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Longitudinal Data Analysis: Autoregressive Linear Mixed Effects Models
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Название: Longitudinal Data Analysis: Autoregressive Linear Mixed Effects Models
Автор: Ikuko Funatogawa, Takashi Funatogawa
Издательство: Springer
Год: 2019 (2018 edition)
Страниц: 150
Язык: английский
Формат: pdf (true), epub
Размер: 15.6 MB

This book provides a new analytical approach for dynamic data repeatedly measured from multiple subjects over time. Random effects account for differences across subjects. Auto-regression in response itself is often used in time series analysis. In longitudinal data analysis, a static mixed effects model is changed into a dynamic one by the introduction of the auto-regression term. Response levels in this model gradually move toward an asymptote or equilibrium which depends on covariates and random effects. The book provides relationships of the autoregressive linear mixed effects models with linear mixed effects models, marginal models, transition models, nonlinear mixed effects models, growth curves, differential equations, and state space representation. State space representation with a modified Kalman filter provides log likelihoods for maximum likelihood estimation, and this representation is suitable for unequally spaced longitudinal data. The extension to multivariate longitudinal data analysis is also provided. Topics in medical fields, such as response-dependent dose modifications, response-dependent dropouts, and randomized controlled trials are discussed. The text is written in plain terms understandable for researchers in other disciplines such as econometrics, sociology, and ecology for the progress of interdisciplinary research.

Chapter 1 introduces longitudinal data, linear mixed effects models, and marginal models before the main theme. Prior knowledge of regression analysis and matrix calculation is desirable. Chapter 2 introduces autoregressive linear mixed effects models, the main theme of this book. Chapter 3 presents two case studies of actual data analysis about the topics of response-dependent dropouts and response-dependent dose modifications. Chapter 4 describes the bivariate extension, along with an example of actual data analysis. Chapter 5 explains the relationships with nonlinear mixed effects models, growth curves, and differential equations. Chapter 6 describes state space representation as an advanced topic for interested readers.

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