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Longitudinal Data Analysis

Autoregressive Linear Mixed Effects Models

  • Book
  • © 2018

Overview

Authors:
  1. Ikuko Funatogawa

    1. Department of Statistical Data Science, The Institute of Statistical Mathematics, Tachikawa, Japan

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  2. Takashi Funatogawa

    1. Clinical Science and Strategy Department, Chugai Pharmaceutical Co. Ltd., Chūō, Japan

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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

Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)

Part of the book sub series: JSS Research Series in Statistics (JSSRES)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
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  2. Longitudinal Data and Linear Mixed Effects Models

    • Ikuko Funatogawa, Takashi Funatogawa
    Pages 1-26

  3. Autoregressive Linear Mixed Effects Models

    • Ikuko Funatogawa, Takashi Funatogawa
    Pages 27-58

  4. Case Studies of Autoregressive Linear Mixed Effects Models: Missing Data and Time-Dependent Covariates

    • Ikuko Funatogawa, Takashi Funatogawa
    Pages 59-75

  5. Multivariate Autoregressive Linear Mixed Effects Models

    • Ikuko Funatogawa, Takashi Funatogawa
    Pages 77-98

  6. Nonlinear Mixed Effects Models, Growth Curves, and Autoregressive Linear Mixed Effects Models

    • Ikuko Funatogawa, Takashi Funatogawa
    Pages 99-117

  7. State Space Representations of Autoregressive Linear Mixed Effects Models

    • Ikuko Funatogawa, Takashi Funatogawa
    Pages 119-138

  8. Back Matter

    Pages 139-141
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Statistical Data Science, The Institute of Statistical Mathematics, Tachikawa, Japan

    Ikuko Funatogawa

  • Clinical Science and Strategy Department, Chugai Pharmaceutical Co. Ltd., Chūō, Japan

    Takashi Funatogawa

About the authors

Ikuko Funatogawa, The Institute of Statistical Mathematics


Takashi Funatogawa, Chugai Pharmaceutical Co. Ltd.


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