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Rick WicklinJune 30, 2021 0

A recent article about how to estimate a two-dimensional distribution function in SAS inspired me to think about a related computation: a 2-D cumulative sum. Suppose you have numbers in a matrix, X. A 2-D cumulative sum is a second matrix, C, such that the C[p,q] gives the sum of

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Analytics | Learn SAS

Rick WicklinJune 28, 2021 16

Estimate a bivariate CDF in SAS

This article shows how to estimate and visualize a two-dimensional cumulative distribution function (CDF) in SAS. SAS has built-in support for this computation. Although the bivariate CDF is not used as much as the univariate CDF, the bivariate version is still a useful tool in understanding the probable values of

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Analytics | Data Visualization

Rick WicklinJune 16, 2021 3

The geometry of the Iman-Conover transformation

A previous article showed how to simulate multivariate correlated data by using the Iman-Conover transformation (Iman and Conover, 1982). The transformation preserves the marginal distributions of the original data but permutes the values (columnwise) to induce a new correlation among the variables. When I first read about the Iman-Conover transformation,

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Analytics | Programming Tips

Rick WicklinJune 14, 2021 5

Simulate correlated variables by using the Iman-Conover transformation

Simulating univariate data is relatively easy. Simulating multivariate data is much harder. The main difficulty is to generate variables that have given univariate distributions but also are correlated with each other according to a specified correlation matrix. However, Iman and Conover (1982, "A distribution-free approach to inducing rank correlation among

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Analytics | Learn SAS

Rick WicklinJune 9, 2021 0

Rank-based scores and tied values

Many nonparametric statistical methods use the ranks of observations to compute distribution-free statistics. In SAS, two procedures that use ranks are PROC NPAR1WAY and PROC CORR. Whereas the SPEARMAN option in PROC CORR (which computes rank correlation) uses only the "raw" tied ranks, PROC NPAR1WAY uses transformations of the ranks,

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Analytics | Programming Tips

Rick WicklinJune 7, 2021 1

Permutation tests and independent sorting of data

For many univariate statistics (mean, median, standard deviation, etc.), the order of the data is unimportant. If you sort univariate data, the mean and standard deviation do not change. However, you cannot sort an individual variable (independently) if you want to preserve its relationship with other variables. This statement is

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Analytics | Programming Tips

Rick WicklinJune 1, 2021 10

The Hampel identifier: Robust outlier detection in a time series

It is well known that classical estimates of location and scale (for example, the mean and standard deviation) are influenced by outliers. In the 1960s, '70s, and '80s, researchers such as Tukey, Huber, Hampel, and Rousseeuw advocated analyzing data by using robust statistical estimates such as the median and the

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Analytics | Programming Tips

Rick WicklinMay 26, 2021 1

The running median as a time series smoother

When data contain outliers, medians estimate the center of the data better than means do. In general, robust estimates of location and sale are preferred over classical moment-based estimates when the data contain outliers or are from a heavy-tailed distribution. Thus, instead of using the mean and standard deviation of

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Analytics | Learn SAS

Rick WicklinMay 17, 2021 0

Standardized regression coefficients in PROC GLIMMIX

I previously wrote about how to understand standardized regression coefficients in PROC REG in SAS. You can obtain the standardized estimates by using the STB option on the MODEL statement in PROC REG. Several readers have written to ask whether I could write a similar article about the STDCOEF option

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Analytics | Learn SAS | Programming Tips

Rick WicklinMay 12, 2021 2

Nonstandard ways to standardize variables

You can standardize a numerical variable by subtracting a location parameter from each observation and then dividing by a scale parameter. Often, the parameters depend on the data that you are standardizing. For example, the most common way to standardize a variable is to subtract the sample mean and divide

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