Getting started with Negative Binomial Regression Modeling

When it comes to modeling counts (ie, whole numbers greater than or equal to 0), we often start with Poisson regression. This is a generalized linear model where a response is assumed to have a Poisson distribution conditional on a weighted sum of predictors. For example, we might model the number of documented concussions to […]

Visualizing the Effects of Logistic Regression

Logistic regression is a popular and effective way of modeling a binary response. For example, we might wonder what influences a person to volunteer, or not volunteer, for psychological research. Some do, some don’t. Are there independent variables that would help explain or distinguish between those who volunteer and those who don’t? Logistic regression gives […]

Reading PDF files into R for text mining

8-DEC-2016 UPDATE: Added section on using the pdftools package for reading PDF files into R. Let’s say we’re interested in text mining the opinions of The Supreme Court of the United States from the 2014 term. The opinions are published as PDF files at the following web page We would probably want to look […]

Understanding 2-way Interactions

When doing linear modeling or ANOVA it’s useful to examine whether or not the effect of one variable depends on the level of one or more variables. If it does then we have what is called an “interaction”. This means variables combine or interact to affect the response. The simplest type of interaction is the […]

Comparing Proportions with Relative Risk and Odds Ratios

The classic two-by-two table displays counts of what may be called “successes” and “failures” versus some two-level grouping variable, such as gender (male and female) or treatment (placebo and active drug). An example of one such table is given in the book An Introduction to Categorical Data Analysis (Agresti, 1996, p. 20). The table classifies […]

Is R-squared Useless?

On Thursday, October 16, 2015, a disbelieving student posted on Reddit My stats professor just went on a rant about how R-squared values are essentially useless, is there any truth to this? It attracted a fair amount of attention, at least compared to other posts about statistics on Reddit. It turns out the student’s stats […]

Fitting and Interpreting a Proportional Odds Model

Take a look at the following table. It is a cross tabulation of data taken from the 1991 General Social Survey that relates political party affiliation to political ideology. (Agresti, An Introduction to Categorical Data Analysis, 1996) Political Ideology by Party Affiliation, from the 1991 General Social Survey Very Liberal SlightlyLiberal Moderate SlightlyConservative Very Conservative […]

Getting Started with Quantile Regression

When we think of regression we usually think of linear regression, the tried and true method for estimating a mean of some variable conditional on the levels or values of independent variables. In other words, we’re pretty sure the mean of our variable of interest differs depending on other variables. For example the mean weight […]

Simulating Endogeneity

First off, what is endogeneity, and why would we want to simulate it? Endogeneity occurs when a statistical model has an independent variable that is correlated with the error term. The reason we would want to simulate it is to understand what exactly that definition means! Let’s first simulate ideal data for simple linear regression […]

Understanding Q-Q Plots

The Q-Q plot, or quantile-quantile plot, is a graphical tool to help us assess if a set of data plausibly came from some theoretical distribution such as a Normal or exponential. For example, if we run a statistical analysis that assumes our dependent variable is Normally distributed, we can use a Normal Q-Q plot to […]