Poisson Regression

The Importance of Including an Exposure Variable in Count Models

When our outcome variable is the frequency of occurrence of an event, we will typically use a count model to analyze the results. There are numerous count models. A few examples are: Poisson, negative binomial, zero-inflated Poisson and truncated negative binomial.

There are specific requirements for which count model to use. The models are not interchangeable. But regardless of the model we use, there is a very important prerequisite that they all share.

The Difference Between Link Functions and Data Transformations

by Kim Love 1 Comment

Generalized linear models—and generalized linear mixed models—are called generalized linear because they connect a model’s outcome to its predictors in a linear way. The function used to make this connection is called a link function. Link functions sounds like an exotic term, but they’re actually much simpler than they sound.

For example, Poisson regression (commonly used for outcomes that are counts) makes use of a natural log link function as follows:

Member Training: Generalized Linear Models

by guest Leave a Comment

In this webinar, we will provide an overview of generalized linear models. You may already be using them (perhaps without knowing it!).

For example, logistic regression is a type of generalized linear model that many people are already familiar with. Alternatively, maybe you’re not using them yet and you are just beginning to understand when they might be useful to you.

[Read more…]

When to Use Logistic Regression for Percentages and Counts

by Karen Grace-Martin 1 Comment

One important yet difficult skill in statistics is choosing a type model for different data situations. One key consideration is the dependent variable.

For linear models, the dependent variable doesn’t have to be normally distributed, but it does have to be continuous, unbounded, and measured on an interval or ratio scale.

Percentages don’t fit these criteria. Yes, they’re continuous and ratio scale. The issue is the [Read more…] about When to Use Logistic Regression for Percentages and Counts

Differences Between the Normal and Poisson Distributions

by Karen Grace-Martin 3 Comments

The normal distribution is so ubiquitous in statistics that those of us who use a lot of statistics tend to forget it’s not always so common in actual data.

And since the normal distribution is continuous, many people describe all numerical variables as continuous. I get it: I’m guilty of using those terms interchangeably, too, but they’re not exactly the same.

Numerical variables can be either continuous or discrete.

The difference? Continuous variables can take any number within a range. Discrete variables can only be whole numbers.

So 3.04873658 is a possible value of a continuous variable, but not discrete.

Count variables, as the name implies, are frequencies of some event or state. Number of arrests, fish [Read more…] about Differences Between the Normal and Poisson Distributions

Count Models: Understanding the Log Link Function

by Jeff Meyer Leave a Comment

by Jeff Meyer

When we run a statistical model, we are in a sense creating a mathematical equation. The simplest regression model looks like this:

Y_i = β₀ + β₁X+ ε_i

The left side of the equation is the sum of two parts on the right: the fixed component, β₀ + β₁X, and the random component, ε_i.

You’ll also sometimes see the equation written [Read more…] about Count Models: Understanding the Log Link Function