Longitudinal Data Analysis
Autoregressive Linear Mixed Effects Models
Authors: Funatogawa, Ikuko, Funatogawa, Takashi
Free Preview- Describes a new analytical approach for longitudinal data, autoregressive linear mixed effects models, in which dynamic models are induced by the auto-regression term
- Provides state space representation of autoregressive linear mixed models with the modified Kalman filter for the calculation of log likelihoods
- Is written in plain English dealing not only with topics for those in medical fields but that is also understandable for researchers in other disciplines
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- About this book
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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.
- About the authors
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Ikuko Funatogawa, The Institute of Statistical Mathematics
Takashi Funatogawa, Chugai Pharmaceutical Co. Ltd.
- Table of contents (6 chapters)
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Longitudinal Data and Linear Mixed Effects Models
Pages 1-26
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Autoregressive Linear Mixed Effects Models
Pages 27-58
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Case Studies of Autoregressive Linear Mixed Effects Models: Missing Data and Time-Dependent Covariates
Pages 59-75
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Multivariate Autoregressive Linear Mixed Effects Models
Pages 77-98
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Nonlinear Mixed Effects Models, Growth Curves, and Autoregressive Linear Mixed Effects Models
Pages 99-117
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Table of contents (6 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Longitudinal Data Analysis
- Book Subtitle
- Autoregressive Linear Mixed Effects Models
- Authors
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- Ikuko Funatogawa
- Takashi Funatogawa
- Series Title
- JSS Research Series in Statistics
- Copyright
- 2018
- Publisher
- Springer Singapore
- Copyright Holder
- The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.
- eBook ISBN
- 978-981-10-0077-5
- DOI
- 10.1007/978-981-10-0077-5
- Softcover ISBN
- 978-981-10-0076-8
- Series ISSN
- 2364-0057
- Edition Number
- 1
- Number of Pages
- X, 141
- Number of Illustrations
- 27 b/w illustrations
- Topics
