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Rick WicklinAugust 12, 2020 2

Use simulation to estimate the power of a statistical test

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

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Programming Tips

Rick WicklinAugust 10, 2020 2

4 ways to standardize data in SAS

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

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Learn SAS | Programming Tips

Rick WicklinAugust 5, 2020 0

Submatrices of matrices

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.

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Learn SAS | Programming Tips

Rick WicklinAugust 3, 2020 0

Run tasks in parallel in SAS Viya

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

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Programming Tips

Rick WicklinJuly 29, 2020 2

Simulate regression models that incorporate CLASS parameterizations

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

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Learn SAS | Programming Tips

Rick WicklinJuly 27, 2020 6

8 ways to use the Kronecker product

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

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Advanced Analytics | Machine Learning | Programming Tips

Rick WicklinJuly 23, 2020 11

Fit a multivariate Gaussian mixture model by using the expectation-maximization (EM) algorithm

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

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Learn SAS | Programming Tips

Rick WicklinJuly 20, 2020 0

Compute within-group multivariate statistics and store them in a list

I recently showed how to compute within-group multivariate statistics by using the SAS/IML language. However, a principal of good software design is to encapsulate functionality and write self-contained functions that compute and return the results. What is the best way to return multiple statistics from a SAS/IML module? A convenient

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Advanced Analytics | Programming Tips

Rick WicklinJuly 15, 2020 1

How to evaluate the multivariate normal log likelihood

The multivariate normal distribution is used frequently in multivariate statistics and machine learning. In many applications, you need to evaluate the log-likelihood function in order to compare how well different models fit the data. The log-likelihood for a vector x is the natural logarithm of the multivariate normal (MVN) density

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Learn SAS | Programming Tips

Rick WicklinJuly 13, 2020 1

A parallel implementation of Monte Carlo simulation in SAS Viya

A previous article introduces the MAPREDUCE function in the iml action. (The iml action was introduced in Viya 3.5.) The MAPREDUCE function implements the map-reduce paradigm, which is a two-step process for distributing a computation to multiple threads. The example in the previous article adds a set of numbers by

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