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Rick WicklinApril 24, 2019 0

The CUSUM test has many incarnations. Different areas of statistics use different assumption and test for different hypotheses. This article presents a brief overview of CUSUM tests and gives an example of using the CUSUM test in PROC AUTOREG for autoregressive models in SAS. A CUSUM test uses the cumulative

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Programming Tips

Rick WicklinApril 22, 2019 2

The CUSUM test for randomness of a binary sequence

Many statistical tests use a CUSUM statistic as part of the test. It can be confusing when a researcher refers to "the CUSUM test" without providing details about exactly which CUSUM test is being used. This article describes a CUSUM test for the randomness of a binary sequence. You start

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Programming Tips

Rick WicklinApril 17, 2019 9

Create your own version of Anscombe's quartet: Dissimilar data that have similar statistics

I think every course in exploratory data analysis should begin by studying Anscombe's quartet. Anscombe's quartet is a set of four data sets (N=11) that have nearly identical descriptive statistics but different graphical properties. They are a great reminder of why you should graph your data. You can read about

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Programming Tips

Rick WicklinApril 15, 2019 0

Efficient evaluation of a quadratic form

A quadratic form is a second-degree polynomial that does not have any linear or constant terms. For multivariate polynomials, you can quickly evaluate a quadratic form by using the matrix expression x` A x This computation is straightforward in a matrix language such as SAS/IML. However, some computations in statistics

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Analytics | Programming Tips

Rick WicklinApril 10, 2019 3

4 ways to compute an SSCP matrix

In numerical linear algebra, there are often multiple ways to solve a problem, and each way is useful in various contexts. In fact, one of the challenges in matrix computations is choosing from among different algorithms, which often vary in their use of memory, data access, and speed. This article

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Learn SAS | Programming Tips

Rick WicklinApril 8, 2019 0

Use the FLOOR-MOD trick to allocate items to groups

Suppose you need to assign 100 patients equally among 3 treatment groups in a clinical study. Obviously, an equal allocation is impossible because the second number does not evenly divide the first, but you can get close by assigning 34 patients to one group and 33 to the others. Mathematically,

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Learn SAS | Programming Tips

Rick WicklinApril 3, 2019 0

Convergence in mixed models: When the estimated G matrix is not positive definite

I've previously written about how to deal with nonconvergence when fitting generalized linear regression models. Most generalized linear and mixed models use an iterative optimization process, such as maximum likelihood estimation, to fit parameters. The optimization might not converge, either because the initial guess is poor or because the model

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Learn SAS | Programming Tips

Rick WicklinApril 1, 2019 0

Matrix operations and BY groups

Many SAS procedures support the BY statement, which enables you to perform an analysis for subgroups of the data set. Although the SAS/IML language does not have a built-in "BY statement," there are various techniques that enable you to perform a BY-group analysis. The two I use most often are

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Programming Tips

Schematic diagram of outliers in bivariate normal data. The point 'A' has large univariate z scores but a small Mahalanobis distance. The point 'B' has a large Mahalanobis distance. Only 'b' is a multivariate outlier.

Rick WicklinMarch 25, 2019 0

The geometry of multivariate versus univariate outliers

An important concept in multivariate statistical analysis is the Mahalanobis distance. The Mahalanobis distance provides a way to measure how far away an observation is from the center of a sample while accounting for correlations in the data. The Mahalanobis distance is a good way to detect outliers in multivariate

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Programming Tips

Rick WicklinMarch 18, 2019 5

Interpolation vs extrapolation: the convex hull of multivariate data

Statisticians often emphasize the dangers of extrapolating from a univariate regression model. A common exercise in introductory statistics is to ask students to compute a model of population growth and predict the population far in the future. The students learn that extrapolating from a model can result in a nonsensical

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