Steven Stillman

English

Research Papers in Economics

The Stata Journal (2003)
3, Number 2, pp. 208 210
Review of Generalized Estimating Equations by
Hardin and Hilbe
Steven Stillman
Labour Market Policy Group, New Zealand Department of Labour
steven.stillman@lmpg.dol.govt.nz
Abstract. The new book by Hardin and Hilbe (2003) is reviewed.
Keywords: gn0008, generalized estimating equations, generalized linear models
1 Introduction
Hardin and Hilbe (2003) have written a very detailed book on the statistical methodol-
ogy of generalized estimating equations (GEE). This work is very much a continuation of
their previous book (Hardin and Hilbe 2001), which focused on generalized linear mod-
els (GLM): for a review in this journal, see Newson (2001). GEE is an extension to GLM
that does not require independent observations and thus can be used to analyze clus-
tered and longitudinal data. At the simplest level, a variance covariance matrix, which
describes the correlation between observations, is speci ed, and multivariate weighted
least squares is used to estimate a GEE model.
The book primarily focuses on explaining this process in detail. It assumes that the
reader has a fundamental understanding of GLM, maximum likelihood estimation, and
distributional statistics. As Hardin and Hilbe are the original authors of the glm and
xtgee commands in Stata, which are used to estimate GLM and GEE models, respectively
(Hilbe 1993), Stata is often used in the book to present various illustrative examples.
The authors also provide detailed information on estimating these models in SAS,S - P l u s ,
and SUDAAN.
2 Detailed comments
The book contains four main chapters, with a  fth chapter that describes various exam-
ple datasets and useful programs for estimating GEE models. The  rst chapter provides
an introduction to the subject matter. It is both detailed and technical, and it im-
mediately becomes clear to the reader how much technical understanding of GLM and
distributional statistics is expected by the authors. Unfortunately, this limits the reach
of the book, as many social scientists, even those with strong empirical training, have
limited experience with GLM methodology. This chapter also reviews diﬀerent software
packages that can estimate GLM and GEE models. Considering the authors  experience
writing the main Stata programs for these models, the reviews are very neutral and
even-handed.
c ￿ 2003 Stata Corporation gn0008S. Stillman 209
The second chapter provides a comprehensive description of GLM estimation, but
again at a level that requires strong prior knowledge of the methodology. The chapter
begins by reviewing general maximum-likelihood estimation methods. Given the high
level of statistical knowledge assumed by the authors in most of the book, this review
seems unnecessary. While the description of GLM is comprehensive, little depth is
provided, especially on how a researcher chooses between diﬀerent models. For example,
the authors describe the choice between random- and  xed-eﬀects models as depending
mainly on whether covariates are constant within panels. No mention is made of the
fundamental diﬀerence between these models: random-eﬀects models are inconsistent
when covariates are correlated with the unobserved individual error term.
The third chapter describes GEE estimation in detail and is the core chapter of the
book. As discussed above, the  rst step in estimating a GEE model is specifying a
variance-covariance matrix that describes the correlation between observations. The
beginning of the chapter is organized around the diﬀerent correlation matrices that
can be speci ed. For each type of structure, the authors demonstrate how the GEE
model is estimated using both an example estimated by hand and one estimated using
the xtgee command in Stata. The authors do a good job describing each type of
correlation structure and the actual process of estimating each model. The chapter then
continues by running through new developments that have extended GEE estimation to
multinomial, robust, instrumental variable, and missing data models. In the last section
of the chapter, the authors discuss how to choose an appropriate model.
As with the GLM chapter, I found the discussion on choosing an appropriate model
to be lacking. The authors write that the choice depends on the scienti c question of
interest and on the characteristics of the data. While I would agree that these are im-
portant factors in model selection, in my mind, it is how the fundamental assumptions
of a particular model interact with these factors that determines model choice. Impor-
tantly, the authors do not discuss these fundamental assumptions. They do not explain
whether the random eﬀects assumptions (i.e., that covariates are uncorrelated with the
individual error term) are necessary for consistent estimates. In addition, no mention
is made of whether choosing the wrong error structure leads to inconsistent estimates,
biased standard errors, or just ineﬃcient estimates.
The fourth chapter further discusses model choice, focusing on residual analysis and
model goodness of  t. The techniques examined in this section are mainly general
ones that apply to regression methods other than GEE. These include using information
criteria and graphical analysis of residuals to determine best model  t and using deletion
methods and in uence measures to identify data outliers. Given the generality of this
chapter, I did not  nd that it added much to the book.
3 Summary
This book is a comprehensive summary of the methodology of generalized estimating
equations. The authors state that the intended audience for this book includes active
researchers as well as theoretical statisticians. I am not sure how much it will appeal210 Review of Hardin and Hilbe
to either group. My main statistical training has been in econometrics, and hence my
knowledge about GEE was fairly limited before reading this book. Now I have a much
better understanding of how GEE models are estimated in practice. However, I have
not gained any insight into why, as a researcher, I should want to use this technique.
Not enough information is given in the book on the assumptions that are required to
estimate GEE models, the advantages that they have over maximum likelihood models,
and what limitations are inherent in using this method. I am guessing that theoretical
statisticians, on the other hand, will be frustrated by the lack of rigor in the book.
While all of the important formulas are presented, the book does not delve into the
theoretical underpinnings of GEE. No proofs are given, and simple examples only are
used to demonstrate the mechanics of particular formulas. Having said this, I think
that this book would make excellent supplemental reading material in a graduate-level
quantitative methods course, as it provides a more comprehensive description of GEE
than is, to my knowledge, available from any other source.
4 References
Hardin, J. W. and J. M. Hilbe. 2001. Generalized Linear Models and Extensions. College
Station, TX: Stata Press.
 . 2003. Generalized Estimating Equations. Boca Raton, FL: Chapman & Hall/CRC.
Hilbe, J. 1993. sg16: Generalized linear models. Stata Technical Bulletin 11: 20 28. In
Stata Technical Bulletin Reprints, vol. 2, 149 159. College Station, TX: Stata Press.
Newson, R. 2001. Review of Generalized Linear Models and Extensions. Stata Journal
1(1): 98 100.
About the Author
Steven Stillman is a Senior Research Economist in the Labour Market Policy Group of the
New Zealand Department of Labour. He is also an aﬃliated Research Fellow at the Institute
for the Study of Labor (IZA), the William Davidson Institute, and the Motu Economic and
Public Policy Research Trust. His current research examines the eﬀect of public policy and
institutions on various dynamic aspects of household well-being in New Zealand, Russia, and
the United States.

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