Modeling and Analysis of Longitudinal Data

1st Edition, Volume 50 - February 1, 2024
Editors: Arni S.R. Srinivasa Rao, Donald E.K. Martin, C.R. Rao
Language: English
Hardback ISBN:
9 7 8 - 0 - 4 4 3 - 1 3 6 5 1 - 1
eBook ISBN:
9 7 8 - 0 - 4 4 3 - 1 3 6 5 2 - 8

Longitudinal Data Analysis, Volume 50 in the Handbook of Statistics series covers how data consists of a series of repeated observations of the same subjects over an extended time… Read more

Modeling and Analysis of Longitudinal Data

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Longitudinal Data Analysis, Volume 50 in the Handbook of Statistics series covers how data consists of a series of repeated observations of the same subjects over an extended time frame and is thus useful for measuring change. Such studies and the data arise in a variety of fields, such as health sciences, genomic studies, experimental physics, sociology, sports and student enrollment in universities. For example, in health studies, intra-subject correlation of responses must be accounted for, covariates vary with time, and bias can arise if patients drop out of the study.

Cover image
Title page
Table of Contents
Series Page
Copyright
Contributors
Preface
Part I: Foundations
Chapter 1 Multivariate and shared parameter mixed-effects models for intensive longitudinal data
Abstract
1 Introduction
2 Multivariate mixed-effects models
3 Example
4 Discussion
Appendix A SAS PROC NLMIXED code
Appendix B STAN code
References
Chapter 2 Hierarchical and incomplete data
Abstract
1 Introduction
2 Case study: Age-related macular degeneration trial
3 Modeling tools for longitudinal data
4 Marginalization and marginal interpretation of hierarchical models
5 Incomplete data
6 Analysis of the ARMD trial
7 Extensions
8 Flexibly accommodating correlation and overdispersion
9 Concluding remarks
References
Chapter 3 Modeling longitudinal trends in event-related potentials
Abstract
1 Introduction
2 An implicit learning paradigm
3 What is an ERP?
4 Preprocessing ERPs
5 Enhancing signal-to-noise ratio for longitudinal modeling
6 Modeling longitudinal trends
References
Part II: Further methods and models
Chapter 4 Longitudinal data analysis by hierarchical state space models
Abstract
1 Introduction
2 Linear Gaussian SSMs
3 Hierarchical state space models
4 Estimation, inference and prediction
5 Applications
6 Extensions to bivariate HSSMs
7 Extensions to nonlinear non-Gaussian HSSMs
8 Bibliographical notes
References
Chapter 5 Latent state-trait analysis
Abstract
1 Introduction
2 Background
3 Latent variables in LST theory
4 Consistency, occasion specificity, and reliability
5 The multitrait-multistate (MTMS) model
6 Illustrative application of the MTMS model
7 The Singletrait-Multistate Model with m – 1 Indicator-Specific Factors
8 Illustrative application of the STMS-IS model
9 Discussion
Appendix A1: Mplus software code for fitting the MTMS model to the MRT data
Appendix A2: Lavaan software code for fitting the MTMS model to the MRT data
Appendix B1: Mplus syntax for fitting the STMS-IS model to the MRT data example
Appendix B2: Lavaan syntax for fitting the STMS-IS model to the MRT data example
References
Chapter 6 Recent advances in longitudinal data analysis
Abstract
1 Introduction
2 Covariance selection
3 Variable selection
4 Machine learning approaches
5 Discussion
References
Part III: Applications
Chapter 7 Government as population: Demographic perspectives on the United States legislative, judicial and executive branches, 1789–2020
Abstract
1 Introduction
2 Data and sources
3 Population perspectives
4 Applications and projections
5 The political destiny of government demography
6 Conclusions
Acknowledgments
References
Chapter 8 Beginnings: Formation and growth of natural phenomena out of Fisher information
Abstract
1 Nature, as evolving, communicating systems: Essential role of background Fisher information
2 What has past use of the MFI principle shown?
3 Information aspects of system coordinates and parameters
4 Nature of the output: Schrodinger's dilemma
5 Concept of system “complexity”
6 Principle of maximum Fisher information (MFI)
7 Definition of Fisher information (FI) I
8 Summary to this point
9 MFI view of the fundamental physical constants per se as statistical entities
10 Discussion
11 Information channels: Basics of MFI principle
12 Application: Early growth laws p(t) for viruses, cancer and the cosmos
13 Regarding the fundamental need for well-defined Planck constants
14 On early growth of cancer, or virus, as quantum-based
15 Growth laws of viruses: Of cancer
16 Experimental verification
17 A sketch of past work on cosmic origins relating to the preceding theory of fluctuations
18 Possible mechanisms for a perpetual input information level J
19 Comparison for early growth of viruses, cancer, the cosmos
Appendix A Appendix: The MFI (or EPI) principle is satisfied by power-law solutions for q(t), p(t)
Appendix B Appendix: The required exponent in power-law solution p(t) is generally the Fibonacci constant '
References
Further reading
Index

Arni S.R. Srinivasa Rao

Arni S.R. Srinivasa Rao works in pure mathematics, applied mathematics, probability, and artificial intelligence and applications in medicine. He is a Professor at the Medical College of Georgia, Augusta University, U.S.A, and the Director of the Laboratory for Theory and Mathematical Modeling housed within the Division of Infectious Diseases, Medical College of Georgia, Augusta, U.S.A. Previously, Dr. Rao conducted research and/or taught at Mathematical Institute, University of Oxford (2003, 2005-07), Indian Statistical Institute (1998-2002, 2006-2012), Indian Institute of Science (2002-04), University of Guelph (2004-06). Until 2012, Dr. Rao held a permanent faculty position at the Indian Statistical Institute. He has won the Heiwa-Nakajima Award (Japan) and Fast Track Young Scientists Fellowship in Mathematical Sciences (DST, New Delhi). Dr. Rao also proved a major theorem in stationary population models, such as, Rao's Partition Theorem in Populations, Rao-Carey Theorem in stationary populations, and developed mathematical modeling-based policies for the spread of diseases like HIV, H5N1, COVID-19, etc. He developed a new set of network models for understanding avian pathogen biology on grid graphs (these were called chicken walk models), AI Models for COVID-19 and received wide coverage in the science media. Recently, he developed concepts such as “Exact Deep Learning Machines”, and “Multilevel Contours” within a bundle of Complex Number Planes.

Affiliations and expertise

Professor, Medical College of Georgia, USA

Donald E.K. Martin

Donald E.K. Martin was born and raised in Baltimore, Maryland. He attended the University of Maryland, College Park both as an undergraduate (B.S. in Mathematics) and as a graduate student (M.A. and Ph.D. in Mathematical Statistics). He worked as a Mathematical Statistician for the U.S. Department of Energy from 1991 to 1994, and was a NASA-ASEE Summer Faculty Fellow at the Goddard Space Flight Center, Greenbelt, Maryland, during the summers of 1997-1999. From 1994 to 2007 he was a faculty member of the Mathematics Department of Howard University in the nation’s capital, and was also a Mathematical Statistician in the Time Series Research Group, Statistical Research Division, U.S. Bureau of the Census, from 2000 to 2007. He has been an Associate Professor in the Department of Statistics of North Carolina State University since 2007.

Dr. Martin has received three National Science Foundation research grants. A major focus of his research is the computation of distributions of patterns in Markovian sequences through an auxiliary Markov chain (AMC). For complicated patterns, the number of states can be extremely large. To mitigate this problem and facilitate the application of AMC-based methods to complicated patterns, he developed an algorithm that allows setting up an AMC with a minimal state space through rules to determine equivalent states during the state space’s setup, so that no extraneous states are entered at any point. He has also developed algorithms to compute the distribution of statistics in sparse Markov models and states of hidden sparse Markov models, joining efficiency from the model and minimal state spaces.

Dr. Martin was one of four African Americans in the U.S. to receive a Ph.D. in Mathematics in 1990. He was honored by the Network of Minorities in Mathematical Sciences in February, 2020 https://mathematicallygiftedandblack.com/circle-of-excellence/. He received the NC State College of Sciences Faculty Diversity Professional Development Award in 2018, has received many Thank-a-Teacher awards, and received the NC State the Dennis Boos Citizenship Award for 2021-22 from the Statistics Department. In 2023, he was a research leader in the African Diaspora Joint Mathematics Workshop (ADJOINT, https://www.msri.org/web/msri/scientific/adjoint).

Affiliations and expertise

Associate Professor, Department of Statistics, North Carolina State University, Raleigh, NC, United States

C.R. Rao

book “Ancient Inhabitants of Jebel Moya” published by the Cambridge Press under the joint authorship of Rao and two anthropologists. On the basis of work done at CU during the two year period, 1946-1948, Rao earned a Ph.D. degree and a few years later Sc.D. degree of CU and the rare honor of life fellowship of Kings College, Cambridge.

He retired from ISI in 1980 at the mandatory age of 60 after working for 40 years during which period he developed ISI as an international center for statistical education and research. He also took an active part in establishing state statistical bureaus to collect local statistics and transmitting them to Central Statistical Organization in New Delhi. Rao played a pivitol role in launching undergraduate and postgraduate courses at ISI. He is the author of 475 research publications and several breakthrough papers contributing to statistical theory and methodology for applications to problems in all areas of human endeavor. There are a number of classical statistical terms named after him, the most popular of which are Cramer-Rao inequality, Rao-Blackwellization, Rao’s Orthogonal arrays used in quality control, Rao’s score test, Rao’s Quadratic Entropy used in ecological work, Rao’s metric and distance which are incorporated in most statistical books.

He is the author of 10 books, of which two important books are, Linear Statistical Inference which is translated into German, Russian, Czec, Polish and Japanese languages,and Statistics and Truth which is translated into, French, German, Japanese, Mainland Chinese, Taiwan Chinese, Turkish and Korean languages.

He directed the research work of 50 students for the Ph.D. degrees who in turn produced 500 Ph.D.’s. Rao received 38 hon. Doctorate degree from universities in 19 countries spanning 6 continents. He received the highest awards in statistics in USA,UK and India: National Medal of Science awarded by the president of USA, Indian National Medal of Science awarded by the Prime Minister of India and the Guy Medal in Gold awarded by the Royal Statistical Society, UK. Rao was a recipient of the first batch of Bhatnagar awards in 1959 for mathematical sciences and and numerous medals in India and abroad from Science Academies. He is a Fellow of Royal Society (FRS),UK, and member of National Academy of Sciences, USA, Lithuania and Europe. In his honor a research Institute named as CRRAO ADVANCED INSTITUTE OF MATHEMATICS, STATISTICS AND COMPUTER SCIENCE was established in the campus of Hyderabad University.

Affiliations and expertise

University of Hyderabad Campus, India