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Graphical comparison of two methods for estimating confidence intervals of eigenvalues of a correlation matrix

Rick WicklinOctober 26, 2020 3

Confidence intervals for eigenvalues of a correlation matrix

A fundamental principle of data analysis is that a statistic is an estimate of a parameter for the population. A statistic is calculated from a random sample. This leads to uncertainty in the estimate: a different random sample would have produced a different statistic. To quantify the uncertainty, SAS procedures

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Analytics | Programming Tips

Rick WicklinOctober 19, 2020 5

Generate random points in a triangle

How can you efficiently generate N random uniform points in a triangular region of the plane? There is a very cool algorithm (which I call the reflection method) that makes the process easy. I no longer remember where I saw this algorithm, but it is different from the "weighted average"

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Analytics | Data Visualization

Rick WicklinOctober 14, 2020 1

A continuous band plot for visualizing uncertainty in regression predictions

A previous article discusses the confidence band for the mean predicted value in a regression model. The article shows a "graded confidence band plot," which I saw in Claus O. Wilke's online book, Fundamentals of Data Visualization (Section 16.3). It communicates uncertainty in the predictions. A graded band plot is

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Analytics | Data Visualization

Rick WicklinOctober 12, 2020 1

Visualize uncertainty in regression predictions

You've probably seen many graphs that are similar to the one at the right. This plot shows a regression line overlaid on a scatter plot of some data. Given a value for the independent variable (x), the regression line gives the best prediction for the mean of the response variable

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Analytics | Programming Tips

Rick WicklinOctober 7, 2020 0

The Poisson-binomial distribution for hundreds of parameters

A previous article shows how to use a recursive formula to compute exact probabilities for the Poisson-binomial distribution. The recursive formula is an O(N2) computation, where N is the number of parameters for the Poisson-binomial (PB) distribution. If you have a distribution that has hundreds (or even thousands) of parameters,

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Analytics | Programming Tips

Rick WicklinSeptember 28, 2020 0

The Poisson-binomial distribution

The Poisson-binomial distribution is a generalization of the binomial distribution. For the binomial distribution, you carry out N independent and identical Bernoulli trials. Each trial has a probability, p, of success. The total number of successes, which can be between 0 and N, is a binomial random variable. The distribution

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Analytics | Learn SAS

Rick WicklinSeptember 21, 2020 0

Regression with inequality constraints on parameters

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

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Analytics | Programming Tips

Rick WicklinSeptember 16, 2020 1

Restricted least squares regression in SAS

A data analyst recently asked a question about restricted least square regression in SAS. Recall that a restricted regression puts linear constraints on the coefficients in the model. Examples include forcing a coefficient to be 1 or forcing two coefficients to equal each other. Each of these problems can be

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Analytics | Programming Tips

Rick WicklinSeptember 10, 2020 0

Iterative proportional fitting in SAS

I previously wrote about the RAS algorithm, which is a simple algorithm that performs matrix balancing. Matrix balancing refers to adjusting the cells of a frequency table to match known values of the row and column sums. Ideally, the balanced matrix will reflect the structural relationships in the original matrix.

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Analytics | Programming Tips

Rick WicklinSeptember 8, 2020 1

Matrix balancing: Update matrix cells to match row and column sums

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

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