Richly parameterized linear models. Additive, time series, and spatial models using random effects (Q2871248)

Richly parameterized linear models are linear models with hundreds or thousands of parameters, and with constraints on the parameters placed in order to make the problems tractable. Despite a formal definition of `Richly parameterized models' is not available, the book illustrates a wide range of possible models with thousands of parameters. Examples of such models come from linear models, random effects models, state-space time series models, and many other classes of models.NEWLINENEWLINE The book is divided into four parts. In Part I the author gives the basis syntax rules needed to write and analyze richly parameterized models under a unified framework, and recalls the basic theory of mixed linear models. Part II introduces several classes of richly parameterized models. For each model, the author shows how to express it as a mixed linear model and how to use that expression to make some observations.NEWLINENEWLINE In Parts III and IV several examples on real data are presented and discussed. This part of the book is somewhat exotic, but provides several insights and pointers to open problems, making this portion of the book very interesting both for researchers in statistical methodology and for practitioners. Using the author's words (Preface, page xxxiii\,ff): Parts III and IV are organized around mysterious, inconvenient, or plainly wrong results that turned up in real problems... Some of these puzzles are now understood to a greater or lesser extent, while others are barely understood at all. In this sense, Parts III and IV are not quite a catalog of unsolved problems and their theory is grossly incomplete. I apologize for that once, now. I hope Parts III and IV stimulate enough research so that a second edition of this book, if there will be one, can report fewer mysteries and, yes, more triumphs.