# Clay Ford

## Understanding Semivariograms

I’ve heard something frightening from practicing statisticians who frequently use mixed effects models. Sometimes when I ask them whether they produced a [semi]variogram to check the correlation structure they reply “what’s that?” –Frank Harrell When it comes to statistical modeling, semivariograms help us visualize and assess correlation in residuals. We can use them for two […]

## Getting Started with Gamma Regression

In this article we plan to get you up and running with gamma regression. But before we dive into that, let’s review the familiar Normal distribution. This will provide some scaffolding to help us transition to the gamma distribution. As you probably know, a Normal distribution is described by its mean and standard deviation. These […]

## Understanding Deviance Residuals

If you have ever performed binary logistic regression in R using the glm() function, you may have noticed a summary of “Deviance Residuals” at the top of the summary output. In this article we talk about how these residuals are calculated and what we can use them for. We also talk about other types of […]

## Getting Started with Bootstrap Model Validation

Let’s say we fit a logistic regression model for the purposes of predicting the probability of low infant birth weight, which is an infant weighing less than 2.5 kg. Below we fit such a model using the “birthwt” data set that comes with the MASS package in R. (This is an example model and not […]

## Mathematical Annotation in R

In this article we demonstrate how to include mathematical symbols and formulas in plots created with R. This can mean adding a formula in the title of the plot, adding symbols to axis labels, annotating a plot with some math, and so on. R provides a $$\LaTeX$$-like language for defining mathematical expressions. It is documented […]

## Comparing Mixed-Effect Models in R and SPSS

Occasionally we are asked to help students or faculty implement a mixed-effect model in SPSS. Our training and expertise is primarily in R, so it can be challenging to transfer and apply our knowledge to SPSS. In this article we document for posterity how to fit some basic mixed-effect models in R using the lme4 […]

## 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 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 better handle on this topic. To begin we simulate some toy […]

## Power and Sample Size Analysis using Simulation

The power of a test is the probability of correctly rejecting a null hypothesis. For example, let’s say we suspect a coin is not fair and lands heads 65% of the time. The null hypothesis is the coin is not biased to land heads. The alternative hypothesis is the coin is biased to land heads. […]