Sandra S.; Marinho, DanielThe aim of this study was to analyse the relative age effect (RAE) in competitive swimming. The best 50 Portuguese swimmers (12- to 18-year-olds) for the main individual swimming pool events of both genders were considered. Analysis was conducted on 7813 swimming event participants, taking account of respective swimmer birth dates and the Fédération Internationale de Natation points gained. Differences in the distribution of birth dates by quarter year were determined using the Chi-square. A one-way analysis of variance ANOVA was used to test for differences measured in points between individuals by quarterly birth year intervals. A two-way analysis of variance ANOVA was also conducted to test the interaction between gender and seasonal birth date with regard to performance. The results show an inequitable distribution (p<0.01) of birth dates by quarter for almost all age groups and both genders. However, the distribution of birth dates by quarter for each considered swim event shows that RAE seems to exist only for 12-year-old females and 12- to 15-year-old males. Analysing mean swimming performance, post-hoc results (p<0.01) show no consistency in RAE. Higher performance occurs among older swimmers only in 100 m butterfly (female 1998, 1st≠2nd quarter, p=0.003). The results also show no interaction between gender and seasonal birth date (p<0.01). Findings of this study show that a higher number of swimmers, particular males, are born in the first two quarters of the year, although there is mostly no effect of seasonal birth date on performance differences within the top 50 swimmers.