Discrete Statistical Models With Social Science Applications.

According to the preface, this is the first book of a series of two. The second book will deal with continuous statistical models. The main subjects of the present book are based on three developments: (1) the theory of exponential families, (2) the theory of log-linear models, and (3) the theory of logistic models in psychometrics. More specifically, some of the models dealt with are loglinear models for contingency tables, latent trait models, Markov chains, and the Bradley-Terry model for paired comparisons. Each chapter contains a large number of examples and exercises. Solutions to the exercises are, however, not given. Before presenting general conclusion about the book, each chapter will be reviewed separately. Overview The first chapter (Statistical Models; 8 pages) gives an introduction to the use of statistical models in the social sciences. Examples from a variety of social disciplines, including medicine, are given. The intention of chapter 2 (Preliminary Theory; 44 pages) is to refresh the reader’s knowledge of probability theory and statistics, which are applied in the rest of the book. The given survey of subjects serves this goal well, except for the treatment of statistical optimality theory. Optimality concepts are introduced; but they are hardly, if ever, used in the rest of the book. A more serious drawback of the