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.
Testing people for coronavirus is a public health measure that reduces the spread of coronavirus. Dr. Anthony Fauci, a US infectious disease expert, recently mentioned the concept of "pool testing." The verb "to pool" means "to combine from different sources." In a USA Today article, Dr. Deborah Birx, the coordinator
A previous article discusses the pooled variance for two or groups of univariate data. The pooled variance is often used during a t test of two independent samples. For multivariate data, the analogous concept is the pooled covariance matrix, which is an average of the sample covariance matrices of the
The first time I saw a formula for the pooled variance, I was quite confused. It looked like Frankenstein's monster, assembled from bits and pieces of other quantities and brought to life by a madman. However, the pooled variance does not have to be a confusing monstrosity. The verb "to
If you have ever run a Kolmogorov-Smirnov test for normality, you have encountered the Kolmogorov D statistic. The Kolmogorov D statistic is used to assess whether a random sample was drawn from a specified distribution. Although it is frequently used to test for normality, the statistic is "distribution free" in
Sometimes in matrix computations, it is important to display the nonzero elements of a matrix. This can be useful for visualizing the structure of a sparse matrix (one that has many zeros) and it is also useful when describing a matrix algorithm (such as Gaussian elimination) that introduces zeros at
A previous article shows how to use the iml action to read a CAS data table into an IML matrix. This article shows how to write a CAS table from data in an IML matrix. You can read an overview of the iml action, which was introduced in SAS Viya
A previous article compares a SAS/IML program that runs in PROC IML to the same program that runs in the iml action. (You can read an overview of the iml action.) The example in the previous article was very simple and did not read or write data. This article compares
A previous article provides an introduction and overview of the iml action, which is available in SAS Viya 3.5. The article compares the iml action to PROC IML and states that most PROC IML programs can be modified to run in the iml action. This article takes a closer look
This article introduces the iml action, which is available in SAS Viya 3.5. The iml action supports most of the same syntax and functionality as the SAS/IML matrix language, which is implemented in PROC IML. With minimal changes, most programs that run in PROC IML also run in the iml
A SAS customer asked how to specify interaction effects between a classification variable and a spline effect in a SAS regression procedure. There are at least two ways to do this. If the SAS procedure supports the EFFECT statement, you can build the interaction term in the MODEL statement. For
I recently read an article that describes ways to compute confidence intervals for the difference in a percentile between two groups. In Eaton, Moore, and MacKenzie (2019), the authors describe a problem in hydrology. The data are the sizes of pebbles (grains) in rivers at two different sites. The authors
In a previous article, I discussed the definition of the Kullback-Leibler (K-L) divergence between two discrete probability distributions. For completeness, this article shows how to compute the Kullback-Leibler divergence between two continuous distributions. When f and g are discrete distributions, the K-L divergence is the sum of f(x)*log(f(x)/g(x)) over all
The Kullback–Leibler divergence is a measure of dissimilarity between two probability distributions. An application in machine learning is to measure how distributions in a parametric family differ from a data distribution. This article shows that if you minimize the Kullback–Leibler divergence over a set of parameters, you can find a
If you have been learning about machine learning or mathematical statistics, you might have heard about the Kullback–Leibler divergence. The Kullback–Leibler divergence is a measure of dissimilarity between two probability distributions. It measures how much one distribution differs from a reference distribution. This article explains the Kullback–Leibler divergence and shows
This article shows how to perform two-dimensional bilinear interpolation in SAS by using a SAS/IML function. It is assumed that you have observed the values of a response variable on a regular grid of locations. A previous article showed how to interpolate inside one rectangular cell. When you have a
I've previously written about linear interpolation in one dimension. Bilinear interpolation is a method for two-dimensional interpolation on a rectangle. If the value of a function is known at the four corners of a rectangle, an interpolation scheme gives you a way to estimate the function at any point in
This article shows how to find local maxima and maxima on a regression curve, which means finding points where the slope of the curve is zero. An example appears at the right, which shows locations where the loess smoother in a scatter plot has local minima and maxima. Except for
I recently showed how to use linear interpolation in SAS. Linear interpolation is a common way to interpolate between a set of planar points, but the interpolating function (the interpolant) is not smooth. If you want a smoother interpolant, you can use cubic spline interpolation. This article describes how to
During this coronavirus pandemic, there are many COVID-related graphs and curves in the news and on social media. The public, politicians, and pundits scrutinize each day's graphs to determine which communities are winning the fight against coronavirus. Interspersed among these many graphs is the oft-repeated mantra, "Flatten the curve!" As
SAS programmers sometimes ask about ways to perform one-dimensional linear interpolation in SAS. This article shows three ways to perform linear interpolation in SAS: PROC IML (in SAS/IML software), PROC EXPAND (in SAS/ETS software), and PROC TRANSREG (in SAS/STAT software). Of these, PROC IML Is the simplest to use and
Recently I read an excellent blog post by Paul von Hippel entitled "How many imputations do you need?". It is based on a paper (von Hippel, 2018), which provides more details. Suppose you are faced with data that has many missing values. One way to address the missing values is
I've previously written about how to generate points that are uniformly distributed in the unit disk. A seemingly unrelated topic is the distribution of eigenvalues (in the complex plane) of various kinds of random matrices. However, I recently learned that these topics are somewhat related! A mathematical result called the
A previous article describes the funnel plot (Spiegelhalter, 2005), which can identify samples that have rates or proportions that are much different than expected. The funnel plot is a scatter plot that plots the sample proportion of some quantity against the size of the sample. The variance of the sample
Death is always a difficult topic to discuss, and death has been in the news a lot during this tragic coronavirus pandemic. Many news stories focus on states, counties, or cities that have the most cases or the most deaths. A related statistic is the case fatality rate, which is
I previously wrote about the advantages of adding horizontal and vertical reference lines to a graph. You can also add a diagonal reference line to a graph. The SGPLOT procedure in SAS supports two primary ways to add a diagonal reference line: The LINEPARM statement enables you to specify a
Data tell a story. A purpose of data visualization is to convey that story to the reader in a clear and impactful way. Sometimes you can let the data "speak for themselves" in an unadorned graphic, but sometimes it is helpful to add reference lines to a graph to emphasize
Every day we face risks. If we drive to work, we risk a fatal auto accident. If we eat red meat and fatty foods, we risk a heart attack. If we go out in public during a pandemic, we risk contracting a disease. A logical response to risk is to
I have written several articles about how to work with continuous probability distributions in SAS. I always emphasize that it is important to be able to compute the four essential functions for working with a statistical distribution. Namely, you need to know how to generate random values, how to compute
During an epidemic, such as the coronavirus pandemic of 2020, the media often shows graphs of the cumulative numbers of confirmed cases for different countries. Often these graphs use a logarithmic scale for the vertical axis. In these graphs, a straight line indicates that new cases are increasing at an
A cumulative curve shows the total amount of some quantity at multiple points in time. Examples include: Total sales of songs, movies, or books, beginning when the item is released. Total views of blog posts, beginning when the post is published. Total cases of a disease for different countries, beginning
