Richly Parameterized Linear Models

"Richly Parameterized Linear Models is a strong addition to the literature on mixed models, offering a much more unified treatment and broader scope than many existing texts. The book also provides an excellent treatment of diagnostics for mixed models. The literature on mixed models has expanded in recent decades, often in disparate ways. Richly Parameterized Linear Models provides a step toward unifying this growing area of research and serves as an excellent resource for applied researchers with experience and interest in mixed models." Journal of the American Statistical Association, Vol. 110, 2015 "This is a thought-provoking book that stimulates discussion and further research. It is a refreshing idea to concentrate on poorly understood mysteries in the class of linear mixed models. If you have ever encountered similar issues in linear mixed models, you will appreciate this book. Furthermore, if you are looking for new scientific challenges, then you will find a large resource of still open questions and useful references. Graduate students will develop a deeper understanding of the linear mixed model and critical thinking in the application of this model class. We recommend this book, as it will stimulate further research, leading to deeper insight into richly parametrized linear models." Biometrical Journal, 2015 "Hodges book is a really recommendable reference for mixed models users. Use of random effects models has exponentially grown during the last few decades mainly due to the availability of software making the fit of these models possible. Such software has made mixed models available to a wide community of users, thus complex analyses with complex covariance structures have filled both applied and theoretical journals. Nevertheless, as masterfully described within this book, the hypotheses underneath these models, and the corresponding covariance structures, are not harmless at all but, on the contrary, they may have a large impact on their fit. Hodges monograph explores and highlights the repercussion of many aspects involved in the definition of most mixed models that are usually unknown or, even worse, ignored. Hodges makes us aware of these issues that should be kept very in mind by any mixed models user and illustrates them with lots of real case studies. This is an extremely clarifying tool for those who usually work with GLMMs in general. Mathematical details underlying GLMMs are usually overwhelming Hodges makes a journey to the grounds of linear mixed models, where mathematical detail is more accessible, providing a deep insight also of use in GLMMs. The approach described in this book yields some intuition about what can be happening underneath the complex GLMMs that are usually used in practice." Miguel Martinez Beneito, Foundation for the Promotion of Health and Biomedical Research in the Valencian Region "I recommend this text to any student/researcher who is interested in mixed models. The book is written in an enthralling and engaging style and is overflowing with interesting observations, has a unique spin, and is very thought provoking. Over the past 20 years there has been a tendency toward the fitting of more and more complex models, with the potential negative implications of this endeavor (which I will loosely term overfitting) being lost amid the enthusiasm for bigger and allegedly more realistic models. Those with such tendencies would definitely benefit from studying this book in order to gain insight into the unexpected consequences that some mixed model choices can have. All of the model types appearing in the title are covered in great detail, including coverage of diagnostics for mixed models, a sorely under-examined topic. Real data analyses are prominent in the discussions, with strange behavior of fitting being highlighted; for example, there is a section entitled, Mysterious, inconve

James S. Hodges

Mixed Linear Models: Syntax, Theory, and Methods: An Opinionated Survey of Methods for Mixed Linear Models. Two More Tools: Alternative Formulation, Measures of Complexity. Richly Parameterized Models as Mixed Linear Models: Penalized Splines as Mixed Linear Models. Additive Models and Models with Interactions. Spatial Models as Mixed Linear Models. Time-Series Models as Mixed Linear Models. Two Other Syntaxes for Richly Parameterized Models. From Linear Models to Richly Parameterized Models: Mean Structure: Adapting Diagnostics from Linear Models. Puzzles from Analyzing Real Datasets. A Random Effect Competing with a Fixed Effect. Differential Shrinkage. Competition between Random Effects. Random Effects Old and New. Beyond Linear Models: Variance Structure: Mysterious, Inconvenient, or Wrong Results from Real Datasets. Re-Expressing the Restricted Likelihood: Two-Variance Models. Exploring the Restricted Likelihood for Two-Variance Models. Extending the Re-Expressed Restricted Likelihood. Zero Variance Estimates. Multiple Maxima in the Restricted Likelihood and Posterior.