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Rick WicklinDecember 11, 2019 1

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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Analytics | Data Visualization | Learn SAS

Rick WicklinNovember 4, 2019 6

How to interpret graphs in a principal component analysis

Understanding multivariate statistics requires mastery of high-dimensional geometry and concepts in linear algebra such as matrix factorizations, basis vectors, and linear subspaces. Graphs can help to summarize what a multivariate analysis is telling us about the data. This article looks at four graphs that are often part of a principal

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Analytics | Data Visualization | Learn SAS

Rick WicklinOctober 21, 2019 3

Compute and visualize binomial proportions in SAS

Computing rates and proportions is a common task in data analysis. When you are computing several proportions, it is helpful to visualize how the rates vary among subgroups of the population. Examples of proportions that depend on subgroups include: Mortality rates for various types of cancers Incarceration rates by race

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