Poisson Regression

When Linear Models Don’t Fit Your Data, Now What?

When your dependent variable is not continuous, unbounded, and measured on an interval or ratio scale, linear models don’t fit. The data just will not meet the assumptions of linear models. But there’s good news, other models exist for many types of dependent variables.

Today I’m going to go into more detail about 6 common types of dependent variables that are either discrete, bounded, or measured on a nominal or ordinal scale and the tests that work for them instead. Some are all of these.

Why Generalized Linear Models Have No Error Term

by Karen Grace-Martin 1 Comment

Even if you’ve never heard the term Generalized Linear Model, you may have run one. It’s a term for a family of models that includes logistic and Poisson regression, among others.

It’s a small leap to generalized linear models, if you already understand linear models. Many, many concepts are the same in both types of models.

But one thing that’s perplexing to many is why generalized linear models have no error term, like linear models do. [Read more…] about Why Generalized Linear Models Have No Error Term

The Importance of Including an Exposure Variable in Count Models

by Jeff Meyer 11 Comments

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.

Count Models: Understanding the Log Link Function

by Jeff Meyer 2 Comments

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

The Difference Between Link Functions and Data Transformations

by Kim Love 2 Comments

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 contributer 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…]