Joseph Hilbe

English

Research Papers in Economics

JSS Journal of Statistical Software
September 2010, Volume 36, Book Review 4. http://www.jstatsoft.org/
Reviewer: Joseph M. Hilbe
Arizona State University
Introduction to Scientic Programming and Scientic Simulation Using R
Owen Jones, Robert Maillardet, Andrew Robinson
Chapman & Hall/CRC, Boca Raton, Florida, 2009.
ISBN 978-1-4200-6872-6. 472 pp. USD 79.95.
http://www.crcpress.com/product/isbn/9781420068726
It is not often that I think that a statistics text is one that most scientic statisticians should
have in their personal libraries. The 2008 text by Owen Jones, Robert Maillardet, and An-
drew Robinson titled, Introduction to Scientic Programming and Simulation Using R is such
a text. I am assuming, however, that R is the primary statistical package that is used among
statisticians who are evaluating biological, geological, astronomical, environmental, and other
scientic research areas. But even if a researcher does not use R as their preferred statistical
tool, authors of research articles in scientic journals now appear to overwhelmingly employ
R for executing and displaying published statistical results. In order to fully understand { or
to referee { these articles, an understanding of R is desirable. This text provides scientic re-
searchers with a working knowledge of R for both reviewing and for engaging in the statistical
evaluation of scientic data.
The text is partitioned into four sections: \Programming", \Numerical techniques", \Prob-
ability and statistics", and \Simulation". Appendices provide a highly useful glossary of R
commands as well as a listing of all programs and functions developed in the book, together
with the page on which each is rst used or dened. Exercises are provided for all chapters
except the rst.
In this review, I shall provide a brief overview of the chapters and discussion presented in
each of the above mentioned sections.
Programming
1. Setting up
Provides directions on installing R, setting up a working directory, and using the help
system. Guidance on getting R ready for work.
2. R as a calculating environment2 Introduction to Scientic Programming and Scientic Simulation Using R
Explains how to use R for basic calculating. Discusses foremost aspects of the R envi-
ronment including variables, functions, vectors, handling missing data, assignments and
expressions, and matrices. Fully worked out examples are given for dening and using
each of the above.
3. Basic programming
Explanation with numerous examples of branching, looping, vector-based programming,
program ow, debugging, and proper programming style.
4. Input and Output
Demonstrates input of data from keyboard or from le, and output to various formats.
5. Programming with functions
Discussion of how to construct properly working functions including vector and recursive
programming.
6. Sophisticated data structures
The chapter presents examples on constructing and manipulating dataframes and lists,
and how to dene the scope of functions.
7. Better graphics
A basic introduction to graphics. A special section on the use of the lattice package is
provided.
8. Pointers to further programming techniques
The nal chapter in this section provides examples on object-oriented programming and
the use of compiled C code in R functions.
Numerical techniques
For those who already have some prociency in R, the important part of the book begins with
this section.
9. Numerical accuracy and program eciency
Signicance of digits, determining the time functions take to run, and looping and
memory control are all addressed with examples in this chapter.
10. Root-nding
The basics of estimation. Constructing Newton-Raphson code and estimation using
secant and bisections methods.
11. Numerical integration
Examples using both the trapezoidal and Simpson's rule, and adaptive quadrature.Journal of Statistical Software { Book Reviews 3
12. Optimization
Discussion and examples are given on how to optimize. Examples using Newton's
method, the golden rule method, steepest ascent, and multivariate optimization are
examined in detail. A fully developed function is presented for curve tting.
Probability and statistics
13. Probability
An introduction to probability theory, including Bayes theorem. No R code is used in
this chapter.
14. Random variables
A general overview of the nature of random and pseudo-random number variables; R
code is developed for their construction. PDF and CDF theory, with the gamma PDF
and an example.
15. Discrete random variables
Focus on details of the binomial, Poisson, and negative binomial distributions.
16. Continuous random variables
Focus on continuous variables including the normal, and 2. Simulations are developed.
An example of the Poisson process and gamma distribution is presented with a fully
worked out example of a discrete queue simulation.
17. Parameter estimation
A major chapter providing theory and examples of the central limit theorem, develop-
ment of condence intervals using various methods, and point estimation.
Simulation
18. Simulation
Methods are given for constructing simulated data sets with specied distributions and
parameter. Rejection method is examined with code for constructing a variety of sim-
ulations based on the method.
19. Monte Carlo integration
Methods of Monte Carlo integration are examined.
20. Variance reduction
Importance and reduction sampling techniques are provided. Methods of variance re-
duction examined.4 Introduction to Scientic Programming and Scientic Simulation Using R
21. Case studies
Several fully worked out examples are given, with complete R code provided. Examples
are given for the SIR (susceptible, infected, and removed) epidemic models, inventory
analysis, and seed dispersal from forestry management. Simulations are demonstrated
with R code provided and explained.
22. Student projects
Projects are specied for reader/student evaluation. The subjects are: (1) level of a
dam, (2) roulette, (3) Buon's needle and cross, (4) insurance risk, (5) squash, and
(6) stock prices. Code is provided on the book's web site for the analysis of each of
these example problems.
As a demonstration of how the book can be used to construct an optimization, I used the
methods discussed in the text to develop code that can be used to estimate an NB-C model
using R. It is a simple optimization function in which the model response and predictors are
specied in the code and the parameter estimates standard errors, z value, and condence
intervals are displayed upon running the script. I later enhanced the model so that the code
could accept any data and not have it specied in the function itself. It is included in my
book, Negative Binomial Regression (Hilbe 2011). It should be noted that, before this, R did
not have any functions to estimate an NB-C model. First, the data is loaded
R> load("medpar.rda")
R> medpar$type <- factor(medpar$type)
Then the function nbc.reg.ml() for NB-C optimization is dened
R> nbc.reg.ml <- function(b.hat, X, y) {
+ a.hat <- b.hat[1]
+ xb.hat <- X %*% b.hat[-1]
+ mu.hat <- 1 / ((exp(-xb.hat)-1)*a.hat)
+ p.hat <- 1 / (1 + a.hat*mu.hat)
+ r.hat <- 1 / a.hat
+ sum(dnbinom(y, size = r.hat, prob = p.hat, log = TRUE))
+ }
The design matrix is
R> nbcX <- model.matrix(~ hmo + white + type, data = medpar)
with starting points (discovered by trial and error!)
R> p.0 <- c(alpha = 0.5, cons = -1, hmo = 0, white = 0, type2 = 0, type3 = 0)
The joint conditional log-likelihood is maximizied by
R> nbc.fit <- optim(p.0, nbc.reg.ml, X = nbcX, y = medpar$los,
+ control = list(fnscale = -1, maxit = 10000), hessian = TRUE)Journal of Statistical Software { Book Reviews 5
and the parameter estimates and asymptotic standard errors are obtained by
R> (nbc.beta.hat <- nbc.fit$par)
alpha cons hmo white type2 type3
0.44516214 -0.20128564 -0.01399781 -0.02491594 0.04101961 0.10723427
R> (nbc.se.beta.hat <- sqrt(diag(solve(-nbc.fit$hessian))))
alpha cons hmo white type2 type3
0.019775949 0.013496886 0.010729402 0.010756500 0.008932639 0.010062008
R> nbc.results <- data.frame(Estimate = nbc.beta.hat,
+ SE = nbc.se.beta.hat, Z = nbc.beta.hat / nbc.se.beta.hat,
+ LCL = nbc.beta.hat - 1.96 * nbc.se.beta.hat,
+ UCL = nbc.beta.hat + 1.96 * nbc.se.beta.hat)
R> rownames(nbc.results) <- c("alpha", colnames(nbcX))
R> nbc.results <- nbc.results[c(2:nrow(nbc.results), 1),]
R> nbc.results
Estimate SE Z LCL UCL
(Intercept) -0.20128564 0.013496886 -14.913488 -0.22773954 -0.174831744
hmo -0.01399781 0.010729402 -1.304622 -0.03502744 0.007031817
white -0.02491594 0.010756500 -2.316361 -0.04599868 -0.003833201
type2 0.04101961 0.008932639 4.592105 0.02351164 0.058527585
type3 0.10723427 0.010062008 10.657343 0.08751273 0.126955803
alpha 0.44516214 0.019775949 22.510280 0.40640128 0.483922999
For comparative purposes, I show the maximum likelihood results of a NB-C model using
Stata. The results are nearly identical to the thousandths place. The Stata code is provided
by Hilbe (2007).
. cnbreg los white hmo type2 type3
Canonical Negative Binomial Regression Number of obs = 1495
Wald chi2(4) = 131.15
Log likelihood = -4796.6997 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
los | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
white | -.0248636 .0107598 -2.31 0.021 -.0459524 -.0037749
hmo | -.0141484 .0107354 -1.32 0.188 -.0351894 .0068926
type2 | .0409448 .0089345 4.58 0.000 .0234335 .0584561
type3 | .1072065 .0100628 10.65 0.000 .0874837 .1269293
_cons | -.2012769 .0135036 -14.91 0.000 -.2277436 -.17481036 Introduction to Scientic Programming and Scientic Simulation Using R
-------------+----------------------------------------------------------------
/lnalpha | -.8091036 .0444641 -18.20 0.000 -.8962516 -.7219556
-------------+----------------------------------------------------------------
alpha | .445257 .0197979 .4080965 .4858013
------------------------------------------------------------------------------
AIC Statistic = 6.424
Scientic Programming and Simulation Using R can be used to develop a host of similar
models as well as functions for a variety of analytic needs. It is particularly useful for un-
derstanding and developing modeling and simulation software. I highly recommend the text,
nding it to be one of the most useful books I have read on the subject.
References
Hilbe J (2007). \hcnbreg: Stata Module to Estimate Heterogeneous Canonical Negative
Binomial Regression." Statistical Software Components, Boston College Department of
Economics. URL http://ideas.repec.org/c/boc/bocode/s456870.html.
Hilbe JM (2011). Negative Binomial Regression. 2nd edition. Cambridge University Press,
Cambridge.
Reviewer:
Joseph M. Hilbe
University of Hawaii, and
Sociology and Statistics, Arizona State University
Tempe, Arizona, United States of America
E-mail: hilbe@asu.edu
Journal of Statistical Software http://www.jstatsoft.org/
published by the American Statistical Association http://www.amstat.org/
Volume 36, Book Review 4 Published: 2010-09-16
September 2010

Introduction to Scientific Programming and Scientific Simulation Using R

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