## Tag: Data Analysis

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What is Kolmogorov's D statistic?

Have you ever run a statistical test to determine whether data are normally distributed? If so, you have probably used Kolmogorov's D statistic. Kolmogorov's D statistic (also called the Kolmogorov-Smirnov statistic) enables you to test whether the empirical distribution of data is different than a reference distribution. The reference distribution

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Discrimination, accuracy, and stability in binary classifiers

At SAS Global Forum 2019, Daymond Ling presented an interesting discussion of binary classifiers in the financial industry. The discussion is motivated by a practical question: If you deploy a predictive model, how can you assess whether the model is no longer working well and needs to be replaced? Daymond

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A CUSUM test for autregressive models

The CUSUM test has many incarnations. Different areas of statistics use different assumption and test for different hypotheses. This article presents a brief overview of CUSUM tests and gives an example of using the CUSUM test in PROC AUTOREG for autoregressive models in SAS. A CUSUM test uses the cumulative

Programming Tips
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The CUSUM test for randomness of a binary sequence

Many statistical tests use a CUSUM statistic as part of the test. It can be confusing when a researcher refers to "the CUSUM test" without providing details about exactly which CUSUM test is being used. This article describes a CUSUM test for the randomness of a binary sequence. You start

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Convergence in mixed models: When the estimated G matrix is not positive definite

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

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Matrix operations and BY groups

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

Programming Tips
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The geometry of multivariate versus univariate outliers

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

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Truncate response surfaces

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

Programming Tips
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Interpolation vs extrapolation: the convex hull of multivariate data

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

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Use PROC BOXPLOT to display hundreds of box plots

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

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Visualize SAT scores in North Carolina

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

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An easier way to create a calibration plot in SAS

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

Programming Tips
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An easier way to perform regression with restricted cubic splines in SAS

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

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4 reasons to use PROC PLM for linear regression models in SAS

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

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Create training, validation, and test data sets in SAS

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

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Three ways to add a line to a Q-Q plot

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

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How to align the Y and Y2 axes in PROC SGPLOT

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,

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10 posts from 2018 that deserve a second look

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

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Deming regression for comparing different measurement methods

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)

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Top posts from The DO Loop in 2018

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

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Visualize a mixed model that has repeated measures or random coefficients

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

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Create a probability plot in SAS

Many data analysts use a quantile-quantile plot (Q-Q plot) to graphically assess whether data can be modeled by a probability distribution such as the normal, lognormal, or gamma distribution. You can use the QQPLOT statement in PROC UNIVARIATE to create a Q-Q plot for about a dozen common distributions. However,

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When is a histogram not a histogram? When it's a table!

Recently a SAS programmer wanted to obtain a table of counts that was based on a histogram. I showed him how you can use the OUTHIST= option on the HISTOGRAM statement in PROC UNIVARIATE to obtain that information. For example, the following call to PROC UNIVARIATE creates a histogram for

Programming Tips
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Singular parameterizations, generalized inverses, and regression estimates

I remember the first time I used PROC GLM in SAS to include a classification effect in a regression model. I thought I had done something wrong because the parameter estimates table was followed by a scary-looking note: Note: The X'X matrix has been found to be singular, and a

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A funnel plot for immunization rates

Last week my colleague, Robert Allison, visualized data regarding immunization rates for kindergarten classes in North Carolina. One of his graphs was a scatter plot that displayed the proportion of unimmunized students versus the size of the class for 1,885 kindergarten classes in NC. This scatter plot is the basis

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Generalized inverses for matrices

A data analyst asked how to compute parameter estimates in a linear regression model when the underlying data matrix is rank deficient. This situation can occur if one of the variables in the regression is a linear combination of other variables. It also occurs when you use the GLM parameterization

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Create and compare ROC curves for any predictive model

An ROC curve graphically summarizes the tradeoff between true positives and true negatives for a rule or model that predicts a binary response variable. An ROC curve is a parametric curve that is constructed by varying the cutpoint value at which estimated probabilities are considered to predict the binary event.

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Fit the Pareto distribution in SAS

Will the real Pareto distribution please stand up? SAS supports three different distributions that are named "Pareto." The Wikipedia page for the Pareto distribution lists five different "Pareto" distributions, including the three that SAS supports. This article shows how to fit the two-parameter Pareto distribution in SAS and discusses the

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Parameter estimates for different parameterizations

In a recent article about nonlinear least squares, I wrote, "you can often fit one model and use the ESTIMATE statement to estimate the parameters in a different parameterization." This article expands on that statement. It shows how to fit a model for one set of parameters and use the

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Get the unique values of a variable in data order

There are several ways to use SAS to get the unique values for a data variable. In Base SAS, you can use the TABLES statement in PROC FREQ to generate a table of unique values (and the counts). You can also use the DISTINCT function in PROC SQL to get