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Programming Tips

Rick WicklinOctober 11, 2017 0

Simulate correlations by using the Wishart distribution

The article "Fisher's transformation of the correlation coefficient" featured a Monte Carlo simulation that generated sample correlations from bivariate normal data. The simulation used three steps: Simulate B samples of size N from a bivariate normal distribution with correlation ρ. Use PROC CORR to compute the sample correlation matrix for

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Programming Tips

Heat map of correlations between variables

Rick WicklinOctober 9, 2017 1

Order correlations by magnitude

Correlations between variables are typically displayed in a matrix. Because the correlation matrix is determined by the order of the variables, it is difficult to find the largest and smallest correlations, which is why analysts sometimes use colors to visualize the correlation matrix. Another visualization option is the pairwise correlation

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Learn SAS | Programming Tips

Results of a data-driven simulation in which parameters are stored in a file and processed by a SAS program

Rick WicklinSeptember 27, 2017 5

Data-driven simulation

In a large simulation study, it can be convenient to have a "control file" that contains the parameters for the study. My recent article about how to simulate multivariate normal clusters demonstrates a simple example of this technique. The simulation in that article uses an input data set that contains

Analytics | Programming Tips

Rick WicklinSeptember 25, 2017 6

Simulate multivariate normal data in SAS by using PROC SIMNORMAL

My article about Fisher's transformation of the Pearson correlation contained a simulation. The simulation uses the RANDNORMAL function in SAS/IML software to simulate multivariate normal data. If you are a SAS programmer who does not have access to SAS/IML software, you can use the SIMNORMAL procedure in SAS/STAT software to

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Advanced Analytics | Learn SAS | Programming Tips

Simulate clustered data from a Gaussian mixture distribution

Rick WicklinSeptember 13, 2017 7

Simulate multivariate clusters in SAS

This article shows how to simulate data from a mixture of multivariate normal distributions, which is also called a Gaussian mixture. You can use this simulation to generate clustered data. The adjacent graph shows three clusters, each simulated from a four-dimensional normal distribution. Each cluster has its own within-cluster covariance,

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Analytics | Programming Tips

Rick WicklinSeptember 11, 2017 1

Symbolic derivatives in SAS

Did you know that you can get SAS to compute symbolic (analytical) derivatives of simple functions, including applying the product rule, quotient rule, and chain rule? SAS can form the symbolic derivatives of single-variable functions and partial derivatives of multivariable functions. Furthermore, the derivatives are output in a form that

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Learn SAS | Programming Tips

Rick WicklinSeptember 7, 2017 2

Construct polynomial effects in SAS regression models

If you use SAS regression procedures, you are probably familiar with the "stars and bars" notation, which enables you to construct interaction effects in regression models. Although you can construct many regression models by using that classical notation, a friend recently reminded me that the EFFECT statement in SAS provides

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Programming Tips

Rick WicklinAugust 23, 2017 1

The arithmetic-geometric mean

All statisticians are familiar with the classical arithmetic mean. Some statisticians are also familiar with the geometric mean. Whereas the arithmetic mean of n numbers is the sum divided by n, the geometric mean of n nonnegative numbers is the n_th root of the product of the numbers. The geometric

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Programming Tips

Rick WicklinAugust 21, 2017 1

6 tips for timing the performance of algorithms

When you implement a statistical algorithm in a vector-matrix language such as SAS/IML, R, or MATLAB, you should measure the performance of your implementation, which means that you should time how long a program takes to analyze data of varying sizes and characteristics. There are some general tips that can

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Programming Tips

Rick WicklinAugust 7, 2017 6

The curse of non-unique eigenvectors

A SAS customer asked, "I computed the eigenvectors of a matrix in SAS and in another software package. I got different answers? How do I know which answer is correct?" I've been asked variations of this question dozens of times. The answer is usually "both answers are correct." The mathematical

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