statistical methods

A Beginner’s Guide to Marginal Effects

What are average marginal effects? (If you’re reading this, chances are you just asked this question.) If we unpack the phrase, it looks like we have effects that are marginal to something, all of which we average. So let’s look at each piece of this phrase and see if we can help you get a […]

The Intuition Behind Confidence Intervals

Say it with me: An X% confidence interval captures the population parameter in X% of repeated samples. In the course of our statistical educations, many of us had that line (or some variant of it) crammed, wedged, stuffed, and shoved into our skulls until definitional precision was leaking out of noses and pooling on our […]

Post Hoc Power Calculations are Not Useful

It is well documented that post hoc power calculations are not useful (Goodman and Berlin 1994, Hoenig and Heisey 2001, Althouse 2020). Also known as observed power or retrospective power, post hoc power purports to estimate the power of a test given an observed effect size. The idea is to show that a “non-significant” hypothesis […]

Understanding Ordered Factors in a Linear Model

Consider the following data from the text Design and Analysis of Experiments, 7 ed (Montgomery, Table 3.1). It has two variables: power and rate. Power is a discrete setting on a tool used to etch circuits into a silicon wafer. There are four levels to choose from. Rate is the distance etched measured in Angstroms […]

Getting Started with Generalized Estimating Equations

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 (ie, model coefficients). If interested, see Agresti (2002) for the computational details. In […]

Getting Started with Binomial Generalized Linear Mixed Models

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 […]

A Brief on Brier Scores

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 […]

Understanding Multiple Comparisons and Simultaneous Inference

When it comes to confidence intervals and hypothesis testing there are two important limitations to keep in mind. The significance level1, \(\alpha\), or the confidence interval coverage, \(1 – \alpha\), only apply to one test or estimate, not to a series of tests or estimates. are only appropriate if the estimate or test was not […]

Understanding Robust Standard Errors

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. To begin, let’s start with the relatively easy part: getting robust standard errors for basic linear models in Stata and […]