A previous article discussed how to solve regression problems in which the parameters are constrained to be a specified constant (such as B1 = 1) or are restricted to obey a linear equation such as B4 = –2*B2. In SAS, you can use the RESTRICT statement in PROC REG to
Matrix balancing is an interesting problem that has a long history. Matrix balancing refers to adjusting the cells of a frequency table to match known values of the row and column sums. One of the early algorithms for matrix balancing is known as the RAS algorithm, but it is also
On discussion forums, many SAS programmers ask about the best way to generate dummy variables for categorical variables. Well-meaning responders offer all sorts of advice, including writing your own DATA step program, sometimes mixed with macro programming. This article shows that the simplest and easiest way to generate dummy variables
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.
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
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
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
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
A previous article discusses the pooled variance for two or groups of univariate data. The pooled variance is often used during a t test of two independent samples. For multivariate data, the analogous concept is the pooled covariance matrix, which is an average of the sample covariance matrices of the
If you have ever run a Kolmogorov-Smirnov test for normality, you have encountered the Kolmogorov D statistic. The Kolmogorov D statistic is used to assess whether a random sample was drawn from a specified distribution. Although it is frequently used to test for normality, the statistic is "distribution free" in
