In this article by David Alexander Lillis, author of the R Graph Essentials, we will talk about R. Developed by Professor Ross Ihaka and Dr. Robert Gentleman at Auckland University (New Zealand) during the early 1990s, the R statistics environment is a real success story. R is open source software, which you can download in a couple of minutes from the Comprehensive R Network (CRAN) website (http://cran.r-project.org/), and combines a powerful programming language, outstanding graphics, and a comprehensive range of useful statistical functions. If you need a statistics environment that includes a programming language, R is ideal. It's true that the learning curve is longer than for spreadsheet-based packages, but once you master the R programming syntax, you can develop your own very powerful analytic tools. Many contributed packages are available on the web for use with R, and very often the analytic tools you need can be downloaded at no cost.

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The main problem for those new to R is the time required to master the programming language, but several nice graphical user interfaces, such as John Fox's R Commander package, are available, which make it much easier for the newcomer to develop proficiency in R than it used to be. For many statisticians and researchers, R is the package of choice because of its powerful programming language, the easy availability of code, and because it can import Excel spreadsheets, comma separated variable (.csv) spreadsheets, and text files, as well as SPSS files, STATA files, and files produced within other statistical packages.

You may be looking for a tool for your own data analysis. If so, let's take a brief look at what R can do for you.

Some basic R syntax

Data can be created in R or else read in from .csv or other files as objects. For example, you can read in the data contained within a .csv file called mydata.csv as follows:

A <- read.csv(mydata.csv, h=T)

A The object A now contains all the data of the original file. The syntax A[3,7] picks out the element in row 3 and column 7. The syntax A[14, ] selects the fourteenth row and A[,6] selects the sixth column. The functions mean(A) and sd(A) find the mean and standard deviation of each column. The syntax 3*A + 7 would triple each element of A and add 7 to each element and store the new array as the object B Now you could save this array as a .csv file called Outputfile.csv as follows:

write.csv(B, file="Outputfile.csv")

Statistical modeling

R provides a comprehensive range of basic statistical functions relating to the commonly-used distributions (normal distribution, t-distribution, Poisson, gamma, and so on), and many less-well known distributions. It also provides a range of non-parametric tests that are appropriate when your data are not distributed normally. Linear and non-linear regressions are easy to perform, and finding the optimum model (that is, by eliminating non-significant independent variables and non-significant factor interactions) is particularly easy. Implementing Generalized Linear Models and other commonly-used models such as Analysis of Variance, Multivariate Analysis of Variance, and Analysis of Covariance is also straightforward and, once you know the syntax, you may find that such tasks can be done more quickly in R than in other packages. The usual post-hoc tests for identifying factor levels that are significantly different from the other levels (for example, Tukey and Sheffe tests) are available, and testing for interactions between factors is easy.

Factor Analysis, and the related Principal Components Analysis, are well known data reduction techniques that enable you to explain your data in terms of smaller sets of independent variables (or factors). Both methods are available in R, and code for complex designs, including One and Two Way Repeated Measures, and Four Way ANOVA (for example, two repeated measures and two between-subjects), can be written relatively easily or downloaded from various websites (for example, http://www.personality-project.org/r/). Other analytic tools include Cluster Analysis, Discriminant Analysis, Multidimensional Scaling, and Correspondence Analysis. R also provides various methods for fitting analytic models to data and smoothing (for example, lowess and spline-based methods).

Miscellaneous packages for specialist methods

You can find some very useful packages of R code for fields as diverse as biometry, epidemiology, astrophysics, econometrics, financial and actuarial modeling, the social sciences, and psychology. For example, if you are interested in Astrophysics, Penn State Astrophysics School offers a nice website that includes both tutorials and code (http://www.iiap.res.in/astrostat/RTutorials.html).

Here I'll mention just a few of the popular techniques:

Monte Carlo methods

A number of sources give excellent accounts of how to perform Monte Carlo simulations in R (that is, drawing samples from multidimensional distributions and estimating expected values). A valuable text is Christian Robert's book Introducing Monte Carlo Methods with R. Murali Haran gives another interesting Astrophysical example in the CAStR website (http://www.stat.psu.edu/~mharan/MCMCtut/MCMC.html).

Structural Equation Modeling

Structural Equation Modelling (SEM) is becoming increasingly popular in the social sciences and economics as an alternative to other modeling techniques such as multiple regression, factor analysis and analysis of covariance. Essentially, SEM is a kind of multiple regression that takes account of factor interactions, nonlinearities, measurement error, multiple latent independent variables, and latent dependent variables. Useful references for conducting SEM in R include those of Revelle, Farnsworth (2008), and Fox (2002 and 2006).

Data mining

A number of very useful resources are available for anyone contemplating data mining using R. For example, Luis Torgo has just published a book on data mining using R, and presents case studies, along with the datasets and code, which the interested student can work through. Torgo's book provides the usual analytic and graphical techniques used every day by data miners, including visualization techniques, dealing with missing values, developing prediction models, and methods for evaluating the performance of your models.

Also of interest to the data miner is the Rattle GUI (R Analytical Tool to Learn Easily). Rattle is a data mining facility for analyzing very large data sets. It provides many useful statistical and graphical data summaries, presents mechanisms for developing a variety of models, and summarizes the performance of your models.

Graphics in R

Quite simply, the quality and range of graphics available through R is superb and, in my view, vastly superior to those of any other package I have encountered. Of course, you have to write the necessary code, but once you have mastered this skill, you have access to wonderful graphics. You can write your own code from scratch, but many websites provide helpful examples, complete with code, which you can download and modify to suit your own needs. R's base graphics (graphics created without the use of any additional contributed packages) are superb, but various graphics packages such as ggplot2 (and the associated qplot function) help you to create wonderful graphs.

R's graphics capabilities include, but are not limited to, the following:

Base graphics in R

• Basic graphics techniques and syntax
• Creating scatterplots and line plots
• Customizing axes, colors, and symbols
• Adding text – legends, titles, and axis labels
• Adding lines – interpolation lines, regression lines, and curves
• Increasing complexity – graphing three variables, multiple plots, or multiple axes
• Saving your plots to multiple formats – PDF, postscript, and JPG
• Including mathematical expressions on your plots
• Making graphs clear and pretty – including a grid, point labels, and shading
• Shading and coloring your plot
• Creating bar charts, histograms, boxplots, pie charts, and dotcharts
• Adding loess smoothers
• Scatterplot matrices
• R's color palettes
• Adding error bars

Creating graphs using qplot

• Using basic qplot graphics techniques and syntax to customize in easy steps
• Creating scatterplots and line plots in qplot
• Mapping symbol size, symbol type and symbol color to categorical data
• Including regressions and confidence intervals on your graphs
• Shading and coloring your graph
• Creating bar charts, histograms, boxplots, pie charts, and dotcharts
• Labelling points on your graph

Creating graphs using ggplot

• Ploting options – backgrounds, sizes, transparencies, and colors
• Superimposing points
• Controlling symbol shapes and using pretty color schemes
• Stacked, clustered, and paneled bar charts
• Methods for detailed customization of lines, point labels, smoothers, confidence bands, and error bars

The following graph records information on the heights in centimeters and weights in kilograms of patients in a medical study. The curve in red gives a smoothed version of the data, created using locally weighted scatterplot smoothing.

Both the graph and the modelling required to produce the smoothed curve, were performed in R.

Here is another graph. It gives the heights and body masses of female patients receiving treatment in a hospital. Each patient is identified by name. This graph was created very easily using ggplot, and shows the default background produced by ggplot (a grey plotting background and white grid lines).

Next, we see a histogram of patients' heights and body masses, partitioned by gender. The bars are given in an orange and an ivory color. The ggplot package provides a wide range of colors and hues, as well as a wide range of color palettes.

Finally, we see a line graph of height against age for a group of four children. The graph includes both points and lines and we have a unique color for each child.

The ggplot package makes it possible to create attractive and effective graphs for research and data analysis.

Summary

For many scientists and data analysts, mastery of R could be an investment for the future, particularly for those who are beginning their careers. The technology for handling scientific computation is advancing very quickly, and is a major impetus for scientific advance. Some level of mastery of R has become, for many applications, essential for taking advantage of these developments. Spatial analysis, where R provides an integrated framework access to abilities that are spread across many different computer programs, is a good example.

A few years ago, I would not have recommended R as a statistics environment for generalist data analysts or postgraduate students, except those working directly in areas involving statistical modeling. However, many tutorials are downloadable from the Internet and a number of organizations provide online tutorials and/or face-to-face workshops (for example, The Analysis Factor http://www.theanalysisfactor.com/). In addition, the appearance of GUIs, such as R Commander and the new iNZight GUI33 (designed for use in schools), makes it easier for non-specialists to learn and use R effectively. I am most happy to provide advice to anyone contemplating learning to use this outstanding statistical and research tool.

References

Some useful material on R are as follows:

• L'analyse des donn´ees. Tome 1: La taxinomie, Tome 2: L'analyse des correspondances, Dunod, Paris, Benz´ecri, J. P (1973).
• Computation of Correspondence Analysis, Blasius J, Greenacre, M. J (1994). In M J Greenacre, J Blasius (eds.), Correspondence Analysis in the Social Sciences, pp. 53–75, Academic Press, London.
• Statistics: An Introduction using R, Crawley, M. J. ([email protected]), Imperial College, Silwood Park, Ascot, Berks, Published in 2005 by John Wiley & Sons, Ltd. http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470022973,subjectCd-ST05.html (ISBN 0-470-02297-3). http://www3.imperial.ac.uk/naturalsciences/research/statisticsusingr.
• Structural Equation Models Appendix to An R and S-PLUS Companion to Applied Regression, Fox, John, http://cran.r-project.org/doc/contrib/Fox-Companion/appendix-sems.pdf.
• Getting Started with the R Commander, Fox, John, 26 August 2006.
• The R Commander: A Basic-Statistics Graphical User Interface to R, Fox, John, Journal of Statistical Software, September 2005, Volume 14, Issue 9. http://www.jstatsoft.org/.
• Structural Equation Modeling With the sem Package in R, Fox, John, Structural Equation Modeling, 13(3), 465–486. Lawrence Erlbaum Associates, Inc. 2006.
• Biplots in Biomedical Research, Gabriel, K, R and Odoroff, C, 9, 469–485, Statistics in Medicine, 1990.
• Theory and Applications of Correspondence Analysis, Greenacre M. J., Academic Press, London, 1984.
• Using R for Data Analysis and Graphics Introduction, Code and Commentary, Maindonald, J. H, Centre for Mathematics and its Applications, Australian National University.
• Introducing Monte Carlo Methods with R, Series Use R, Robert, Christian P., Casella, George, 2010, XX, 284 p., Softcover, ISBN 978-1-4419-1575-7.

<p>Useful tutorials available on the web are as follows:</p>

• An Introduction to R: examples for Actuaries, De Silva, N, 2006, http://toolkit.pbworks.com/f/R%20Examples%20for%20Actuaries%20v0.1-1.pdf.
• Econometrics in R, Farnsworth, Grant, V, October 26, 2008, http://cran.r-project.org/doc/contrib/Farnsworth-EconometricsInR.pdf.
• An Introduction to the R Language, Harte, David, Statistics Research Associates Limited, www.statsresearch.co.nz.
• Quick R, Kabakoff, Rob, http://www.statmethods.net/index.html.
• R for SAS and SPSS Users, Muenchen, Bob, http://RforSASandSPSSusers.com.
• Statistical Analysis with R - a quick start, Nenadi´,C and Zucchini, Walter.
• R for Beginners, Paradis, Emannuel ([email protected]), Institut des Sciences de l' Evolution, Universite Montpellier II, F-34095 Montpellier c_edex 05, France.
• Data Mining with R learning by case studies, Torgo, Luis, http://www.liaad.up.pt/~ltorgo/DataMiningWithR/.
• SimpleR - Using R for Introductory Statistics, Verzani, John, http://cran.r-project.org/doc/contrib/Verzani-SimpleR.pdf.
• Time Series Analysis and Its Applications: With R Examples, http://www.stat.pitt.edu/stoffer/tsa2/textRcode.htm#ch2.
• The irises of the Gaspé peninsula, E. Anderson, Bulletin of the American Iris Society, 59, 2-5. 1935.
• Introducing Monte Carlo Methods with R, Series Use R, Robert, Christian P., Casella, George. 2010, XX, 284 p., Softcover, ISBN: 978-1-4419-1575-7.

Resources for Article:

Further resources on this subject:

• Aspects of Data Manipulation in R [Article]
• Learning Data Analytics with R and Hadoop [Article]
• First steps with R [Article]