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.
I got a lot of feedback about my recent article about how to find roots of nonlinear functions by using the SOLVE function in PROC FCMP. A colleague asked how the FCMP procedure stores the functions. Specifically, why the OUTLIB= option on the PROC FCMP statement use a three-level syntax:
Finding the root (or zero) of a nonlinear function is an important computational task. In the case of a one-variable function, you can use the SOLVE function in PROC FCMP to find roots of nonlinear functions in the DATA step. This article shows how to use the SOLVE function to
I recently showed how to use simulation to estimate the power of a statistical hypothesis test. The example (a two-sample t test for the difference of means) is a simple SAS/IML module that is very fast. Fast is good because often you want to perform a sequence of simulations over
A previous article about standardizing data in groups shows how to simulate data from two groups. One sample (with n1=20 observations) is simulated from an N(15, 5) distribution whereas a second (with n2=30 observations) is simulated from an N(16, 5) distribution. The sample means of the two groups are close
A common operation in statistical data analysis is to center and scale a numerical variable. This operation is conceptually easy: you subtract the mean of the variable and divide by the variable's standard deviation. Recently, I wanted to perform a slight variation of the usual standardization: Perform a different standardization
Have you ever seen the "brain teaser" for children that shows a 4 x 4 grid and asks "how many squares of any size are in this grid?" To solve this problem, the reader must recognize that there are sixteen 1 x 1 squares, nine 2 x 2 squares, four 3 x 3 squares, and one 4 x 4 square.
The iml action was introduced in Viya 3.5. As shown in a previous article, the iml action supports ways to implement the map-reduce paradigm, which is a way to distribute a computation by using multiple threads. The map-reduce paradigm is ideal for “embarrassingly parallel” computations, which are composed of many
When you write a program that simulates data from a statistical model, you should always check that the simulation code is correct. One way to do this is to generate a large simulated sample, estimate the parameters in the simulated data, and make sure that the estimates are close to
The Kronecker product (also called the direct product) is a binary operation that combines two matrices to form a new matrix. The Kronecker product appears in textbooks about the design of experiments and multivariate statistics. The Kronecker product seems intimidating at first, but often one of the matrices in the
Last month a SAS programmer asked how to fit a multivariate Gaussian mixture model in SAS. For univariate data, you can use the FMM Procedure, which fits a large variety of finite mixture models. If your company is using SAS Viya, you can use the MBC or GMM procedures, which
