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Negative Binomial Regression, by Joseph M. Hilbe
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At last - a book devoted to the negative binomial model and its many variations. Every model currently offered in commercial statistical software packages is discussed in detail - how each is derived, how each resolves a distributional problem, and numerous examples of their application. Many have never before been thoroughly examined in a text on count response models: the canonical negative binomial; the NB-P model, where the negative binomial exponent is itself parameterized; and negative binomial mixed models. As the models address violations of the distributional assumptions of the basic Poisson model, identifying and handling overdispersion is a unifying theme. For practising researchers and statisticians who need to update their knowledge of Poisson and negative binomial models, the book provides a comprehensive overview of estimating methods and algorithms used to model counts, as well as specific guidelines on modeling strategy and how each model can be analyzed to access goodness-of-fit.
- Sales Rank: #2090153 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2007-07-29
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x .71" w x 5.98" l, 1.22 pounds
- Binding: Hardcover
- 251 pages
- Used Book in Good Condition
Review
"The test is well-written, easy-to-read but once started, is difficult to put down as each chapter unfolds the intracacies of the distribution."
C.M. O'Brien, International Statistical Review
"A good starting point for those who are not familiar with this topic... I would recommend this book to researchers and students who would like to gain an overview of the negative binomial distribution and its extensions."
Fiona McElduff, University College, London
About the Author
Joseph M. Hilbe is a Solar System Ambassador with NASA's Jet Propulsion Laboratory at the California Institute of Technology, an adjunct professor of statistics at Arizona State University, and an emeritus professor at the University of Hawaii. Professor Hilbe is an elected fellow of the American Statistical Association and an elected member of the International Statistical Institute (ISI), for which he is Chair of the ISI International Astrostatistics Network. He is the author of Logistic Regression Models (Chapman and Hall/CRC, 2009), a leading text on the subject, and co-author of R for Stata Users (Springer, 2010, with R. Muenchen), Generalized Estimating Equations (Chapman and Hall/CRC, 2002, with J. Hardin) and Generalized Linear Models and Extensions (Stata Press, 2001 and 2007, also with J. Hardin).
Most helpful customer reviews
13 of 13 people found the following review helpful.
A very thorough and clearly written reference on negative binomial regression.
By Hanjoo Kim
"Negative Binomial Regression" is an excellent reference for any statisticians, practitioners and students who are working and/or interested in the subject. I highly recommend this book. There are numerous features and strengths. Here I summarize some important ones as follow:
1. This book is very through in the topic of negative binomial regression which makes it an invaluable source for both researchers and practitioners.
2. As with other books written by Hilbe, e.g. Generalized Estimating Equations, this book is also very clearly written, easy-to-read and understand with minimal background in elementary maximum likelihood theory and calculus.
3. This book focuses on application of various NB models, but it contains enough mathematical details to show proper elements in the derivation of each model explained.
4. The book does an excellent job in describing almost all the practical encounters of when to use and what to use NB regression models.
5. Most of the programs used in this book are in either Stata, or user written program, called "ado" files that are readily downloadable from the website.
Hilbe discusses the derivation of the model from 2 perspectives - as a Poisson-gamma mixture model, and, with the heterogeneity parameter set as a constant, as a full member of the exponential family of distributions. As such the NB, actually the NB-2, model is a member of the family of generalized linear models, and is now found in most all GLM software implications.
The book discusses most every NB parameterization conceived, and provides details and examples of every commercial NB software application, including NB longitudinal and mixed models. It is clearly written, yet covers details mostly unavailable in other texts.
I think that an overview of content would be very helpful. Here I provide the book content in detail:
Introduction
1. Overview of count response models
1.1 Varieties of count response model
1.2 Estimation
1.3 Fit considerations
1.4 Brief history of the negative binomial
1.5 Summary
2. Method of estimation
2.1 Derivation of the IRLS algorithm
2.2 Newton Raphson algorithms
2.3 The exponential family
2.4 Residuals for count response models
2.5 Summary
3 Poisson regression
3.1 Derivations of the Poisson model
3.2 Parameterization as a rate model
3.3. Testing overdispersion
3.4 Summary
4 Overdispersion
4.1 What is overdispersion?
4.2 Handling apparent overdispersion
4.3 Method of handling real overdispersion
4.4 Summary
5 Negative binomial regression
5.1 Varieties of negative binomial
5.2 Derivation of the negative binomial
5.3 Negative binomial distributions
5.4 Algorithms
5.5 Summary
6 Negative binomial regression: modeling
6.1 Poisson versus negative binomial
6.2 Binomial versus count models
6.3 Examples: negative binomial regression
6.4 Summary
7 Alternative variance parameterizations
7.1 Geometric regression
7.2 NB-1: The linear constant model
7.3 NB-H: Heteroheneous negative binomial regression
7.4 The NB-P model
7.5 Generalized Poisson regression
7.6 Summary
8 Problems with zero counts
8.1 Zero-truncated negative binomial
8.2 Negative binomial with endogenous stratification
8.3 Hurdle models
8.4 Zero-inflated count models
8.5 Summary
9 Negative binomial with censoring, truncation, and sample selection
9.1 Censored and truncated models--econometric parameterization
9.2 Censored passion and NB-2 models--survival parameterization
9.3 Sample selection models
9.4 Summary
10 Negative binomial panel models
10.1 Unconditional fixed-effects negative binomial model
10.2 Conditional fixed-effects negative binomial model
10.3 Random-effects negative binomial
10.4 Generalized estimating equation
10.5 Multilevel negative binomial models
10.6 Summary
Appendix A: Negative binomial log-likelihood functions
Appendix B: Deviance functions
Appendix C: Stata negative binomial--ML algorithm
Appendix D: Negative binomial variance functions
Appendix E: Data sets
4 of 5 people found the following review helpful.
comprehensive but with confusing notation
By CA hiker
This book is a comprehensive description of when and how to apply negative binomial statistical models to count data. Through many examples using the Stata statistics system, the book addresses common practical issues such as censored data and excessive numbers of zero counts. Especially useful is chapter four's discussion of overdispersion in statistical models, which identifies negative binomial regression as one among several approaches to this problem.
This book is a good reference for readers already familiar with count models such as Poisson regression, but others will find the book challenging. For example, much of the discussion assumes familiarity with generalized linear modeling (GLM) concepts, such as link functions and exponential families. These concepts are used intensively throughout chapter two but not described until section 2.3, and then only tersely. The book would be much more accessible if section 2.3 summarized the GLM concepts and modeling notation used later in the book, and was placed at the beginning of the chapter. Moreover, the notation is unnecessarily confusing. In particular, there's no clear indication of which variables correspond to scalars, vectors of observations or model parameters, or matrices. The ranges of indices in sums are often unstated, e.g., whether they range over the data observations, the explanatory variables or the model parameters. Many equations have a confusing mix of traditional mathematical and programming language notation, including the summaries of the models in the appendices. Adding to readers' difficulties are numerous typos throughout the text (even in the corrected printing of 2008). This lack of proofreading is below the standards of other technical publications from Cambridge University Press. These notation issues and the typos are minor, but potentially confusing to non-expert readers who may not easily figure out what the author really meant.
1 of 1 people found the following review helpful.
The word "earlier" and "previously" are overly used in the text
By Academic Book Reviewer
This review is only focused on the inexact reference style of the text and various other issues mentioned below(2nd edition). These problems hinders me to understand more technical details that addressed in the book. Only after the authors fix these inexact references, I'll be able to understand the book better to have a more comprehensive review on the book.
I found the word "earlier" and "previously" (or "previous") overly used in the books. According to my count, there are over 10 "earlier"s and about 30 "previously"s (or "previous"es). For example,
1. As seen earlier, an individual or observation level format may be converted to grouped format by using code similar to the following: (page 120)
2. This topic, with graphs, was discussed earlier. (page 167)
3. As previously mentioned, GLIM was the first commercial software implementation of GLM. (page 20)
4. Additionally, as previously discussed, both Poisson and negative binomial models can themselves be extended to address the specific reasons why overdispersion arises in the data. (page 74)
5. As previously discussed, two foremost methods used to accommodate Poisson overdispersion are post-hoc scaling and application of a modified variance estimator. (page 110)
In addition, when a book is referred it is better to refer the section number as well.
1. However, as discussed in Cameron and Trivedi (1998) these models are not appropriate for count response models. (page 191)
Some implicit references like the following should also be spelled out so that reader can see where they were first discussed.
1. I have indicated that extended negative binomial models are generally developed to solve either a distributional or variance problem arising in the base NB-2 model. (page 160)
2. I shall use the well-known ships data set that was used in McCullagh and NeIder (1989). (page 200)
For reference to equation, it should specify equation number.
1. Note the similarity to that of the standard Poisson log-likelihood function defined in Chapter 3 as ... (page 200)
These inexact references can take readers who are not familiar with the text yet a lot of time to figure out where "earlier" or "previously" the author actually refers. Since the author read reviews on Amazon, I'd suggest the author post on the book website a table (could be in the errata) of explicit references (e.g., by giving page numbers, section numbers, or equation numbers) these inexact references refer to.
This would be a relative easy task for the author (I'd estimate 1-2 hour work, by searching the word "earlier", "previously", "previous" book referencs in the digital text and writing up the table) but could help an average reader a lot.
Also the terminology seems not very consistent in some places. I found "bootstrapped standard errors" (page 198), "bootstrapping of standard errors" (page 5) and "boostrap standard error" (section 4.3.4 title).
Some acronyms appear before the whole words are spelled out. For example, GEE on page 3.
Typo:
Eq (10.2) L(x beta_i; y_i) should be L(beta_i; y_i) (page 199), so does the equation right on the next page (page 200)
Also Eq(10.2), X_ik should be x_ik.
The index of the second sum sign in Eq (10.2) should be at the bottom.
The first entry in the reference (as shown below) is not unpublished. It is published as Sociological Methodology Volume 32, Issue 1, pages 247-265, 2002
Allison, P. D. and R. Waterman (2002). Fixed-effects negative binomial regression models, unpublished manuscript
Although there are already many typos been corrected in the errata, I think that a professional editor should be hired to work on the text a bit more.
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