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# DESENVOLVIMENTO DE UM MODELO LINEAR DE EFEITO MISTO NA ESTIMATIVA DO CRESCIMENTO E PRODUÇÃO DE POVOAMENTOS CLONAIS DE Eucalyptus

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**ABSTRACT:**This book deals with various aspects of modeling and analysis for longitudinal data and repeated measurement designs. According to the authors it contains a reasonable mixture of theory, methodology, and applications. The flavor of the book reflects the area of specialty of the authors – life sciences, epidemiology, and biomedical research. However, the results can be applied in a variety of other fields as well. The book contains nine chapters. A computer disk is provided that contains a SAS macro called MIXNLIN (MIXed-effects NonLINear Regression) which is specifically written by the authors for applications involving the analysis of mixed-effects nonlinear regression models for repeated measurements. Chapter 1 is an introductory chapter containing important results from matrix theory, univariate and multivariate distribution theory, and asymptotic theory. A discussion of various mechanisms leading to missing data in longitudinal studies is also provided. Chapter 2 overviews the multivariate analysis of variance (MANOVA) model and analysis procedures. A multivariate extension of the Box-Cox transformation family is discussed. Methods for investigating violation of assumptions and diagnostics for identifying influential cases are provided. A Bayesian approach is discussed for a MANOVA model in the general setting. Finally, some special cases of the MANOVA model – one-way MANOVA, multiway MANOVA, multivariate regression, and multivariate analysis of covariance – are examined. Chapter 3 focusses on the repeated measurements analysis of variance model for balanced and complete data. By balanced data it is meant that the occassions of measurement are the same for all the experimental units and by complete data it is meant that there are no missing values. Both univariate and multivariate analyses are considered. Multiway repeated measurement designs with or without covariates are discussed. Estimation and hypothesis testing are discussed for models with various standard covariance structures. Diagnostics, sample size considerations, and efficiency of designs are also discussed. Chapter 4 is devoted to a fairly in-depth discussion of various crossover designs including multigroup multiperiod designs. Models are proposed which allow the random subject effects to depend on sequence and treatment. Three scenarios are considered for carryover effects: (1) carryover effects are absent, (2) they are equal, and (3) they are unequal. Inference procedures based on the method of least squares are given along with procedures based on the likelihood. Several specific types of crossover designs are treated and a comparison of various standard designs is given. Statistical inference for a general crossover design with covariates is studied. Many of the results are extended to the case of a multivariate response for each unit at each time point. Chapter 5 introduces linear regression type approaches for repeated measurement data. In particular a Generalized MANOVA (GMANOVA) for growth curve data is discussed. Data are required to be balanced but not necessarily complete. Chapter 6 discusses the random coefficient growth model and the generalized linear mixed model. The data are not required to be balanced or complete. Maximum Likelihood and Estimated Generalized Least Squares (EGLS) methods are discussed along with some asymptotic results. Prediction of a new future observation is considered. Analysis for informatively censored data is provided. Chapter 7 is devoted to various nonlinear models and estimation procedures for analyzing continuous repeated measurement data or longitudinal data. Nonlinear versions of GMANOVA model and the linear mixed-effects model are derived. Several estimation methods are considered for continuous normally distributed data. Examples are given to illustrate the procedures. Chapter 8 extends the discussion in chapter 7 so as to include both continuous and discrete data. This is done by employing generalized nonlinear mixed-effects models. Several methods of estimation are considered including maximum likelihood, generalized estimating equations (GEE) and EGLS. Methods for model selection and for assessing the goodness of fit of models are also provided. Chapter 9 attempts to show the interconnections among various inference techniques proposed for the analysis of repeated measurements data – ML, pseudo-likelihood, and generalized least squares. This is done using the principle of least squares and the notion of generalized estimating equations. The appendix is essentially a manual for the accompanying software (MIXNLIN). Examples are given there to illustrate the use of the software. The book ends with a bibliography, an author index, and a subject index. This book will be a valuable resource for researchers as well as practitioners interested in analysis of longitudinal data. It will also serve as a textbook for a graduate level course in longitudinal data analysis.01/1997; Marcel Dekker Inc.. - [Show abstract] [Hide abstract]

**ABSTRACT:**This article investigates the impact of the normality assumption for random effects on their estimates in the linear mixed-effects model. It shows that if the distribution of random effects is a finite mixture of normal distributions, then the random effects may be badly estimated if normality is assumed, and the current methods for inspecting the appropriateness of the model assumptions are not sound. Further, it is argued that a better way to detect the components of the mixture is to build this assumption in the model and then “compare” the fitted model with the Gaussian model. All of this is illustrated on two practical examples.Journal of The American Statistical Association - J AMER STATIST ASSN. 01/1996; 91(433):217-221. - [Show abstract] [Hide abstract]

**ABSTRACT:**Mixed models have become very popular for the analysis of longitudinal data, partly because they are flexible and widely applicable, partly also because many commercially available software packages offer procedures to fit them. They assume that measurements from a single subject share a set of latent, unobserved, random effects which are used to generate an association structure between the repeated measurements. In this chapter, we give an overview of frequently used mixed models for continuous as well as discrete longitudinal data, with emphasis on model formulation and parameter interpretation. The fact that the latent structures generate associations implies that mixed models are also extremely convenient for the joint analysis of longitudinal data with other outcomes such as dropout time or some time-to-event outcome, or for the analysis of multiple longitudinally measured outcomes. All models will be extensively illustrated with the analysis of real data.05/2010: pages 37-96;

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