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.
Many people have an intuitive feel for residuals in least square models and know that the sum of squared residuals is a goodness-of-fit measure. Generalized linear regression models use a different but related idea, called deviance residuals. What are deviance residuals, and how can you compute them? Deviance residuals (and
A previous article describes how to use SAS to find the inflection points of a 1-D function that you can evaluate at any point. The function must be given by a formula (or by an algorithm) because the root-finding algorithm needs to evaluate the function at arbitrary locations. However, sometimes
A SAS programmer asked if it is possible to numerically find an inflection point for a univariate function, f(x). Yes! This can be solved as a variation of a classic numerical root-finding problem. Recall that an inflection point is a value (call it x0) in the domain where the graph
I previously wrote an article about the Lambert W function. The Lambert W function is the inverse of the function g(x) = x exp(x). This means that you can use it to find the value of x such that g(x)=c for any value of c in the range of g, which
A SAS programmer had many polynomials for which he wanted to compute the real roots. By the Fundamental Theorem of Algebra, every polynomial of degree d has d complex roots. You can find these complex roots by using the POLYROOT function in SAS IML. The programmer only wanted to output
Here's a SAS tip for you. Most SAS programmers know that SAS provides syntax that makes it easy to specify a list of variables. For example, you can use the hyphen and colon operators to specify lists of variables on many SAS statements: You can use the hyphen operator (-)
A colleague asked me an interesting question: Suppose you have a structured correlation matrix, such as a matrix that has a compound symmetric, banded, or an AR1(ρ) structure. If you generate a random correlation matrix that has the same eigenvalues as the structured matrix, does the random matrix have the
In a previous article, I presented some of the most popular blog posts from The DO Loop in 2024. In general, popular articles deal with elementary topics that have broad appeal. However, I also write technical articles about advanced topics, which typically do not make it onto a Top 10
A previous article discusses covariance matrices that have the same set of eigenvalues. The set of eigenvalues is called the spectrum of the matrix. For symmetric matrices, the spectrum contains real numbers. For covariance matrices, which are positive semidefinite, the eigenvalues are nonnegative. It turns out that two symmetric matrices
In 2024, I wrote about 80 articles for The DO Loop blog. My most popular articles were about SAS programming, data visualization, and statistics. If you missed any of these articles, here is the "Reader's Choice Awards" for some of the most popular articles from 2024! SAS Programming The following
