The DO Loop

Programming Tips

Strengthen your programming skills with tips and techniques from the experts

Rick WicklinAugust 9, 2021 0

Never multiply with a large permutation matrix

Do you ever use a permutation matrix to change the order of rows or columns in a matrix? Did you know that there is a more efficient way in matrix-oriented languages such as SAS/IML, MATLAB, and R? Remember the following tip: Never multiply with a large permutation matrix! Instead, use

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Programming Tips

Rick WicklinAugust 2, 2021 5

The art of rotations and reflections

Art evokes an emotional response in the viewer, but sometimes art also evokes a cerebral response. When I see patterns and symmetries in art, I think about a related mathematical object or process. Recently, a Twitter user tweeted about a painting called "Phantom’s Shadow, 2018" by the Nigerian-born artist, Odili

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Programming Tips

Rick WicklinJuly 26, 2021 4

Compare the default definitions for sample quantiles in SAS, R, and Python

A SAS programmer recently asked why his SAS program and his colleague's R program display different estimates for the quantiles of a very small data set (less than 10 observations). I pointed the programmer to my article that compares the nine common definitions for sample quantiles. The article has a

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Analytics | Data Visualization | Programming Tips

Rick WicklinJuly 19, 2021 1

Copulas and multivariate distributions with normal marginals

After my recent articles on simulating data by using copulas, many readers commented about the power of copulas. Yes, they are powerful, and the geometry of copulas is beautiful. However, it is important to be aware of the limitations of copulas. This article creates a bizarre example of bivariate data,

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Analytics | Programming Tips

Rick WicklinJuly 14, 2021 0

Compare computational methods for least squares regression

In a previous article, I discussed various ways to solve a least-square linear regression model. I discussed the SWEEP operator (used by many SAS regression routines), the LU-based methods (SOLVE and INV in SAS/IML), and the QR decomposition (CALL QR in SAS/IML). Each method computes the estimates for the regression

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Analytics | Programming Tips

Rick WicklinJuly 7, 2021 10

Simulate multivariate correlated data by using PROC COPULA in SAS

In general, it is hard to simulate multivariate data that has a specified correlation structure. Copulas make that task easier for continuous distributions. A previous article presented the geometry behind a copula and explained copulas in an intuitive way. Although I strongly believe that statistical practitioners should be familiar with

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Analytics | Programming Tips

Rick WicklinJune 30, 2021 0

Compute 2-D cumulative sums and ogives

A recent article about how to estimate a two-dimensional distribution function in SAS inspired me to think about a related computation: a 2-D cumulative sum. Suppose you have numbers in a matrix, X. A 2-D cumulative sum is a second matrix, C, such that the C[p,q] gives the sum of

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Programming Tips

Rick WicklinJune 23, 2021 2

The probability integral transform

This article uses simulation to demonstrate the fact that any continuous distribution can be transformed into the uniform distribution on (0,1). The function that performs this transformation is a familiar one: it is the cumulative distribution function (CDF). A continuous CDF is defined as an integral, so the transformation is

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Programming Tips

Rick WicklinJune 21, 2021 4

The case of the missing blanks: Why SAS output might not show multiple blanks in strings

A SAS programmer noticed that his SAS output was not displaying multiple blanks in his strings. He had some strings with leading blanks, others with trailing blanks, and others with multiple blanks in the middle. Yet, every time he used SAS to print the strings to the HTML destination, something

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Analytics | Programming Tips

Rick WicklinJune 14, 2021 5

Simulate correlated variables by using the Iman-Conover transformation

Simulating univariate data is relatively easy. Simulating multivariate data is much harder. The main difficulty is to generate variables that have given univariate distributions but also are correlated with each other according to a specified correlation matrix. However, Iman and Conover (1982, "A distribution-free approach to inducing rank correlation among

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