StatLab Articles

Generalized estimating equations, or GEE, is a method for modeling longitudinal or clustered data. It is usually used with non-normal data such as binary or count data. The name refers to a set of equations that are solved to obtain parameter estimates (i.e., model coefficients). If interested, see Agresti (2002) for the computational details. In this article we simply aim to get you started with implementing and interpreting GEE using the R statistical computing environment.

Binomial generalized linear mixed models, or binomial GLMMs, are useful for modeling binary outcomes for repeated or clustered measures. For example, let’s say we design a study that tracks what college students eat over the course of 2 weeks, and we’re interested in whether or not they eat vegetables each day. For each student, we’ll have 14 binary events: eat vegetables or not.

"Web scraping," or "data scraping," is simply the process of extracting data from a website. This can, of course, be done manually: You could go to a website, find the relevant data or information, and enter that information into some data file that you have stored locally. But imagine that you want to pull a very large dataset or data from hundreds or thousands of individual URLs. In this case, extracting the data manually sounds overwhelming and time-consuming.

Not all predictions are created equal, even if, in categorical terms, the predictions suggest the same outcome: “X will (or won’t) happen.” Say that I estimate that there’s a 60% chance that 100 million COVID-19 vaccines will be administered in the US during the first 100 days of Biden’s presidency, but my friend estimates that there’s a 90% chance of that outcome.

The pandas package is an open-source software library written for data analysis in Python. Pandas allows users to import data from various file formats (comma-separated values, JSON, SQL, fits, etc.) and perform data manipulation operations, including cleaning and reshaping the data, summarizing observations, grouping data, and merging multiple datasets. In this article, we'll explore briefly some of the most commonly used functions and methods for understanding, formatting, and vizualizing data with the pandas package.

When it comes to confidence intervals and hypothesis testing there are two important limitations to keep in mind.

The significance level,¹ \(\alpha\), or the confidence interval coverage, \(1 - \alpha\),

1. only apply to one test or estimate, not to a series of tests or estimates.
2. are only appropriate if the estimate or test was not suggested by the data.

Let’s illustrate both of these limitations via simulation using R.

Note: This version of the article contains static images of maps generated with Leaflet. You can view a version with interactive maps here. 

What are robust standard errors? How do we calculate them? Why use them? Why not use them all the time if they’re so robust? Those are the kinds of questions this post intends to address.

Multinomial logit models allow us to model membership in a group based on known variables. For example, the operating system preferences of a university’s students could be classified as “Windows,” “Mac,” or “Linux.” Perhaps we would like to better understand why students choose one OS versus another. We might want to build a statistical model that allows us to predict the probability of selecting an OS based on information such as sex, major, financial aid, and so on. Multinomial logit modeling allows us to propose and fit such models.

What are empirical cumulative distribution functions and what can we do with them? To answer the first question, let’s first step back and make sure we understand "distributions", or more specifically, "probability distributions".

A Basic Probability Distribution

Imagine a simple event, say flipping a coin 3 times. Here are all the possible outcomes, where H = head and T = tails: