StatLab Articles

Take a look at the following correlation matrix for Olympic decathlon data calculated from 280 scores from 1960 through 2004 (Johnson & Wichern, 2007, p. 499):

Loglinear models model cell counts in contingency tables. They're a little different from other modeling methods in that they don't distinguish between response and explanatory variables. All variables in a loglinear model are essentially "responses."

To learn more about loglinear models, we'll explore the following data from Agresti (1996, Table 6.3). It summarizes responses from a survey that asked high school seniors in a particular city whether they had ever used alcohol, cigarettes, or marijuana.

Plotting with color in R is kind of like painting a room in your house: You have to pick some colors. R has some default colors ready to go, but it's only natural to want to play around and try some different combinations. In this article, we'll look at some ways you can define new color palettes for plotting in R.

To begin, let's use the palette() function to see what colors are currently available:

Hurdle Models are a class of models for count data that help handle excess zeros and overdispersion. To motivate their use, let's look at some data in R. The following data come with the AER package. It is a sample of 4,406 individuals, aged 66 and over, who were covered by Medicare in 1988. One of the variables the data provide is number of physician office visits.

Note: This post is not about hierarchical linear modeling (HLM; multilevel modeling). Hierarchical regression is model comparison of nested regression models.

When it comes to modeling counts (i.e., 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 NFL quarterbacks as a function of snaps played and the total years experience of his offensive line. However, one potential drawback of Poisson regression is that it may not accurately describe the variability of the counts.

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 us a mathematical model that we can we use to estimate the probability of someone volunteering given certain independent variables.

This post intends to introduce the basics of mediation analysis and does not explain statistical details. For details, please refer to the articles at the end of this post.

Let’s say previous studies have suggested that higher grades predict higher happiness: X (grades) → Y (happiness). (This research example is made up for illustration purposes. Please don’t consider it a scientific statement.)

Let's say we're interested in text mining the opinions of the Supreme Court of the United States. At the time of this writing, the opinions are published as PDF files at the following web page in the section titled "Opinions of the Court": https://www.supremecourt.gov/opinions/opinions.aspx. For the purposes of this introductory tutorial, we'll look at just three opinions from the 2014 term: (1) Glossip v. Gross, (2) State Legislature v.

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 interaction between two two-level categorical variables. Let’s say we have gender (male and female), treatment (yes or no), and a continuous response measure. If the response to treatment depends on gender, then we have an interaction.