This article is an excerpt from my forthcoming book Simulating Data with SAS. Not every matrix with 1 on the diagonal and off-diagonal elements in the range [–1, 1] is a valid correlation matrix. A correlation matrix has a special property known as positive semidefiniteness. All correlation matrices are positive
Tag: Simulation
Over the past few years, and especially since I posted my article on eight tips to make your simulation run faster, I have received many emails (often with attached SAS programs) from SAS users who ask for advice about how to speed up their simulation code. For this reason, I
I received the following query regarding the RAND function in Base SAS: In SAS, is specifying 0 as a random number seed the same as not specifying a seed at all? The question concerns initializing the SAS random number stream by using the internal system clock. You can do this
"Help! My simulation is taking too long to run! How can I make it go faster?" I frequently talk with statistical programmers who claim that their "simulations are too slow" (by which they mean, "they take too long"). They suspect that their program is inefficient, but they aren't sure why.
I've been a fan of statistical simulation and other kinds of computer experimentation for many years. For me, simulation is a good way to understand how the world of statistics works, and to formulate and test conjectures. Last week, while investigating the efficiency of the power method for finding dominant
In a previous post I showed how to implement Stewart's (1980) algorithm for generating random orthogonal matrices in SAS/IML software. By using the algorithm, it is easy to generate a random matrix that contains a specified set of eigenvalues. If D = diag(λ1, ..., λp) is a diagonal matrix and
Because I am writing a new book about simulating data in SAS, I have been doing a lot of reading and research about how to simulate various quantities. Random integers? Check! Random univariate samples? Check! Random multivariate samples? Check! Recently I've been researching how to generate random matrices. I've blogged
After my post on detecting outliers in multivariate data in SAS by using the MCD method, Peter Flom commented "when there are a bunch of dimensions, every data point is an outlier" and remarked on the curse of dimensionality. What he meant is that most points in a high-dimensional cloud
Covariance, correlation, and distance matrices are a few examples of symmetric matrices that are frequently encountered in statistics. When you create a symmetric matrix, you only need to specify the lower triangular portion of the matrix. The VECH and SQRVECH functions, which were introduced in SAS/IML 9.3, are two functions
A variance-covariance matrix expresses linear relationships between variables. Given the covariances between variables, did you know that you can write down an invertible linear transformation that "uncorrelates" the variables? Conversely, you can transform a set of uncorrelated variables into variables with given covariances. The transformation that works this magic is