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Rick WicklinJune 14, 2017 20

Two ways to compute maximum likelihood estimates in SAS

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

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Analytics | Programming Tips

Log-likelihood function for the binomial distribution

Rick WicklinJune 12, 2017 3

Two simple ways to construct a log-likelihood function in SAS

Maximum likelihood estimation (MLE) is a powerful statistical technique that uses optimization techniques to fit parametric models. The technique finds the parameters that are "most likely" to have produced the observed data. SAS provides many tools for nonlinear optimization, so often the hardest part of maximum likelihood is writing down

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Analytics | Data Visualization

Rick WicklinMay 24, 2017 7

Sample quantiles: A comparison of 9 definitions

According to Hyndman and Fan ("Sample Quantiles in Statistical Packages," TAS, 1996), there are nine definitions of sample quantiles that commonly appear in statistical software packages. Hyndman and Fan identify three definitions that are based on rounding and six methods that are based on linear interpolation. This blog post shows

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Analytics | Learn SAS

Visualization of percentile definitions in SAS

Rick WicklinMay 22, 2017 1

Quantile definitions in SAS

In last week's article about the Flint water crisis, I computed the 90th percentile of a small data set. Although I didn't mention it, the value that I reported is different from the the 90th percentile that is reported in Significance magazine. That is not unusual. The data only had

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Analytics | Data Visualization

Distribution of Lead Levels in Flint, Michigan, in 71 Water Samples

Rick WicklinMay 17, 2017 11

Quantiles and the Flint water crisis

The April 2017 issue of Significance magazine features a cover story by Robert Langkjaer-Bain about the Flint (Michigan) water crisis. For those who don't know, the Flint water crisis started in 2014 when the impoverished city began using the Flint River as a source of city water. The water was

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Analytics

Split data into groups that have the same mean and variance

Rick WicklinMay 1, 2017 15

Split data into groups that have the same mean and variance

A frequently asked question on SAS discussion forums concerns randomly assigning units (often patients in a study) to various experimental groups so that each group has approximately the same number of units. This basic problem is easily solved in SAS by using PROC SURVEYSELECT or a DATA step program. A

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Analytics | Data Visualization | Programming Tips

Rick WicklinApril 26, 2017 0

Visualize a design matrix

Most SAS regression procedures support a CLASS statement which internally generates dummy variables for categorical variables. I have previously described what dummy variables are and how are they used. I have also written about how to create design matrices that contain dummy variables in SAS, and in particular how to

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Analytics | Data Visualization

Rick WicklinApril 24, 2017 1

Visualize an ANOVA with two-way interactions

There are several ways to visualize data in a two-way ANOVA model. Most visualizations show a statistical summary of the response variable for each category. However, for small data sets, it can be useful to overlay the raw data. This article shows a simple trick that you can use to

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Analytics | Programming Tips

Optimal value of quadratic function of two variables

Rick WicklinApril 12, 2017 3

Quadratic optimization in SAS

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

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Analytics | Data Visualization

Rick WicklinFebruary 20, 2017 48

The distribution of colors for plain M&M candies

Many introductory courses in probability and statistics encourage students to collect and analyze real data. A popular experiment in categorical data analysis is to give students a bag of M&M® candies and ask them to estimate the proportion of colors in the population from the sample data. In some classes,

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