Methods of statistical model estimation

"Preface Methods of Statistical Model Estimation has been written to develop a particular pragmatic viewpoint of statistical modelling. Our goal has been to try to demonstrate the unity that underpins statistical parameter estimation for a wide range of models. We have sought to represent the techniques and tenets of statistical modelling using executable computer code. Our choice does not preclude the use of explanatory text, equations, or occasional pseudo-code. However, we have written computer code that is motivated by pedagogic considerations first and foremost. An example is in the development of a single function to compute deviance residuals in Chapter 4. We defer the details to Section 4.7, but mention here that deviance residuals are an important model diagnostic tool for GLMs. Each distribution in the exponential family has its own deviance residual, defined by the likelihood. Many statistical books will present tables of equations for computing each of these residuals. Rather than develop a unique function for each distribution, we prefer to present a single function that calls the likelihood appropriately itself. This single function replaces five or six, and in so doing, demonstrates the unity that underpins GLM. Of course, the code is less efficient and less stable than a direct representation of the equations would be, but our goal is clarity rather than speed or stability. This book also provides guidelines to enable statisticians and researchers from across disciplines to more easily program their own statistical models using R. R, more than any other statistical application, is driven by the contributions of researchers who have developed scripts, functions, and complete packages for the use of others in the general research community"-- Read more... Programming and R Introduction R Specifics Programming Making R Packages Further Reading Statistics and Likelihood-Based Estimation Introduction Statistical Models Maximum Likelihood Estimation Interval Estimates Simulation for Fun and Profit Ordinary Regression Introduction Least-Squares Regression Maximum-Likelihood Regression Infrastructure Conclusion Generalized Linear Models Introduction GLM: Families and Terms The Exponential Family The IRLS Fitting Algorithm Bernoulli or Binary Logistic Regression Grouped Binomial Models Constructing a GLM Function GLM Negative Binomial Model Offsets Dispersion, Over and Under Goodness-of-Fit and Residual Analysis Weights Conclusion Maximum Likelihood Estimation Introduction MLE for GLM Two-Parameter MLE Panel Data What Is a Panel Model? Fixed-Effects Model Random-Intercept Model Handling More Advanced Models The EM Algorithm Further Reading Model Estimation Using Simulation Simulation: Why and When? Synthetic Statistical Models Bayesian Parameter Estimation Discussion Bibliography Index Exercises appear at the end of each chapter. Methods of Statistical Model Estimation examines the most important and popular methods used to estimate parameters for statistical models and provide informative model summary statistics. Designed for R users, the book is also ideal for anyone wanting to better understand the algorithms used for statistical model fitting. The text presents algorithms for the estimation of a variety of regression procedures using maximum likelihood estimation, iteratively reweighted least squares regression, the EM algorithm, and MCMC sampling. Fully developed, working R code is constructed for each method. The book starts with OLS regression and generalized linear models, building to two-parameter maximum likelihood models for both pooled and panel models. It then covers a random effects model estimated using the EM algorithm and concludes with a Bayesian Poisson model using Metropolis-Hastings sampling. The book's coverage is innovative in several ways. First, the authors use executable computer code to present and connect the theoretical content. Therefore, code is written for clarity of exposition rather than stability or speed of execution. Second, the book focuses on the performance of statistical estimation and downplays algebraic niceties. In both senses, this book is written for people who wish to fit statistical models and understand them. See Professor Hilbe discuss the book. Front Cover 1 Contents 6 Preface 10 Chapter 1 - Programming and R 14 Chapter 2 - Statistics and Likelihood-Based Estimation 52 Chapter 3 - Ordinary Regression 74 Chapter 4 - Generalized Linear Models 110 Chapter 5 - Maximum Likelihood Estimation 158 Chapter 6 - Panel Data 190 Chapter 7 - Model Estimation Using Simulation 216 Back Cover 246