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.
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
