Stephen P. Jenkins

English

Research Papers in Economics

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a registered trademark of StataCorp LP.The Stata Journal (2003)
3, Number 4, pp. 440 444
Review of Maximum Likelihood Estimation with
Stata by Gould, Pitblado, and Sribney
Stephen P. Jenkins
Institute for Social and Economic Research
University of Essex, UK
stephenj@essex.ac.uk
Abstract. The new book by Gould, Pitblado, and Sribney (2003) is reviewed.
Keywords: gn0009, maximum likelihood, Stata programming
1 Introduction
This is the second edition of a book originally published in 1999, when Stata 6 was
current. There are signi cant additions, not only of Jeﬀ Pitblado to the list of authors
and the use of a larger font size (which de nitely assists readability). Several changes
re ect the updating of Stata itself: this edition was timed to coincide with the release
of Stata 8.1, which incorporated several notable extensions to the maximum likelihood
command ml. For example, you can now  t models to complex survey data (there
are svy options), and there are three new optimization algorithms (Berndt Hall Hall 
Hausman, Davidon Fletcher Powell, and Broyden Fletcher Goldfarb Shanno) in ad-
dition to the modi ed Newton Raphson algorithm, and you can switch between them.
Variance estimates can be calculated using the outer product of gradients (not just via
the inverse Hessian). These additions are all discussed in the new edition; so, too, is the
 tting of models with linear constraints using the constraint command. But arguably
you do not need a book to take advantage of these features: there is always the online
help, for example. So, what does the book actually provide?
2 What is in the book?
Like the  rst edition, it is essentially an instruction manual for researchers who need
maximum likelihood estimators for models that are not already prepackaged in Stata.
Not so many years ago, if the ML estimation command that you wanted was not in Stata,
you would most likely seek the command in another package or think about writing a
special program in Gauss, C, or Fortran, or simply give up. Stata s ml command provides
another route. Use of the command does not require special programming skills, and it
oﬀers access to many features that we have come to expect of built-in Stata commands.
With such power comes complexity, however, and I doubt whether many researchers
could use the ml command eﬀectively relying entirely on the online help and Reference
manual entries. You have to draw on a book like this. As a nonprogrammer, I found
the  rst edition invaluable in helping me to write a number of diﬀerent ML estimation
c ￿ 2003 StataCorp LP gn0009S. P. Jenkins 441
commands. That said, I also had to consult StataCorp Technical Support on each
occasion to complete my programs. The book made things substantially easier but not
easy; that is the nature of the subject. The same can be said for this edition.
The book opens, as in the  rst edition, with a nice overview of ML estimation
theory and numerical optimization methods, now extended to discuss the alternative
optimization algorithms. The authors communicate the key issues with a clarity and
succinctness that a number of textbook authors could aspire to. Chapter 2 is an overview
of what the ml command does (without getting bogged down in the detail of syntax
diagrams) and is a notable improvement on its earlier counterpart. Chapters 3 8 go
through in detail how to use Stata to maximize your own likelihood function. Chapters 9
and 10 are about how to package your code into a do- le and write your own command
using ado- les. Chapter 11 (new) details how to add survey estimation features to your
estimator.
Six examples are worked through in  ne detail in chapter 12. Although there are
examples scattered throughout the book (and the previous edition), this is a welcome
addition. As in many learning contexts, it is by consideration of a number of illustrations
in detail that you begin to understand why you have to do certain things in a particular
way. You are then better placed to apply and adapt them to diﬀerent applications. The
particular examples are the logit and probit models, Weibull and Cox continuous time
hazard regression models, random eﬀects linear regression for panel data, and seemingly
unrelated regression. The seemingly unrelated regression example is new compared
with the  rst edition and is important because it shows how the use of a concentrated
likelihood function can ensure convergence in diﬃcult maximization problems. In fact,
this is the  rst mention of this strategy, and it would have helped if there were greater
elaboration of it and its wider applicability (perhaps in chapter 1).
The book is completed by three appendices, references, and indices. The appendices
are valuable reference points; they provide syntax diagrams, checklists for the diﬀerent
maximization methods (lf, d0, d1, d2), and complete listings of the code used to
estimate the models considered in chapter 12. The subject index is rather thin and
could do with more entries. For example, there is no entry for  weights .
The most valuable addition to this edition, from my personal perspective, is sec-
tion 4.5 about panel-data likelihoods. Many of ml s great features are available by
default only if the likelihood function takes the canonical  linear form . In essence, this
means that the overall sample likelihood is the sum of the likelihood contributions from
each subject (person or  rm, etc.), and there is one row in the dataset for each subject.
One can then use maximization method lf; features such as robust variance calculations
are very easy to incorporate, and speed and accuracy are hardly compromised. With
panel data likelihoods, there are repeated observations (multiple rows in the dataset)
for each subject and the linear form property does not hold. (These likelihoods include
not only those for standard time-series cross-sectional data, but also those for discrete
time hazard regression models.) One can use maximization method d0 (with numerical
derivatives and Hessian matrix calculations) relatively straightforwardly, but estimators
may be slow to converge, and one cannot have robust variance estimates, survey op-442 Review of Gould, Pitblado, and Sribney
tions, or outer product of gradients variances. To get these features, and to speed up
convergence, requires calculation of analytical  rst derivatives, implying use of method
d1 (or d2, which requires coding of the negative Hessian matrix calculation as well).
Coding these derivative calculations is a formidable exercise in my experience. For
example, I recall spending several weeks in the summer of 2000 trying to write my
command spsurv to use method d1 rather than d0. Despite having the  rst edition of
this book as my constant companion (and also getting helpful assistance from StataCorp
Technical Support), I  nally gave up. It seemed as though my model was not of the
type that could be estimated in the way that was suggested. Things are diﬀerent now.
Section 4.5 of the current edition provides a much clearer and extended discussion of how
to maximize panel-data likelihoods, and I now understand how the mlvecsum function
may provide a route to writing a d1 evaluator for my likelihood (though I have not yet
tested this idea). Observe, too, the advent of new function mlmatbysum for use with
ml when coding a d2 evaluator. It enables calculation of various components of second
derivative formulas that mlmatsum cannot handle. Of course, coding has to be preceded
by production of the formulas for the derivatives, and this remains a complex task for
many likelihoods, with plenty of scope for making errors. It is of some consolation
that at least we have methods d1debug and d2debug to check analytical derivative
calculations against numerically calculated ones (chapter 5).
3 What is missing from the book?
More examples would be very welcome, not only for the reasons I gave earlier, but also
because some types of models are not discussed at all. For instance, there is no discussion
of how to  t parametric statistical distributions to sample data. As it happens, it is
relatively straightforward to do this (once you know how!); see inter alia my commands
smfit and dagumfit for  tting the three parameter Singh Maddala (Burr type 12)
and Dagum (Burr type 3) distributions (Jenkins 1999). I only learned how to use
ml to estimate these models after consulting Technical Support. Other candidates for
examples might be a model with sample selection (for example, a Tobit model allowing
for sample selection) or a double-hurdle model. In both cases, the model consists of two
equations, with error terms correlated across equations.
I would have also liked to have seen more about the writing of ado- les to maximize
likelihoods. For many researchers, getting estimation results is all that they are inter-
ested in, and for them the emphasis in the book will be about right; why go to the extra
trouble of writing a new estimation command? However, experience tells us that there
are substantial bene ts to the Stata user community from the increased availability of
new and well-written estimation commands. So, there is an important role that a book
like this can play in supporting budding command writers. Chapter 10 is a helpful start,
but it could go further. Several examples that come to mind from personal experience
are how to (1) pass variable names (permanent and temporary) from the main com-
mand ado  le to the evaluator subroutine that is called by ml, (2) write code for parsing
multi-equation model commands, and (3) save items using ereturn in an estimationS. P. Jenkins 443
program and access them in the associated display program. I concede that some of
these topics might be labeled general programming ones, but they arise commonly in
the ML estimation context and so deserve treatment there.
There are other areas where readers could bene t more generally from the authors 
accumulated experience and undoubted wisdom. One example is a more exhaustive
and systematic discussion of numerical accuracy and precision issues to add to those
scattered about in the book already (for example, why it is better to code norm(-x)
rather than 1 - norm(x), and so on). Also, model parameters other than regression
coeﬃcients typically have theoretical bounds (for example, correlations lie between −1
and 1), and one should incorporate these into the estimation process. This points to
the need for a more explicit and systematic cataloging of the transformations that are
available, together with discussion of how to reverse the transformation post-estimation
and derive the variance covariance matrix of the relevant parameters in their original
metric ( diparm is your friend). Extended discussion of the types of models for which
likelihood maximization may prove diﬃcult, and what to do in such cases, would be
useful. Another, rather more advanced, example would be illustration of how to incorpo-
rate numerical methods such as Gauss Hermite quadrature into user-written programs.
More generally, the examples considered could be more systematically classi ed accord-
ing to the issues that each of them raised so that budding users could more easily see
which case or cases was most relevant to their problem.
4 Conclusions
If you are considering whether to buy this book, look  rst at
http://www.stata-press.com/books/ml.html. This web page gives the full table of con-
tents, and you can download for free the preface, chapter 1 (Theory and Practice), the
subject index, and the datasets referred to in the book (although not the code used
in the examples). Researchers who already have the  rst edition and who are only
occasional users of ml might well wait for the next edition and rely on the online help
and the references manuals in the interim. But if you are a regular user of ml or are a
potential new user without the  rst edition, I would strongly recommend getting this
edition. The book costs US$42, which is not too expensive for books of this sort, but
choose your shipping option carefully. (The speediest shipping option to Europe costs
only a dollar less than the book itself!)
5 References
Gould, W., J. Pitblado, and W. Sribney. 2003. Maximum Likelihood Estimation with
Stata. 2d ed. College Station, TX: Stata Press.
Jenkins, S. P. 1999. sg106: Fitting Singh Maddala and Dagum distributions by max-
imum likelihood. Stata Technical Bulletin 48: 19 25. In Stata Technical Bulletin
Reprints, vol. 8, 261 268. College Station, TX: Stata Press.444 Review of Gould, Pitblado, and Sribney
About the Author
Stephen Jenkins is a professor at the Institute for Social and Economic Research, University of
Essex, Colchester UK, and an Associate Editor of the Stata Journal. He has written a number
of commands using ml (all available using ssc): smfit, dagumfit, pgmhaz, spsurv, and (with
Lorenzo Cappellari) mvprobit.

sg106: Fitting Singh Maddala and Dagum distributions by maximum likelihood. Stata Technical Bulletin 48: 19 25. In Stata Technical Bulletin Reprints,

Review of Maximum Likelihood Estimation with Stata by Gould, Pitblado, and Sribney

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Review of Maximum Likelihood Estimation with Stata by Gould, Pitblado, and Sribney

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