© 2018

Longitudinal Data Analysis

Autoregressive Linear Mixed Effects Models


Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Also part of the JSS Research Series in Statistics book sub series (JSSRES)

Table of contents

  1. Front Matter
    Pages i-x
  2. Ikuko Funatogawa, Takashi Funatogawa
    Pages 1-26
  3. Ikuko Funatogawa, Takashi Funatogawa
    Pages 27-58
  4. Ikuko Funatogawa, Takashi Funatogawa
    Pages 77-98
  5. Ikuko Funatogawa, Takashi Funatogawa
    Pages 119-138
  6. Back Matter
    Pages 139-141

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.


Longitudinal Mixed Effects Autoregressive Dynamic State Space

Authors and affiliations

  1. 1.Department of Statistical Data ScienceThe Institute of Statistical MathematicsTachikawaJapan
  2. 2.Clinical Science and Strategy DepartmentChugai Pharmaceutical Co. Ltd.ChūōJapan

About the authors

Ikuko Funatogawa, The Institute of Statistical Mathematics

Takashi Funatogawa, Chugai Pharmaceutical Co. Ltd.

Bibliographic information

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