West B. et al. Linear Mixed Models.. A Practical Guide Using Statistical Software ISBN 15848848.pdf

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LINEAR MIXED MODELS
A Practical Guide Using Statistical Software
Brady T. West
Kathleen B. Welch
Andrzej T. Ga
/
ecki
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with contributions from Brenda W. Gillespie
© 2007 by Taylor & Francis Group, LLC
Chapman & Hall/CRC
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© 2007 by Taylor & Francis Group, LLC
Dedication
To Laura
To all of my teachers, especially my parents and grandparents
—B.T.W.
To Jim, Tracy, and Brian
To the memory of Fremont and June
—K.B.W.
To Viola, Pawe , Marta, and Artur
To my parents
—A.T.G.
© 2007 by Taylor & Francis Group, LLC
Preface
The development of software for fitting linear mixed models was propelled by advances
in statistical methodology and computing power in the late 20th century. These develop-
ments, while providing applied researchers with new tools, have produced a sometimes
confusing array of software choices. At the same time, parallel development of the meth-
odology in different fields has resulted in different names for these models, including
mixed models, multilevel models, and hierarchical linear models. This book provides a
reference on the use of procedures for fitting linear mixed models available in five popular
statistical software packages (SAS, SPSS, Stata, R/S-plus, and HLM). The intended audi-
ence includes applied statisticians and researchers who want a basic introduction to the
topic and an easy-to-navigate software reference.
Several existing texts provide excellent theoretical treatment of linear mixed models and
the analysis of variance components (e.g., McCulloch and Searle, 2001; Searle, Casella,
and McCulloch, 1992; Verbeke and Molenberghs, 2000); this book is not intended to be
one of them. Rather, we present the primary concepts and notation, and then focus on
the software implementation and model interpretation. This book is intended to be a
reference for practicing statisticians and applied researchers, and could be used in an
advanced undergraduate or introductory graduate course on linear models.
Given the ongoing development and rapid improvements in software for fitting linear
mixed models, the specific syntax and available options will likely change as newer
versions of the software are released. The most up-to-date versions of selected portions
of the syntax associated with the examples in this book, in addition to many of the data
sets used in the examples, are available at the following Web site:
http://www.umich.edu/~bwest/almmussp.html
© 2007 by Taylor & Francis Group, LLC
The Authors
Brady West
is a senior statistician and statistical software consultant at the Center for
Statistical Consultation and Research (CSCAR) at the University of Michigan–Ann Arbor.
He received a B.S. in statistics (2001) and an M.A. in applied statistics (2002) from the
University of Michigan–Ann Arbor. Mr. West has developed short courses on statistical
analysis using SPSS, R, and Stata, and regularly consults on the use of procedures in SAS,
SPSS, R, Stata, and HLM for the analysis of longitudinal and clustered data.
Kathy Welch
is a senior statistician and statistical software consultant at the Center for
Statistical Consultation and Research (CSCAR) at the University of Michigan–Ann Arbor.
She received a B.A. in sociology (1969), an M.P.H. in epidemiology and health education
(1975), and an M.S. in biostatistics (1984) from the University of Michigan (UM). She
regularly consults on the use of SAS, SPSS, Stata, and HLM for analysis of clustered and
longitudinal data, teaches a course on statistical software packages in the University of
Michigan Department of Biostatistics, and teaches short courses on SAS software. She has
also co-developed and co-taught short courses on the analysis of linear mixed models and
generalized linear models using SAS.
Andrzej Gałecki
is a research associate professor in the Division of Geriatric Medicine,
Department of Internal Medicine, and Institute of Gerontology at the University of Mich-
igan Medical School, and has a joint appointment in the Department of Biostatistics at the
University of Michigan School of Public Health. He received a M.Sc. in applied mathe-
matics (1977) from the Technical University of Warsaw, Poland, and an M.D. (1981) from
the Medical Academy of Warsaw. In 1985 he earned a Ph.D. in epidemiology from the
Institute of Mother and Child Care in Warsaw (Poland). Since 1990, Dr. Gałecki has
collaborated with researchers in gerontology and geriatrics. His research interests lie in
the development and application of statistical methods for analyzing correlated and over-
dispersed data. He developed the SAS macro NLMEM for nonlinear mixed-effects models,
specified as a solution of ordinary differential equations. In a 1994 paper, he proposed a
general class of covariance structures for two or more within-subject factors. Examples of
these structures have been implemented in SAS Proc Mixed.
Brenda Gillespie
is the associate director of the Center for Statistical Consultation and
Research (CSCAR) at the University of Michigan in Ann Arbor. She received an A.B. in
mathematics (1972) from Earlham College in Richmond, Indiana, an M.S. in statistics (1975)
from The Ohio State University, and earned a Ph.D. in statistics (1989) from Temple
University in Philadelphia, Pennsylvania. Dr. Gillespie has collaborated extensively with
researchers in health-related fields, and has worked with mixed models as the primary
statistician on the Collaborative Initial Glaucoma Treatment Study (CIGTS), the Dialysis
Outcomes Practice Pattern Study (DOPPS), the Scientific Registry of Transplant Recipients
(SRTR), the University of Michigan Dioxin Study, and at the Complementary and Alter-
native Medicine Research Center at the University of Michigan.
© 2007 by Taylor & Francis Group, LLC

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