Clay Ford

Comparing the accuracy of two binary diagnostic tests in a paired study design

There are many medical tests for detecting the presence of a disease or condition. Some examples include tests for lesions, cancer, pregnancy, or COVID-19. While these tests are usually accurate, they’re not perfect. In addition, some tests are designed to detect the same condition, but use a different method. A recent example are PCR and […]

Correlation of Fixed Effects in lme4

If you have ever used the R package lme4 to perform mixed-effect modeling you may have noticed the “Correlation of Fixed Effects” section at the bottom of the summary output. This article intends to shed some light on what this section means and how you might interpret it. To begin, let’s simulate some data. Below […]

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 […]

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 […]

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 […]