Toe bone connected to the foot bone, Foot bone connected to the leg bone, Leg bone connected to the knee bone,... — American Spiritual, "Dem Bones" Last week I read an interesting article on Robert Kosara's data visualization blog. Kosara connected the geographic centers of the US zip codes in
Visualizing the correlations between variables often provides insight into the relationships between variables. I've previously written about how to use a heat map to visualize a correlation matrix in SAS/IML, and Chris Hemedinger showed how to use Base SAS to visualize correlations between variables. Recently a SAS programmer asked how
Recently, I was asked whether SAS can perform a principal component analysis (PCA) that is robust to the presence of outliers in the data. A PCA requires a data matrix, an estimate for the center of the data, and an estimate for the variance/covariance of the variables. Classically, these estimates
A SAS customer asked how to use SAS to conduct a Z test for the equality of two proportions. He was directed to the SAS Usage Note "Testing the equality of two or more proportions from independent samples." The note says to "specify the CHISQ option in the TABLES statement
My presentation at SAS Global Forum 2017 was "More Than Matrices: SAS/IML Software Supports New Data Structures." The paper was published in the conference proceedings several months ago, but I recently recorded a short video that gives an overview of using the new data structures in SAS/IML 14.2: If your
In a previous article, I showed two ways to define a log-likelihood function in SAS. This article shows two ways to compute maximum likelihood estimates (MLEs) in SAS: the nonlinear optimization subroutines in SAS/IML and the NLMIXED procedure in SAS/STAT. To illustrate these methods, I will use the same data
At SAS Global Forum last week, I saw a poster that used SAS/IML to optimized a quadratic objective function that arises in financial portfolio management (Xia, Eberhardt, and Kastin, 2017). The authors used the Newton-Raphson optimizer (NLPNRA routine) in SAS/IML to optimize a hypothetical portfolio of assets. The Newton-Raphson algorithm
Many intervals in statistics have the form p ± δ, where p is a point estimate and δ is the radius (or half-width) of the interval. (For example, many two-sided confidence intervals have this form, where δ is proportional to the standard error.) Many years ago I wrote an article
Most regression models try to model a response variable by using a smooth function of the explanatory variables. However, if the data are generated from some nonsmooth process, then it makes sense to use a regression function that is not smooth. A simple way to model a discontinuous process in
One of the advantages of the new mixed-type tables in SAS/IML 14.2 (released with SAS 9.4m4) is the greatly enhanced printing functionality. You can control which rows and columns are printed, specify formats for individual columns, and even use templates to completely customize how tables are printed. Printing a table
Lists are collections of objects. SAS/IML 14.2 supports lists as a way to store matrices, data tables, and other lists in a single object that you can pass to functions. SAS/IML lists automatically grow if you add new items to them and shrink if you remove items. You can also
Prior to SAS/IML 14.2, every variable in the Interactive Matrix Language (IML) represented a matrix. That changed when SAS/IML 14.2 (released with SAS 9.4m4) introduced two new data structures: data tables and lists. This article gives an overview of data tables. I will blog about lists in a separate article.
A categorical response variable can take on k different values. If you have a random sample from a multinomial response, the sample proportions estimate the proportion of each category in the population. This article describes how to construct simultaneous confidence intervals for the proportions as described in the 1997 paper
A common question on SAS discussion forums is how to repeat an analysis multiple times. Most programmers know that the most efficient way to analyze one model across many subsets of the data (perhaps each country or each state) is to sort the data and use a BY statement to
On discussion forums, I often see questions that ask how to Winsorize variables in SAS. For example, here are some typical questions from the SAS Support Community: I want an efficient way of replacing (upper) extreme values with (95th) percentile. I have a data set with around 600 variables and
In a previous article, I showed how to simulate data for a linear regression model with an arbitrary number of continuous explanatory variables. To keep the discussion simple, I simulated a single sample with N observations and p variables. However, to use Monte Carlo methods to approximate the sampling distribution
If you are a SAS programmer and use the GROUP= option in PROC SGPLOT, you might have encountered a thorny issue: if you use a WHERE clause to omit certain observations, then the marker colors for groups might change from one plot to another. This happens because the marker colors
Many SAS procedure compute statistics and also compute confidence intervals for the associated parameters. For example, PROC MEANS can compute the estimate of a univariate mean, and you can use the CLM option to get a confidence interval for the population mean. Many parametric regression procedures (such as PROC GLM)
A previous post discusses how the loess regression algorithm is implemented in SAS. The LOESS procedure in SAS/STAT software provides the data analyst with options to control the loess algorithm and fit nonparametric smoothing curves through points in a scatter plot. Although PROC LOESS satisfies 99.99% of SAS users who
Although statisticians often assume normally distributed errors, there are important processes for which the error distribution has a heavy tail. A well-known heavy-tailed distribution is the t distribution, but the t distribution is unsuitable for some applications because it does not have finite moments (means, variance,...) for small parameter values.
A kernel density estimate (KDE) is a nonparametric estimate for the density of a data sample. A KDE can help an analyst determine how to model the data: Does the KDE look like a normal curve? Like a mixture of normals? Is there evidence of outliers in the data? In
Graphs enable you to visualize how the predicted values for a regression model depend on the model effects. You can gain an intuitive understanding of a model by using the EFFECTPLOT statement in SAS to create graphs like the one shown at the top of this article. Many SAS regression
SAS software can fit many different kinds of regression models. In fact a common question on the SAS Support Communities is "how do I fit a <name> regression model in SAS?" And within that category, the most frequent questions involve how to fit various logistic regression models in SAS. There
Last week I showed how to use PROC EXPAND to compute moving averages and other rolling statistics in SAS. Unfortunately, PROC EXPAND is part of SAS/ETS software and not every SAS site has a license for SAS/ETS. For simple moving averages, you can write a DATA step program, as discussed
In SAS, the aspect ratio of a graph is the physical height of the graph divided by the physical width. Recently I demonstrated how to set the aspect ratio of graphs in SAS by using the ASPECT= option in PROC SGPLOT or by using the OVERLAYEQUATED statement in the Graph
I began 2016 by compiling a list of popular articles from my blog in 2015. This "People's Choice" list contains many interesting articles, but some of my personal favorites did not make the list. Today I present the "Editor's Choice" list of articles that deserve a second look. I've grouped
A matrix is a convenient way to store an array of numbers. However, often you need to extract certain elements from a matrix. The SAS/IML language supports two ways to extract elements: by using subscripts or by using indices. Use subscripts when you are extracting a rectangular portion of a
Sometimes I can't remember where I put things. If I lose my glasses or garden tools, I am out of luck. But when I can't remember where I put some data, I have SAS to help me find it. When I can remember the name of the data set, my
Did you know that the FREQ procedure in SAS can compute exact p-values for more than 20 statistical tests and statistics that are associated with contingency table? Mamma mia! That's a veritable smorgasbord of options! Some of the tests are specifically for one-way tables or 2 x 2 tables, but many apply
A friend who teaches courses about statistical regression asked me how to create a graph in SAS that illustrates an important concept: the conditional distribution of the response variable. The basic idea is to draw a scatter plot with a regression line, then overlay several probability distributions along the line,
