Rick Wicklin, PhD, is a distinguished researcher in computational statistics at SAS and is a principal developer of SAS/IML software. His areas of expertise include computational statistics, simulation, statistical graphics, and modern methods in statistical data analysis. Rick is author of the books Statistical Programming with SAS/IML Software and Simulating Data with SAS.
Last week I blogged about how to draw the Cantor function in SAS. The Cantor function is used in mathematics as a pathological example of a function that is constant almost everywhere yet somehow manages to "climb upwards," thus earning the nickname "the devil's staircase." The Cantor function has three
I was a freshman in college the first time I saw the Cantor middle-thirds set and the related Cantor "Devil's staircase" function. (Shown at left.) These constructions expanded my mind and led me to study fractals, real analysis, topology, and other mathematical areas. The Cantor function and the Cantor middle-thirds
'Tis a gift to be simple. -- Shaker hymn In June 2015 I published a short article for Significance, a magazine that features statistical and data-related articles that are of general interest to a wide a range of scientists. The title of my article is "In Praise of Simple Graphics."
Graphs enable you to visualize how the predicted values for a regression model depend on the model effects. You can gain an intuitive understanding of a model by using the EFFECTPLOT statement in SAS to create graphs like the one shown at the top of this article. Many SAS regression
Every beginning SAS programmer learns the simple IF-THEN/ELSE statement for conditional processing in the SAS DATA step. The basic If-THEN statement handles two cases: if a condition is true, the program does one thing, otherwise the program does something else. Of course, you can handle more cases by using multiple
I have previously shown how to overlay basic plots on box plots when all plots share a common discrete X axis. It is interesting to note that box plots can also be overlaid on a continuous (interval) axis. You often need to bin the data before you create the plot.
Box plots summarize the distribution of a continuous variable. You can display multiple box plots in a single graph by specifying a categorical variable. The resulting graph shows the distribution of subpopulations, such as different experimental groups. In the SGPLOT procedure, you can use the CATEGORY= option on the VBOX
Last week I discussed how to create spaghetti plots in SAS. A spaghetti plot is a type of line plot that contains many lines. Spaghetti plots are used in longitudinal studies to show trends among individual subjects, which can be patients, hospitals, companies, states, or countries. I showed ways to
I got several positive comments about a recent tip, "How to fit a variety of logistic regression models in SAS." A reader asked if I knew any other similar resources about statistical analysis in SAS. Absolutely! One gem that comes to mind is "Examples of writing CONTRAST and ESTIMATE statements."
What is a spaghetti plot? Spaghetti plots are line plots that involve many overlapping lines. Like spaghetti on your plate, they can be hard to unravel, yet for many analysts they are a delicious staple of data visualization. This article presents the good, the bad, and the messy about spaghetti
A grid is a set of evenly spaced points. You can use SAS to create a grid of points on an interval, in a rectangular region in the plane, or even in higher-dimensional regions like the parallelepiped shown at the left, which is generated by three vectors. You can use
Children in primary school learn that every positive number has a real square root. The number x is a square root of s, if x2 = s. Did you know that matrices can also have square roots? For certain matrices S, you can find another matrix X such that X*X
SAS software can fit many different kinds of regression models. In fact a common question on the SAS Support Communities is "how do I fit a <name> regression model in SAS?" And within that category, the most frequent questions involve how to fit various logistic regression models in SAS. There
I was eleven years old when I first saw Newton's method. No, I didn't go to a school for geniuses. I didn't even know it was Newton's method until decades later. However, in sixth grade I learned an iterative algorithm that taught me (almost) everything I need to know about
When I was in the sixth grade, I learned an iterative procedure for computing square roots by hand. Yes, I said by hand. Scientific calculators with a square root key were not yet widely available, so I and previous generations of children suffered through learning to calculate square roots by
Optimization is a primary tool of computational statistics. SAS/IML software provides a suite of nonlinear optimizers that makes it easy to find an optimum for a user-defined objective function. You can perform unconstrained optimization, or define linear or nonlinear constraints for constrained optimization. Over the years I have seen many
Last week I analyzed 12 million records of taxi cab transactions in New York City. As part of that analysis, I used a DATA step view to create a new variable, which was the ratio of the tip amount to the fare amount. A novice SAS programmer told me that
In a previous post I showed how to download, install, and use packages in SAS/IML 14.1. SAS/IML packages incorporate source files, documentation, data sets, and sample programs into a ZIP file. The PACKAGE statement enables you to install, uninstall, and manage packages. You can load functions and data into your
When I read Robert Allison's article about the cost of a taxi ride in New York City, I was struck by the scatter plot (shown at right; click to enlarge) that plots the tip amount against the total bill for 12 million taxi rides. The graph clearly reveals diagonal and
My previous post highlighted presentations at SAS Global Forum 2016 that heavily used SAS/IML software. Several of the authors clearly want to share their work with the wider SAS analytical community. They include their SAS/IML program in an appendix or mention a web site or email address from which the
Last week I attended SAS Global Forum 2016 in Las Vegas. I and more than 5,000 other attendees discussed and shared tips about data analysis and statistics. Naturally, I attended many presentations that featured using SAS/IML software to implement advanced analytical algorithms. Several speakers showed impressive mastery of SAS/IML programming
You can visualize missing data. It sounds like an oxymoron, but it is true. How can you draw graphs of something that is missing? In a previous article, I showed how you can use PROC MI in SAS/STAT software to create a table that shows patterns of missing data in
Missing data can be informative. Sometimes missing values in one variable are related to missing values in another variable. Other times missing values in one variable are independent of missing values in other variables. As part of the exploratory phase of data analysis, you should investigate whether there are patterns
I saw an interesting mathematical result in Wired magazine. The original article was about mathematical research into prime numbers, but the article included the following tantalizing fact: If Alice tosses a [fair]coin until she sees a head followed by a tail, and Bob tosses a coin until he sees two
The SG procedures in SAS use aesthetically pleasing default colors, shapes, and styles, but sometimes it is necessary to override the default attributes. The MARKERATTRS= option enables you to override the default colors, symbols, and sizes of markers in scatter plots and other graphs. Similarly, the LINEATTRS= option enables you
Last week I showed how to generate random points uniformly inside a 2-d circular region. That article showed that the distance of a point to the circle's center cannot be distributed uniformly. Instead, you should use the square root of a uniform variate to generate 2-D distances to the origin.
In SAS procedures, the WHERE clause is a useful way to filter observations so that the procedure receives only a subset of the data to analyze. The IML procedure supports the WHERE clause in two separate statements. On the USE statement, the WHERE clause acts as a global filter. The
It is easy to generate random points that are uniformly distributed inside a rectangle. You simply generate independent random uniform values for each coordinate. However, nonrectangular regions are more complicated. An instructive example is to simulate points uniformly inside the ball with a given radius. The two-dimensional case is to
Descriptive univariate statistics are the foundation of data analysis. Before you create a statistical model for new data, you should examine descriptive univariate statistics such as the mean, standard deviation, quantiles, and the number of nonmissing observations. In SAS, there is an easy way to create a data set that
Last weekend was the 2016 NCAA Division I wrestling tournament. In collegiate wrestling there are ten weight classes. The top eight wrestlers in each weight class are awarded the title "All-American" to acknowledge that they are the best wrestlers in the country. I saw a blog post on the InterMat
