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Generalized, Linear, and Mixed Models
01 Jan 2001-
TL;DR: In this paper, the authors present a model for estimating the effect of random effects on a set of variables in a linear mixed model with the objective of finding the probability of a given variable having a given effect.
Abstract: Preface. Preface to the First Edition. 1. Introduction. 1.1 Models. 1.2 Factors, Levels, Cells, Effects And Data. 1.3 Fixed Effects Models. 1.4 Random Effects Models. 1.5 Linear Mixed Models (Lmms). 1.6 Fixed Or Random? 1.7 Inference. 1.8 Computer Software. 1.9 Exercises. 2. One-Way Classifications. 2.1 Normality And Fixed Effects. 2.2 Normality, Random Effects And MLE. 2.3 Normality, Random Effects And REM1. 2.4 More On Random Effects And Normality. 2.5 Binary Data: Fixed Effects. 2.6 Binary Data: Random Effects. 2.7 Computing. 2.8 Exercises. 3. Single-Predictor Regression. 3.1 Introduction. 3.2 Normality: Simple Linear Regression. 3.3 Normality: A Nonlinear Model. 3.4 Transforming Versus Linking. 3.5 Random Intercepts: Balanced Data. 3.6 Random Intercepts: Unbalanced Data. 3.7 Bernoulli - Logistic Regression. 3.8 Bernoulli - Logistic With Random Intercepts. 3.9 Exercises. 4. Linear Models (LMs). 4.1 A General Model. 4.2 A Linear Model For Fixed Effects. 4.3 Mle Under Normality. 4.4 Sufficient Statistics. 4.5 Many Apparent Estimators. 4.6 Estimable Functions. 4.7 A Numerical Example. 4.8 Estimating Residual Variance. 4.9 Comments On The 1- And 2-Way Classifications. 4.10 Testing Linear Hypotheses. 4.11 T-Tests And Confidence Intervals. 4.12 Unique Estimation Using Restrictions. 4.13 Exercises. 5. Generalized Linear Models (GLMs). 5.1 Introduction. 5.2 Structure Of The Model. 5.3 Transforming Versus Linking. 5.4 Estimation By Maximum Likelihood. 5.5 Tests Of Hypotheses. 5.6 Maximum Quasi-Likelihood. 5.7 Exercises. 6. Linear Mixed Models (LMMs). 6.1 A General Model. 6.2 Attributing Structure To VAR(y). 6.3 Estimating Fixed Effects For V Known. 6.4 Estimating Fixed Effects For V Unknown. 6.5 Predicting Random Effects For V Known. 6.6 Predicting Random Effects For V Unknown. 6.7 Anova Estimation Of Variance Components. 6.8 Maximum Likelihood (Ml) Estimation. 6.9 Restricted Maximum Likelihood (REMl). 6.10 Notes And Extensions. 6.11 Appendix For Chapter 6. 6.12 Exercises. 7. Generalized Linear Mixed Models. 7.1 Introduction. 7.2 Structure Of The Model. 7.3 Consequences Of Having Random Effects. 7.4 Estimation By Maximum Likelihood. 7.5 Other Methods Of Estimation. 7.6 Tests Of Hypotheses. 7.7 Illustration: Chestnut Leaf Blight. 7.8 Exercises. 8. Models for Longitudinal data. 8.1 Introduction. 8.2 A Model For Balanced Data. 8.3 A Mixed Model Approach. 8.4 Random Intercept And Slope Models. 8.5 Predicting Random Effects. 8.6 Estimating Parameters. 8.7 Unbalanced Data. 8.8 Models For Non-Normal Responses. 8.9 A Summary Of Results. 8.10 Appendix. 8.11 Exercises. 9. Marginal Models. 9.1 Introduction. 9.2 Examples Of Marginal Regression Models. 9.3 Generalized Estimating Equations. 9.4 Contrasting Marginal And Conditional Models. 9.5 Exercises. 10. Multivariate Models. 10.1 Introduction. 10.2 Multivariate Normal Outcomes. 10.3 Non-Normally Distributed Outcomes. 10.4 Correlated Random Effects. 10.5 Likelihood Based Analysis. 10.6 Example: Osteoarthritis Initiative. 10.7 Notes And Extensions. 10.8 Exercises. 11. Nonlinear Models. 11.1 Introduction. 11.2 Example: Corn Photosynthesis. 11.3 Pharmacokinetic Models. 11.4 Computations For Nonlinear Mixed Models. 11.5 Exercises. 12. Departures From Assumptions. 12.1 Introduction. 12.2 Misspecifications Of Conditional Model For Response. 12.3 Misspecifications Of Random Effects Distribution. 12.4 Methods To Diagnose And Correct For Misspecifications. 12.5 Exercises. 13. Prediction. 13.1 Introduction. 13.2 Best Prediction (BP). 13.3 Best Linear Prediction (BLP). 13.4 Linear Mixed Model Prediction (BLUP). 13.5 Required Assumptions. 13.6 Estimated Best Prediction. 13.7 Henderson's Mixed Model Equations. 13.8 Appendix. 13.9 Exercises. 14. Computing. 14.1 Introduction. 14.2 Computing Ml Estimates For LMMs. 14.3 Computing Ml Estimates For GLMMs. 14.4 Penalized Quasi-Likelihood And Laplace. 14.5 Exercises. Appendix M: Some Matrix Results. M.1 Vectors And Matrices Of Ones. M.2 Kronecker (Or Direct) Products. M.3 A Matrix Notation. M.4 Generalized Inverses. M.5 Differential Calculus. Appendix S: Some Statistical Results. S.1 Moments. S.2 Normal Distributions. S.3 Exponential Families. S.4 Maximum Likelihood. S.5 Likelihood Ratio Tests. S.6 MLE Under Normality. References. Index.
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14 Apr 2005
TL;DR: Cardiac resynchronization has been shown to reduce symptoms and improve left ventricular function in patients with heart failure due to systolic dysfunction and cardiac dyssynchrony.
Abstract: background Cardiac resynchronization reduces symptoms and improves left ventricular function in many patients with heart failure due to left ventricular systolic dysfunction and cardiac dyssynchrony We evaluated its effects on morbidity and mortality methods Patients with New York Heart Association class III or IV heart failure due to left ventricular systolic dysfunction and cardiac dyssynchrony who were receiving standard pharmacologic therapy were randomly assigned to receive medical therapy alone or with cardiac resynchronization The primary end point was the time to death from any cause or an unplanned hospitalization for a major cardiovascular event The principal secondary end point was death from any cause results A total of 813 patients were enrolled and followed for a mean of 294 months The primary end point was reached by 159 patients in the cardiac-resynchronization group, as compared with 224 patients in the medical-therapy group (39 percent vs 55 percent; hazard ratio, 063; 95 percent confidence interval, 051 to 077; P<0001) There were 82 deaths in the cardiac-resynchronization group, as compared with 120 in the medical-therapy group (20 percent vs 30 percent; hazard ratio 064; 95 percent confidence interval, 048 to 085; P<0002) As compared with medical therapy, cardiac resynchronization reduced the interventricular mechanical delay, the end-systolic volume index, and the area of the mitral regurgitant jet; increased the left ventricular ejection fraction; and improved symptoms and the quality of life (P<001 for all comparisons) conclusions In patients with heart failure and cardiac dyssynchrony, cardiac resynchronization improves symptoms and the quality of life and reduces complications and the risk of death These benefits are in addition to those afforded by standard pharmacologic therapy The implantation of a cardiac-resynchronization device should routinely be considered in such patients
5,493 citations
TL;DR: The R package MCMCglmm implements Markov chain Monte Carlo methods for generalized linear mixed models, which provide a flexible framework for modeling a range of data, although with non-Gaussian response variables the likelihood cannot be obtained in closed form.
Abstract: Generalized linear mixed models provide a flexible framework for modeling a range of data, although with non-Gaussian response variables the likelihood cannot be obtained in closed form. Markov chain Monte Carlo methods solve this problem by sampling from a series of simpler conditional distributions that can be evaluated. The R package MCMCglmm implements such an algorithm for a range of model fitting problems. More than one response variable can be analyzed simultaneously, and these variables are allowed to follow Gaussian, Poisson, multi(bi)nominal, exponential, zero-inflated and censored distributions. A range of variance structures are permitted for the random effects, including interactions with categorical or continuous variables (i.e., random regression), and more complicated variance structures that arise through shared ancestry, either through a pedigree or through a phylogeny. Missing values are permitted in the response variable(s) and data can be known up to some level of measurement error as in meta-analysis. All simu- lation is done in C/ C++ using the CSparse library for sparse linear systems.
4,156 citations
Cites background from "Generalized, Linear, and Mixed Mode..."
...However, generalizing these models to non-Gaussian data has proved difficult because integrating over the random effects is intractable (McCulloch and Searle 2001)....
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TL;DR: The types of research questions that diary methods are best equipped to answer are reviewed, the main designs that can be used, current technology for obtaining diary reports, and appropriate data analysis strategies are reviewed.
Abstract: In diary studies, people provide frequent reports on the events and experiences of their daily lives. These reports capture the particulars of experience in a way that is not possible using traditional designs. We review the types of research questions that diary methods are best equipped to answer, the main designs that can be used, current technology for obtaining diary reports, and appropriate data analysis strategies. Major recent developments include the use of electronic forms of data collection and multilevel models in data analysis. We identify several areas of research opportunities: 1. in technology, combining electronic diary reports with collateral measures such as ambulatory heart rate; 2. in measurement, switching from measures based on between-person differences to those based on within-person changes; and 3. in research questions, using diaries to (a) explain why people differ in variability rather than mean level, (b) study change processes during major events and transitions, and (c) study interpersonal processes using dyadic and group diary methods.
3,258 citations
Cites background from "Generalized, Linear, and Mixed Mode..."
...Advanced treatments can be found in Diggle & Liang (2001), McCulloch & Searle (2001), and Verbeke & Molenberghs (2000)....
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01 Jan 2009
2,933 citations
Cites methods from "Generalized, Linear, and Mixed Mode..."
...McCulloch and Searle (2001) also discuss the use of PQL for GLMMs....
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TL;DR: Brainstorm as discussed by the authors is a collaborative open-source application dedicated to magnetoencephalography (MEG) and EEG data visualization and processing, with an emphasis on cortical source estimation techniques and their integration with anatomical magnetic resonance imaging (MRI) data.
Abstract: Brainstorm is a collaborative open-source application dedicated to magnetoencephalography (MEG) and electroencephalography (EEG) data visualization and processing, with an emphasis on cortical source estimation techniques and their integration with anatomical magnetic resonance imaging (MRI) data. The primary objective of the software is to connect MEG/EEG neuroscience investigators with both the best-established and cutting-edge methods through a simple and intuitive graphical user interface (GUI).
2,637 citations