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Rick WicklinDecember 18, 2019 0

Create a conditional quantile bin plot in SAS

A 2-D "bin plot" counts the number of observations in each cell in a regular 2-D grid. The 2-D bin plot is essentially a 2-D version of a histogram: it provides an estimate for the density of a 2-D distribution. As I discuss in the article, "The essential guide to

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Analytics

Rick WicklinDecember 16, 2019 3

Math-ing around the Christmas tree: Can the SVD de-noise an image?

Rockin' around the Christmas tree At the Christmas party hop. – Brenda Lee Last Christmas, I saw a fun blog post that used optimization methods to de-noise an image of a Christmas tree. Although there are specialized algorithms that remove random noise from an image, I am not going to

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Analytics | Programming Tips

Rick WicklinDecember 11, 2019 1

Swap elements in binary matrices

Binary matrices are used for many purposes. I have previously written about how to use binary matrices to visualize missing values in a data matrix. They are also used to indicate the co-occurrence of two events. In ecology, binary matrices are used to indicate which species of an animal are

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Analytics | Data Visualization

Rick WicklinDecember 5, 2019 3

Longitudinal data: The mixed model

This is a second article about analyzing longitudinal data, which features measurements that are repeatedly taken on subjects at several points in time. The previous article discusses a response-profile analysis, which uses an ANOVA method to determine differences between the means of an experimental group and a placebo group. The

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Analytics

Rick WicklinDecember 3, 2019 3

Longitudinal data: The response-profile model

Longitudinal data are used in many health-related studies in which individuals are measured at multiple points in time to monitor changes in a response variable, such as weight, cholesterol, or blood pressure. There are many excellent articles and books that describe the advantages of a mixed model for analyzing longitudinal

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Analytics | Data Visualization

Rick WicklinNovember 27, 2019 0

Evaluate a function on a linear subspace

This article discusses how to restrict a multivariate function to a linear subspace. This is a useful technique in many situations, including visualizing an objective function that is constrained by linear equalities. For example, the graph to the right is from a previous article about how to evaluate quadratic polynomials.

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Analytics | Data Visualization | Programming Tips

Rick WicklinNovember 25, 2019 1

Evaluate a quadratic polynomial in SAS

What is an efficient way to evaluate a multivariate quadratic polynomial in p variables? The answer is to use matrix computations! A multivariate quadratic polynomial can be written as the sum of a purely quadratic term (degree 2), a purely linear term (degree 1), and a constant term (degree 0).

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Analytics | Learn SAS

Rick WicklinNovember 20, 2019 7

Predicted values in generalized linear models: The ILINK option in SAS

In a linear regression model, the predicted values are on the same scale as the response variable. You can plot the observed and predicted responses to visualize how well the model agrees with the data, However, for generalized linear models, there is a potential source of confusion. Recall that a

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Analytics | Data Visualization

Rick WicklinNovember 13, 2019 10

Create biplots in SAS

Biplots are two-dimensional plots that help to visualize relationships in high dimensional data. A previous article discusses how to interpret biplots for continuous variables. The biplot projects observations and variables onto the span of the first two principal components. The observations are plotted as markers; the variables are plotted as

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Analytics | Data Visualization | Programming Tips

Rick WicklinNovember 6, 2019 5

What are biplots?

Principal component analysis (PCA) is an important tool for understanding relationships in continuous multivariate data. When the first two principal components (PCs) explain a significant portion of the variance in the data, you can visualize the data by projecting the observations onto the span of the first two PCs. In

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