Mixed-Effects Models in Sand S-PLUS

Abstract

Mixed-effects models provide a flexible and powerful tool for the analysis of grouped data, which arise in many areas as diverse as agriculture, biology, economics, manufacturing, and geophysics. Examples of grouped data include longitudinal data, repeated measures, blocked designs, and multilevel data. The increasing popularity of mixed-effects models is explained by the flexibility they offer in modeling the within-group correlation often present in grouped data, by the handling of balanced and unbalanced data in a unified framework, and by the availability of reliable and efficient software for fitting them.This book provides an overview of the theory and application of linear and nonlinear mixed-effects models in the analysis of grouped data. A unified model-building strategy for both linear and nonlinear models is presented and applied to the analysis of over 20 real datasets from a wide variety of areas, including pharmacokinetics, agriculture, and manufacturing. A strong emphasis is placed on the use of graphical displays at the various phases of the model-building process, starting with exploratory plots of the data and concluding with diagnostic plots to assess the adequacy of a fitted model. Over 170 figures are included in the book.The class of mixed-effects models considered in this book assumes that both the random effects and the errors follow Gaussian distributions. These models are intended for grouped data in which the response variable is (at least approximately) continuous. This covers a large number of practical applications of mixed-effects models, but does not include, for example, generalized linear mixed-effects models (Diggle, Liang and Zeger, 1994).viii Preface Preface ix nesses of mixed-effects models, we emphasize the applied aspects of these. Readers who desire to learn in more detail the theory of mixed-effects are referred to the excellent book by Davidian and Giltinan (1995). Some knowledge of the S language is definitely desireable, but not a pre-requisite for following the material in the book. For those who are new to, or less familiar with S, we suggest using in conjunction with this book the, by now, classic reference Venables and Ripley (1999), which provides an overview of S and an introduction to a wide variety of statistical models to be used with S.

A dominance shift in arid savanna: An herbaceous legume outcompetes local C4 grasses

“…Possible correlation between NInt A and annual rainfall was rejected using Spearman’s correlation coefficient ( r  = 0.31, p  = 0.54; Figure S2). We further quantified the effect of Crotalaria density on the productivity of Stipagrostis tussocks in relation to rainfall (average tussock area/seasonal rainfall) using a linear mixed‐effects model with plot as a random factor to ensure independence of errors with respect to temporal autocorrelations (Pinheiro & Bates, 2000). Rainfall lower than 40 mm was excluded in this model, as here the area covered by grass tussocks was reduced to their basal area and due to a high frequency of outliers.…”

Rapid eye movements during sleep in mice: High trait-like stability qualifies rapid eye movement density for characterization of phenotypic variation in sleep patterns of rodents

“…Comparison between sleep stages, days and time periods were undertaken with linear mixed models [77] that treated animals as the random factor. In addition, we quantified trait-like stability of REM density and sleep stage duration with the intraclass correlation coefficient (ICC).…”

Mathematical modeling and statistical analysis of calcium-regulated insulin granule exocytosis in β-cells from mice and humans

“…Here we have carefully reanalyzed previously published data (Eliasson et al, 2003) with attention to the positive effect of forskolin on exocytosis by using a statistical mixed-effects model (Pinheiro and Bates, 2000). We find that the data show a linear relation between depolarization-evoked membrane capacitance increase (∆C m ) and the Ca 2+ -charge entering during a depolarization (Q), and argue that this indicates that pool depletion is negligible in response to short depolarizations in mouse β-cells.…”