Preface

Linear mixed-effects models (LMMs) are powerful modeling tools that allow for the analysis of datasets with complex, hierarchical structures. Intensive research during the past decade has led to a better understanding of their properties. The growing body of literature, including recent monographs, has considerably increased their popularity among applied researchers. There are several statistical software packages containing routines for LMMs. These include, for instance, SAS, SPSS, STATA, S+, and R. The major advantage of R is that it is a freely available, dynamically developing, open-source environment for statistical computing and graphics. The goal of our book is to provide a description of tools available for fitting LMMs in R. The description is accompanied by a presentation of the most important theoretical concepts of LMMs. Additionally, examples of applications from various research areas illustrate the main features of both theory and software. The presented material should allow readers to obtain a basic understanding of LMMs and to apply them in practice. In particular, we elected to present several theoretical concepts and their practical implementation in R in the context of simpler, more familiar classes of models such as e.g., the classical linear regression model. Based on these concepts, more advanced classes of models, such as models with heterogenous variance and correlated residual errors, along with related concepts are introduced. In this way, we incrementally set the stage for LMMs, so that the exposition of the theory and R tools for these models becomes simpler and clearer. This structure naturally corresponds to the object-oriented programming concept, according to which R functions/methods for simpler models are also applicable to the more complex ones. We assume that readers are familiar with intermediate linear algebra, calculus, and the basic theory of statistical inference and linear modeling. Thus, the intended audience for this book is graduate students of statistics and applied researchers in other fields. Our exposition of the theory of various classes of models presented in the book focuses on concepts, which are implemented in the functions available in R. Readers