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.
You might know that you can use the ODS SELECT statement to display only some of the tables and graphs that are created by a SAS procedure. But did you know that you can use a WHERE clause on the ODS SELECT statement to display tables that match a pattern?
An ROC curve graphically summarizes the tradeoff between true positives and true negatives for a rule or model that predicts a binary response variable. An ROC curve is a parametric curve that is constructed by varying the cutpoint value at which estimated probabilities are considered to predict the binary event.
The SGPLOT procedure enables you to use the value of a response variable to color markers or areas in a graph. For example, you can use the COLORRESPONSE= option to define a variable whose values will be used to color markers in a scatter plot or cells in a heat
When solving optimization problems, it is harder to specify a constrained optimization than an unconstrained one. A constrained optimization requires that you specify multiple constraints. One little typo or a missing minus sign can result in an infeasible problem or a solution that is unrelated to the true problem. This
Will the real Pareto distribution please stand up? SAS supports three different distributions that are named "Pareto." The Wikipedia page for the Pareto distribution lists five different "Pareto" distributions, including the three that SAS supports. This article shows how to fit the two-parameter Pareto distribution in SAS and discusses the
A useful feature in PROC SGPLOT is the ability to easily visualize subgroups of data. Most statements in the SGPLOT procedure support a GROUP= option that enables you to overlay plots of subgroups. When you use the GROUP= option, observations are assigned attributes (colors, line patterns, symbols, ...) that indicate
If you want to bootstrap the parameters in a statistical regression model, you have two primary choices. The first, case resampling, is discussed in a previous article. This article describes the second choice, which is resampling residuals (also called model-based resampling). This article shows how to implement residual resampling in
If you want to bootstrap the parameters in a statistical regression model, you have two primary choices. The first is case resampling, which is also called resampling observations or resampling pairs. In case resampling, you create the bootstrap sample by randomly selecting observations (with replacement) from the original data. The
A SAS programmer asked how to rearrange elements of a matrix. The rearrangement he wanted was rather complicated: certain blocks of data needed to move relative to other blocks, but the values within each block were to remain unchanged. It turned out that the mathematical operation he needed is called
In a recent article about nonlinear least squares, I wrote, "you can often fit one model and use the ESTIMATE statement to estimate the parameters in a different parameterization." This article expands on that statement. It shows how to fit a model for one set of parameters and use the
There are several ways to use SAS to get the unique values for a data variable. In Base SAS, you can use the TABLES statement in PROC FREQ to generate a table of unique values (and the counts). You can also use the DISTINCT function in PROC SQL to get
This article shows how to use SAS to fit a growth curve to data. Growth curves model the evolution of a quantity over time. Examples include population growth, the height of a child, and the growth of a tumor cell. This article focuses on using PROC NLIN to estimate the
This article compares several ways to find the elements that are common to multiple sets. I test which method is the fastest in the SAS/IML language. However, all algorithms are intrinsically fast, which raises an important question: when is it worth the time and effort to optimize an algorithm? The
It is sometimes necessary for researchers to simulate data with thousands of variables. It is easy to simulate thousands of uncorrelated variables, but more difficult to simulate thousands of correlated variables. For that, you can generate a correlation matrix that has special properties, such as a Toeplitz matrix or a
Programmers on a SAS discussion forum recently asked about the chi-square test for proportions as implemented in PROC FREQ in SAS. One person asked the basic question, "how do I test the null hypothesis that the observed proportions are equal to a set of known proportions?" Another person said that
A radial basis function is a scalar function that depends on the distance to some point, called the center point, c. One popular radial basis function is the Gaussian kernel φ(x; c) = exp(-||x – c||2 / (2 σ2)), which uses the squared distance from a vector x to the
Last week I compared the overhand shuffle to the riffle shuffle. I used random operations to simulate both kinds of shuffles and then compared how well they mix cards. The article caused one my colleague and fellow blogger, Rob Pratt, to ask if I was familiar with a bit of
Every day I’m shufflin'. Shufflin', shufflin'. -- "Party Rock Anthem," LMFAO The most popular way to mix a deck of cards is the riffle shuffle, which separates the deck into two pieces and interleaves the cards from each piece. Besides being popular with card players, the riffle shuffle is
The SAS/IML language and the MATLAB language are similar. Both provide a natural syntax for performing high-level computations on vectors and matrices, including basic linear algebra subroutines. Sometimes a SAS programmer will convert an algorithm from MATLAB into SAS/IML. Because the languages are not identical, I am sometimes asked, "what
Have you ever tried to type a movie title by using a TV remote control? Both Netflix and Amazon Video provide an interface (a virtual keyboard) that enables you to use the four arrow keys of a standard remote control to type letters. The letters are arranged in a regular
Given a rectangular grid with unit spacing, what is the expected distance between two random vertices, where distance is measured in the L1 metric? (Here "random" means "uniformly at random.") I recently needed this answer for some small grids, such as the one to the right, which is a 7 x 6
Continued fractions show up in surprising places. They are used in the numerical approximations of certain functions, including the evaluation of the normal cumulative distribution function (normal CDF) for large values of x (El-bolkiny, 1995, p. 75-77) and in approximating the Lambert W function, which has applications in the modeling
In the SAS/IML language, you can only concatenate vectors that have conforming dimensions. For example, to horizontally concatenate two vectors X and Y, the symbols X and Y must have the same number of rows. If not, the statement Z = X || Y will produce an error: ERROR: Matrices
A SAS programmer recently asked me how to compute a kernel regression in SAS. He had read my blog posts "What is loess regression" and "Loess regression in SAS/IML" and was trying to implement a kernel regression in SAS/IML as part of a larger analysis. This article explains how to
A frequent topic on SAS discussion forums is how to check the assumptions of an ordinary least squares linear regression model. Some posts indicate misconceptions about the assumptions of linear regression. In particular, I see incorrect statements such as the following: Help! A histogram of my variables shows that they
A SAS programmer recently asked how to interpret the "standardized regression coefficients" as computed by the STB option on the MODEL statement in PROC REG and other SAS regression procedures. The SAS documentation for the STB option states, "a standardized regression coefficient is computed by dividing a parameter estimate by
Video killed the radio star.... We can't rewind, we've gone too far. -- The Buggles (1979) "You kids have it easy," my father used to tell me. "When I was a kid, I didn't have all the conveniences you have today." He's right, and I could say the same
This article shows how to perform an optimization in SAS when the parameters are restricted by nonlinear constraints. In particular, it solves an optimization problem where the parameters are constrained to lie in the annular region between two circles. The end of the article shows the path of partial solutions
My colleague, Robert Allison, recently published an interesting visualization of the relationship between chess ratings and age. His post was inspired by the article "Age vs Elo — Your battle against time," which was published on the chess.com website. ("Elo" is one of the rating systems in chess.) Robert Allison's
The SGPLOT procedure in SAS makes it easy to create graphs that overlay various groups in the data. Many statements support the GROUP= option, which specifies that the graph should overlay group information. For example, you can create side-by-side bar charts and box plots, and you can overlay multiple scatter
