Assign the diagonal elements of a matrix

SAS/IML programmers know that the VECDIAG matrix can be used to extract the diagonal elements of a matrix. For example, the following statements extract the diagonal of a 3 x 3 matrix: proc iml; m = {1 2 3, 4 5 6, 7 8 9}; v = vecdiag(m); /* v = {1,5,9} […]
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Count the number of unique rows in a matrix

How do you count the number of unique rows in a matrix? The simplest algorithm is to sort the data and then iterate down the rows, comparing each row with the previous row. However, this algorithm has two shortcomings: it physically sorts the data (which means that the original locations […]
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Using simulation to estimate the power of a statistical test

The power of a statistical test measures the test's ability to detect a specific alternate hypothesis. For example, educational researchers might want to compare the mean scores of boys and girls on a standardized test. They plan to use the well-known two-sample t test. The null hypothesis is that the […]
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How to vectorize computations in a matrix language

Last week someone posted an interesting question to the SAS/IML Support Community. The problem involved four nested DO loops and took hours to run. By transforming several nested DO loops into an equivalent matrix operation, I was able to reduce the run time to about one second. The process of […]
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Oh, those pesky temporary variables!

The SAS/IML language secretly creates temporary variables. Most of the time programmers aren't even aware that the language does this. However, there is one situation where if you don't think carefully about temporary variables, your program will silently produce an error. And as every programmer knows, silent wrong numbers are […]
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Generate binary outcomes with varying probability

A while ago I saw a blog post on how to simulate Bernoulli outcomes when the probability of generating a 1 (success) varies from observation to observation. I've done this often in SAS, both in the DATA step and in the SAS/IML language. For example, when simulating data that satisfied […]
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Remove or keep: Which is faster?

In a recent article on efficient simulation from a truncated distribution, I wrote some SAS/IML code that used the LOC function to find and exclude observations that satisfy some criterion. Some readers came up with an alternative algorithm that uses the REMOVE function instead of subscripts. I remarked in a […]
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Efficient acceptance-rejection simulation: Part II

Last week I wrote about using acceptance-rejection algorithms in vector languages to simulate data. The main point I made is that in a vector language it is efficient to generate many more variates than are needed, with the knowledge that a certain proportion will be rejected. In last week's article, […]
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Efficient acceptance-rejection simulation

A few days ago on the SAS/IML Support Community, there was an interesting discussion about how to simulate data from a truncated Poisson distribution. The SAS/IML user wanted to generate values from a Poisson distribution, but discard any zeros that are generated. This kind of simulation is known as an […]
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Constructing block matrices with applications to mixed models

The other day I was constructing covariance matrices for simulating data for a mixed model with repeated measurements. I was using the SAS/IML BLOCK function to build up the "R-side" covariance matrix from smaller blocks. The matrix I was constructing was block-diagonal and looked like this: The matrix represents a […]
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