StatLab Articles

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.

What is mediation?

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.

The classic two-by-two table displays counts of what may be called “successes” and “failures” versus some two-level grouping variable, such as sex (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 myocardial infarction (Yes/No) with treatment group (Placebo/Aspirin).

Cronbach's alpha is a measure used to assess the reliability, or internal consistency, of a set of scale or test items. In other words, the reliability of any given measurement refers to the extent to which it is a consistent measure of a concept, and Cronbach’s alpha is one way of measuring the strength of that consistency.

On Thursday, October 15, 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.

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).