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.
Differential equations arise in the modeling of many physical processes, including mechanical and chemical systems. You can solve systems of first-order ordinary differential equations (ODEs) by using the ODE subroutine in the SAS/IML language, which solves initial value problems. This article uses the equations of motion for the classic simple
Last week I presented two talks at the University of Wisconsin at Milwaukee, which has established a new Graduate Certificate in Applied Data Analysis Using SAS. While in Milwaukee, I ran into an old friend: the ODS LISTING destination. One of my presentations was a hands-on workshop titled Getting Started
Sometimes it is useful in the SAS/IML language to convert a character string into a vector of one-character values. For example, you might want to count the frequency distribution of characters, which is easy when each character is an element of a vector. The question of how to convert a
Finding the maximum value of a function is an important task in statistics. There are three approaches to finding a maxima: When the function is available as an analytic expression, you can use an optimization algorithm to find the maxima. For example, in the SAS/IML language, you can use any
Recently I wrote about how to determine the age of your SAS release. Experienced SAS programmers know that you can programatically determine information about your SAS release by using certain automatic macro variables that SAS provides: SYSVER: contains the major and minor version of the SAS release SYSVLONG: contains the
A common visualization is to compare characteristics of two groups. This article emphasizes two tips that will help make the comparison clear. First, consider graphing the differences between the groups. Second, in any plot that has a categorical axis, sort the categories by a meaningful quantity. This article is motivated
Even the best programmers make mistakes. For most errors, SAS software displays the nature and location of the error, returns control to the programmer, and awaits further instructions. However, there are a handful of insidious errors that cause SAS to think that a statement or program is not finished. For
Earlier this week I posted a "guest blog" in which my 8th grade son described a visualization of data for the 2013 ASA Poster Competition. The purpose of today's blog post is to present a higher-level statistical analysis of the same data. I will use a t test and a
Editor's Note: My 8th grade son, David, created a poster that he submitted to the 2013 ASA Poster Competition. The competition encourages students to display "two or more related graphics that summarize a set of data, look at the data from different points of view, and answer specific questions about
My previous post described the multinomial distribution and showed how to generate random data from the multinomial distribution in SAS by using the RANDMULTINOMIAL function in SAS/IML software. The RANDMULTINOMIAL function is simple to use and implements an efficient algorithm called the sequential conditional marginal method (see Gentle (2003), p.
This article describes how to generate random samples from the multinomial distribution in SAS. The content is taken from Chapter 8 of my book Simulating Data with SAS. The multinomial distribution is a discrete multivariate distribution. Suppose there are k different types of items in a box, such as a
How old is your version of SAS software? The graph on the left shows the release dates for various releases of SAS software, beginning with SAS 8.0. The graph is based on a graph on Jiangtang Hu's blog that shows the major SAS releases up through the initial release of
Do you have dozens (or even hundreds) of SAS data sets that you want to read into SAS/IML matrices? In a previous blog post, I showed how to iterate over a series of data sets and analyze each one. Inside the loop, I read each data set into a matrix
One of my favorite features of SAS/IML 12.1 (released with 9.3m2) is that the USE and CLOSE statements support reading data set names that are specified in a SAS/IML matrix. The IMLPlus language in SAS/IML Studio has supported this syntax since the early 2000s, so I am pleased that this
The truncated normal distribution TN(μ, σ, a, b) is the distribution of a normal random variable with mean μ and standard deviation σ that is truncated on the interval [a, b]. I previously blogged about how to implement the truncated normal distribution in SAS. A friend wanted to simulate data
This article describes how to implement the truncated normal distribution in SAS. Although the implementation in this article uses the SAS/IML language, you can also implement the ideas and formulas by using the DATA step and PROC FCMP. For reference, I recommend the Wikipedia article on the truncated normal distribution.
There are many techniques for generating random variates from a specified probability distribution such as the normal, exponential, or gamma distribution. However, one technique stands out because of its generality and simplicity: the inverse CDF sampling technique. If you know the cumulative distribution function (CDF) of a probability distribution, then
In a previous article I discussed how to bin univariate observations by using the BIN function, which was added to the SAS/IML language in SAS/IML 9.3. You can generalize that example and bin bivariate or multivariate data. Over two years ago I wrote a blog post on 2D binning in
It is often useful to partition observations for a continuous variable into a small number of intervals, called bins. This familiar process occurs every time that you create a histogram, such as the one on the left. In SAS you can create this histogram by calling the UNIVARIATE procedure. Optionally,
Are you still using the old RANUNI, RANNOR, RANBIN, and other "RANXXX" functions to generate random numbers in SAS? If so, here are six reasons why you should switch from these older (1970s) algorithms to the newer (late 1990s) Mersenne-Twister algorithm, which is implemented in the RAND function. The newer
Every programming language has an IF-THEN statement that branches according to whether a Boolean expression is true or false. In SAS, the IF-THEN (or IF-THEN/ELSE) statement evaluates an expression and braches according to whether the expression is nonzero (true) or zero (false). The basic syntax is if numeric-expression then do-computation;
On the Web site for the book Statistical Programming with SAS/IML Software, I provide instructions on how to download the sample data sets and install them so that they can be used from within SAS/IML Studio. When I wrote the book I did not anticipate that SAS users might want
As I wrote in my previous post, a SAS customer noticed that he was getting some duplicate values when he used the RAND function to generate a large number of random uniform values on the interval [0,1]. He wanted to know if this result indicates a bug in the RAND
Tossing dice is a simple and familiar process, yet it can illustrate deep and counterintuitive aspects of random numbers. For example, if you toss four identical six-sided dice, what is the probability that the faces are all distinct, as shown to the left? Many people would guess that the probability
The CLUSTER procedure in SAS/STAT software creates a dendrogram automatically. The black-and-white dendrogram is nice, but plain. A SAS customer wanted to know whether it is possible to add color to the dendrogram to emphasize certain clusters. For example, the plot at the left emphasizes a four-cluster scenario for clustering
How do you count the number of unique rows in a matrix? The simplest algorithm is to sort the data and then iterate down the rows, comparing each row with the previous row. However, this algorithm has two shortcomings: it physically sorts the data (which means that the original locations
I am not a big fan of the macro language, and I try to avoid it when I write SAS/IML programs. I find that the programs with many macros are hard to read and debug. Furthermore, the SAS/IML language supports loops and indexing, so many macro constructs can be replaced
A regular reader noticed my post on initializing vectors by using repetition factors and asked whether that technique would be useful to expand data that are given in value-frequency pairs. The short answer is "no." Repetition factors are useful for defining (static) matrix literals. However, if you want to expand
In a previous blog post, I described how to use a spread plot to compare the distributions of several variables. Each spread plot is a graph of centered data values plotted against the estimated cumulative probability. Thus, spread plots are similar to a (rotated) plot of the empirical cumulative distribution
Suppose that you have several data distributions that you want to compare. Questions you might ask include "Which variable has the largest spread?" and "Which variables exhibit skewness?" More generally, you might be interested in visualizing how the distribution of one variable differs from the distribution of other variables. The
