The DO Loop

Analytics

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Rick WicklinDecember 2, 2024 3

A historical method of generating random normal variates

Decades ago, it was a challenge to generate (pseudo-) random numbers that had good statistical properties. The proliferation of desktop computers in the 1980s and '90s led to many advances in computational mathematics, including better ways to generate pseudorandom variates from a wide range of probability distributions. (For brevity, I

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Analytics | Data Visualization

Rick WicklinNovember 25, 2024 1

Order variables by using a loading plot

The article "Order two-dimensional vectors by using angles" shows how to re-order a set of 2-D vectors by their angles. Because angles are on a circle, which has no beginning and no end, you must specify which vector will appear first in the list. The previous article finds the largest

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Analytics | Learn SAS | Programming Tips

Rick WicklinNovember 20, 2024 1

Order two-dimensional vectors by using angles

Order matters. The order of variables in tables and rows of a correlation matrix can make a big difference in how easy it is to observed correlations between variables or groups of variables. There are many ways to order the variables, but this article shows how to display the variables

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Analytics | Learn SAS

Rick WicklinNovember 18, 2024 0

The correlation between two sets of variables

In a correlation analysis, it is common to consider the correlations between all pairs of numerical variables. That is, if there are k numerical variables, most people examine the complete k x k matrix of correlations. This matrix is symmetric and has 1s on the diagonal, so more than half of the

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Analytics | Programming Tips

Rick WicklinOctober 21, 2024 1

The correlogram: Visualize correlations by fitting angles

A common way to visualize the sample correlations between many numeric variables is to display a heat map that shows the Pearson correlation for each pair of variables, as shown in the image to the right. The correlation is a number in the range [-1, 1], where -1 indicated perfect

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Analytics | Learn SAS | Programming Tips

Rick WicklinOctober 7, 2024 0

The three-sigma rule

A remarkable result in probability theory is the "three-sigma rule," which is a generic name for theorems that bound the probability that a univariate random variable will appear near the center of its distribution. This article discusses the familiar three-sigma rule for the normal distribution, a less-familiar rule for unimodal

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Analytics | Learn SAS

Rick WicklinAugust 7, 2024 0

Simulate data from a Poisson regression model

This article shows how to simulate data from a Poisson regression model, including how to account for an offset variable. If you are not familiar with how to run a Poisson regression in SAS, see the article "Poisson regression in SAS." A Poisson regression model is a specific type of

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Analytics | Learn SAS

Rick WicklinAugust 5, 2024 5

Poisson regression in SAS

This article demonstrates how to use PROC GENMOD to perform a Poisson regression in SAS. There are different examples in the SAS documentation and in conference papers, but I chose this example because it uses two categorical explanatory variables. Therefore, the Poisson regression can be visualized by using a contingency

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Analytics | Machine Learning

Rick WicklinJuly 31, 2024 0

Fit, simulate, fit: How models can collapse after generations of recursive fitting

An article published in Nature has the intriguing title, "AI models collapse when trained on recursively generated data." (Shumailov, et al., 2024). The article is quite readable, but I also recommend a less technical overview of the result: "AI models fed AI-generated data quickly spew nonsense" (Gibney, 2024). The Gibney

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Analytics | Programming Tips

Rick WicklinJuly 29, 2024 0

A geometric solution to isotonic regression

A previous article shows that you can run a simple (one-variable) isotonic regression by using a quadratic programming (QP) formulation. While I was reading a book about computational geometry, I learned that there is a connection between isotonic regression and the convex hull of a certain set of points. Whaaaaat?

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