# statistical methods

## 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 […]

## Nonparametric and Parametric Power: Comparing the Wilcoxon Test and the t-test

From 2004 to 2008, a series of four brief, disagreeing papers in the journal Medical Education took up the question of whether and when it’s appropriate to analyze data from Likert scales (i.e., integers reflecting degrees of agreement with statements) with parametric or nonparametric statistical methods. Although no overly convincing consensus emerged, at least in […]

## 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 […]

## Logistic Regression Four Ways with Python

What is Logistic Regression? Logistic regression is a predictive analysis that estimates/models the probability of an event occurring based on a given dataset. This dataset contains both independent variables, or predictors, and their corresponding dependent variable, or response. To model the probability of a particular response variable, logistic regression assumes that the log-odds for the […]

## 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 […]

## Detecting Influential Points in Regression with DFBETA(S)

In regression modeling, influential points are observations that, individually, exert large effects on a model’s results—the parameter estimates ($$\hat{\beta_0}, \hat{\beta_1}, …, \hat{\beta_j}$$) and, consequently, the model’s predictions ($$\hat{y_1}, \hat{y_2}, …, \hat{y_i}$$). Influential points aren’t necessarily troublesome, but observations flagged as highly influential warrant follow-up. A large value on an influence measure can signal anything from […]

## 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 […]

## ROC Curves and AUC for Models Used for Binary Classification

This article assumes basic familiarity with the use and interpretation of logistic regression, odds and probabilities, and true/false positives/negatives. The examples are coded in R. ROC curves and AUC have important limitations, and I encourage reading through the section at the end of the article to get a sense of when and why the tools […]

## 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 […]