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
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
I was looking at some SAS documentation when I saw a Base SAS function that I never knew existed. The NWKDOM function returns the date for the nth occurrence of a weekday for the specified month and year. I surely could have used that function last spring when I blogged
There are a lot of useful probability distributions that are not featured in standard statistical textbooks. Some of them have distinctive names. In the past year I have had contact with SAS customers who use the Tweedie distribution, the slash distribution, and the PERT distribution. Often these distributions are used
What's in a name? As Shakespeare's Juliet said, "That which we call a rose / By any other name would smell as sweet." A similar statement holds true for the names of colors in SAS: "Rose" by any other name would look as red! SAS enables you to specify a
Sometimes a graph is more interpretable if you assign specific colors to categories. For example, if you are graphing the number of Olympic medals won by various countries at the 2012 London Olympics, you might want to assign the colors gold, silver, and bronze to represent first-, second-, and third-place
The New York Times has an excellent staff that produces visually interesting graphics for the general public. However, because their graphs need to be understood by all Times readers, the staff sometimes creates a complicated infographic when a simpler statistical graph would show the data in a clearer manner. A
Last week I wrote a SAS/IML program that computes the odds of winning the game of craps. I noted that the program remains valid even if the dice are not fair. For convenience, here is a SAS/IML function that computes the probability of winning at craps, given the probability vector
It is easy to simulate data that is uniformly distributed in the unit cube for any dimension. However, it is less obvious how to generate data in the unit simplex. The simplex is the set of points (x1,x2,...,xd) such that Σi xi = 1 and 0 ≤ xi ≤ 1
Gambling games that use dice, such as the game of "craps," are often used to demonstrate the laws of probability. For two dice, the possible rolls and probability of each roll are usually represented by a matrix. Consequently, the SAS/IML language makes it easy to compute the probabilities of various
