Rick Wicklin, PhD, is a distinguished researcher in computational statistics at SAS and is a principal developer of SAS/IML software. His areas of expertise include computational statistics, simulation, statistical graphics, and modern methods in statistical data analysis. Rick is author of the books Statistical Programming with SAS/IML Software and Simulating Data with SAS.
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,
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
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
In simulation studies, sometimes you need to simulate outliers. For example, in a simulation study of regression techniques, you might want to generate outliers in the explanatory variables to see how the technique handles high-leverage points. This article shows how to generate outliers in multivariate normal data that are a
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
An analyst was using SAS to analyze some data from an experiment. He noticed that the response variable is always positive (such as volume, size, or weight), but his statistical model predicts some negative responses. He posted the data and asked if it is possible to modify the graph so
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
It's time to celebrate Pi Day! Every year on March 14th (written 3/14 in the US), math-loving folks celebrate "all things pi-related" because 3.14 is the three-decimal approximation to the mathematical constant, π. Although children learn that pi is approximately 3.14159..., the actual definition of π is the ratio of
A SAS programmer posted an interesting question on a SAS discussion forum. The programmer wanted to iterate over hundreds of SAS data sets, read in all the character variables, and then do some analysis. However, not every data set contains character variables, and SAS complains when you ask it to
A previous article shows how to use a scatter plot to visualize the average SAT scores for all high schools in North Carolina. The schools are grouped by school districts and ranked according to the median value of the schools in the district. For the school districts that have many
Standardized tests like the SAT and ACT can cause stress for both high school students and their parents, but according to a Wall Street Journal article, the SAT and ACT "provide an invaluable measure of how students are likely to perform in college and beyond." Naturally, students wonder how their
Box plots are a great way to compare the distributions of several subpopulations of your data. For example, box plots are often used in clinical studies to visualize the response of patients in various cohorts. This article describes three techniques to visualize responses when the cohorts have a nested or
When I run a bootstrap analysis, I create graphs to visualize the distribution of the bootstrap statistics. For example, in my article about how to bootstrap the difference of means in a two-sample t test, I included a histogram of the bootstrap distribution and added reference lines to indicate a
Last year I published a series of blogs posts about how to create a calibration plot in SAS. A calibration plot is a way to assess the goodness of fit for a logistic model. It is a diagnostic graph that enables you to qualitatively compare a model's predicted probability of
Maybe if we think and wish and hope and pray It might come true. Oh, wouldn't it be nice? The Beach Boys Months ago, I wrote about how to use the EFFECT statement in SAS to perform regression with restricted cubic splines. This is the modern way to use splines
When you use maximum likelihood estimation (MLE) to find the parameter estimates in a generalized linear regression model, the Hessian matrix at the optimal solution is very important. The Hessian matrix indicates the local shape of the log-likelihood surface near the optimal value. You can use the Hessian to estimate
Have you ever run a regression model in SAS but later realize that you forgot to specify an important option or run some statistical test? Or maybe you intended to generate a graph that visualizes the model, but you forgot? Years ago, your only option was to modify your program
Feature generation (also known as feature creation) is the process of creating new features to use for training machine learning models. This article focuses on regression models. The new features (which statisticians call variables) are typically nonlinear transformations of existing variables or combinations of two or more existing variables. This
I previously discussed how you can use validation data to choose between a set of competing regression models. In that article, I manually evaluated seven models for a continuous response on the training data and manually chose the model that gave the best predictions for the validation data. Fortunately, SAS
Machine learning differs from classical statistics in the way it assesses and compares competing models. In classical statistics, you use all the data to fit each model. You choose between models by using a statistic (such as AIC, AICC, SBC, ...) that measures both the goodness of fit and the
This article shows how to use SAS to simulate data that fits a linear regression model that has categorical regressors (also called explanatory or CLASS variables). Simulating data is a useful skill for both researchers and statistical programmers. You can use simulation for answering research questions, but you can also
Recently I was asked to explain the result of an ANOVA analysis that I posted to a statistical discussion forum. My program included some simulated data for an ANOVA model and a call to the GLM procedure to estimate the parameters. I was asked why the parameter estimates from PROC
Recently I was asked to explain the result of an ANOVA analysis that I posted to a statistical discussion forum. My program included some simulated data for an ANOVA model and a call to the GLM procedure to estimate the parameters. I was asked why the parameter estimates from PROC
In machine learning and other model building techniques, it is common to partition a large data set into three segments: training, validation, and testing. Training data is used to fit each model. Validation data is a random sample that is used for model selection. These data are used to select
A quantile-quantile plot (Q-Q plot) is a graphical tool that compares a data distribution and a specified probability distribution. If the points in a Q-Q plot appear to fall on a straight line, that is evidence that the data can be approximately modeled by the target distribution. Although it is
When you overlay two series in PROC SGPLOT, you can either plot both series on the same axis or you can assign one series to the main axis (Y) and another to a secondary axis (Y2). If you use the Y and Y2 axes, they are scaled independently by default,
Numbers don't lie, but sometimes they don't reveal the full story. Last week I wrote about the most popular articles from The DO Loop in 2018. The popular articles are inevitably about elementary topics in SAS programming or statistics because those topics have broad appeal. However, I also write about
Deming regression (also called errors-in-variables regression) is a total regression method that fits a regression line when the measurements of both the explanatory variable (X) and the response variable (Y) are assumed to be subject to normally distributed errors. Recall that in ordinary least squares regression, the explanatory variable (X)
Last year, I wrote more than 100 posts for The DO Loop blog. Of these, the most popular articles were about data visualization, SAS programming tips, and statistical data analysis. Here are the most popular articles from 2018 in each category. Data Visualization Visualize repetition in song lyrics: In one
I regularly see questions on a SAS discussion forum about how to visualize the predicted values for a mixed model that has at least one continuous variable, a categorical variable, and possibly an interaction term. SAS procedures such as GLM, GENMOD, and LOGISTIC can automatically produce plots of the predicted
