StatLab Articles

Logistic regression is a predictive analysis that estimates/models the probability of event occurring based on a given dataset. This dataset contains both independent variables, or predictors, and their corresponding dependent variables, or responses.

Let’s say we fit a logistic regression model for the purpose 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 to be used as medical advice.)

We first subset the data to select four variables:

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.

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 (\(\hat{y_1}, \hat{y_2}, ..., \hat{y_i}\)).

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 and nlme packages, and how to replicate the results in SPSS.

In this article we work with R 4.2.0, lme4 version 1.1-29, nlme version 3.1-157, and SPSS version 28.0.1.1.

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 can be of limited use.

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 antigen tests for COVID-19. In these cases we might want to compare the two tests on the same subjects. This is known as a paired study design.

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.

One of the most well-known statistical tests to analyze the differences between means of given groups is the ANOVA (analysis of variance) test. While ANOVA is a great tool, it assumes that the data in question follows a normal distribution. What if your data doesn’t follow a normal distribution or if your sample size is too small to determine a normal distribution? That’s where the Kruskal-Wallis test comes in.

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.