The first-order autoregressive (AR(1)) correlation structure is important for applications in time series modeling and for repeated measures analysis. The AR(1) model provides a simple situations where measurements (on the same subject) that are closer in time are correlated more strongly than measurements recorded far apart. The AR(1) model uses
In a binomial regression model, the response variable is the proportion of successes for a given number of trials. In SAS regression procedures, you specify a binomial model by using the EVENTS/TRIALS syntax on the MODEL statement. Many analysts use the LOGISTIC or GENMOD procedures to fit binomial models. Visualizing
Many people have an intuitive feel for residuals in least square models and know that the sum of squared residuals is a goodness-of-fit measure. Generalized linear regression models use a different but related idea, called deviance residuals. What are deviance residuals, and how can you compute them? Deviance residuals (and
A previous article describes how to use SAS to find the inflection points of a 1-D function that you can evaluate at any point. The function must be given by a formula (or by an algorithm) because the root-finding algorithm needs to evaluate the function at arbitrary locations. However, sometimes
A SAS programmer asked if it is possible to numerically find an inflection point for a univariate function, f(x). Yes! This can be solved as a variation of a classic numerical root-finding problem. Recall that an inflection point is a value (call it x0) in the domain where the graph
I previously wrote an article about the Lambert W function. The Lambert W function is the inverse of the function g(x) = x exp(x). This means that you can use it to find the value of x such that g(x)=c for any value of c in the range of g, which
A SAS programmer had many polynomials for which he wanted to compute the real roots. By the Fundamental Theorem of Algebra, every polynomial of degree d has d complex roots. You can find these complex roots by using the POLYROOT function in SAS IML. The programmer only wanted to output
Here's a SAS tip for you. Most SAS programmers know that SAS provides syntax that makes it easy to specify a list of variables. For example, you can use the hyphen and colon operators to specify lists of variables on many SAS statements: You can use the hyphen operator (-)
A colleague asked me an interesting question: Suppose you have a structured correlation matrix, such as a matrix that has a compound symmetric, banded, or an AR1(ρ) structure. If you generate a random correlation matrix that has the same eigenvalues as the structured matrix, does the random matrix have the
In a previous article, I presented some of the most popular blog posts from The DO Loop in 2024. In general, popular articles deal with elementary topics that have broad appeal. However, I also write technical articles about advanced topics, which typically do not make it onto a Top 10
