Tag: Matrix Computations

Rick Wicklin 0
Constructing common covariance structures

I recently encountered a SUGI30 paper by Chuck Kincaid entitled "Guidelines for Selecting the Covariance Structure in Mixed Model Analysis." I think Kincaid does a good job of describing some common covariance structures that are used in mixed models. One of the many uses for SAS/IML is as a language

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Rick Wicklin 0
Compute the log-determinant of a matrix

The determinant of a matrix arises in many statistical computations, such as in estimating parameters that fit a distribution to multivariate data. For example, if you are using a log-likelihood function to fit a multivariate normal distribution, the formula for the log-likelihood involves the expression log(det(Σ)), where Σ is the

Rick Wicklin 0
Construct a magic square of any size

Magic squares are cool. Algorithms that create magic squares are even cooler. You probably remember magic squares from your childhood: they are n x n matrices that contain the numbers 1,2,...,n2 and for which the row sum, column sum, and the sum of both diagonals are the same value. There are many

Rick Wicklin 0
The curious case of random eigenvalues

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

Rick Wicklin 0
Generating a random orthogonal matrix

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

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Rick Wicklin 0
Use the Cholesky transformation to correlate and uncorrelate variables

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

Rick Wicklin 0
Matrices and mattresses

Birds migrate south in the fall. Squirrels gather nuts. Humans also have behavioral rituals in the autumn. I change the batteries in my smoke detectors, I switch my clocks back to daylight standard time, and I turn the mattress on my bed. The first two are relatively easy. There's even